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Sample records for nonlinear chaotic gyros

  1. Chaotic and steady state behaviour of a nonlinear controlled gyro subjected to harmonic disturbances

    International Nuclear Information System (INIS)

    Perez Polo, Manuel F.; Perez Molina, Manuel

    2007-01-01

    Chaotic and steady state motions of a nonlinear controlled gimbals suspension gyro used to stabilize an external body are studied in this paper. The equations of the gyro without nonlinear control are deduced from the Euler-Lagrange equations by using the nutation theory. The equations of the system show that a cyclic variable appears. Its elimination allows us to find an auxiliary nonlinear system from which it is possible to deduce a nonlinear control law in order to obtain a desired equilibrium point. From the analysis of the nonlinear control law it is possible to show that due to both harmonic disturbances in the platform of the gyro and in the body to stabilize, regular and chaotic motions can appear. The chaotic motion is researched by means of chaos maps, bifurcation diagrams, sensitivity to initial conditions, Lyapunov exponents and Fourier spectrum density. The transition from chaotic to steady state motion by eliminating the harmonic disturbances from the modification of the initial nonlinear control law is also researched. Next, the paper shows how to use the chaotic motion in order to obtain small input signals so that the desired equilibrium state of the gyro can be reached. The developed methodology and its compared performance are evaluated through analytical methods and numerical simulations

  2. Chaotic and steady state behaviour of a nonlinear controlled gyro subjected to harmonic disturbances

    Energy Technology Data Exchange (ETDEWEB)

    Perez Polo, Manuel F. [Department of Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)]. E-mail: manolo@dfists.ua.es; Perez Molina, Manuel [Facultad de Ciencias Matematicas, Universidad Nacional de Educacion a Distancia, UNED, C/Boyero 12-1A, Alicante 03007 (Spain)]. E-mail: ma_perez_m@hotmail.com

    2007-07-15

    Chaotic and steady state motions of a nonlinear controlled gimbals suspension gyro used to stabilize an external body are studied in this paper. The equations of the gyro without nonlinear control are deduced from the Euler-Lagrange equations by using the nutation theory. The equations of the system show that a cyclic variable appears. Its elimination allows us to find an auxiliary nonlinear system from which it is possible to deduce a nonlinear control law in order to obtain a desired equilibrium point. From the analysis of the nonlinear control law it is possible to show that due to both harmonic disturbances in the platform of the gyro and in the body to stabilize, regular and chaotic motions can appear. The chaotic motion is researched by means of chaos maps, bifurcation diagrams, sensitivity to initial conditions, Lyapunov exponents and Fourier spectrum density. The transition from chaotic to steady state motion by eliminating the harmonic disturbances from the modification of the initial nonlinear control law is also researched. Next, the paper shows how to use the chaotic motion in order to obtain small input signals so that the desired equilibrium state of the gyro can be reached. The developed methodology and its compared performance are evaluated through analytical methods and numerical simulations.

  3. Generalized projective synchronization of chaotic nonlinear gyros coupled with dead-zone input

    International Nuclear Information System (INIS)

    Hung, M.-L.; Yan, J.-J.; Liao, T.-L.

    2008-01-01

    This paper addresses the synchronization problem of drive-response chaotic gyros coupled with dead-zone nonlinear input. Using the sliding mode control technique, a novel control law is established which guarantees generalized projective synchronization even when the dead-zone nonlinearity is present. Numerical simulations are presented to verify that the synchronization can be achieved by using the proposed synchronization scheme

  4. Stability and chaotic dynamics of a perturbed rate gyro

    International Nuclear Information System (INIS)

    Chen, H.-H.

    2006-01-01

    An analysis of stability and chaotic dynamics is presented by a single-axis rate gyro subjected to linear feedback control loops. This rate gyro is supposed to be mounted on a space vehicle which undergoes an uncertain angular velocity ω Z (t) around its spin axis and simultaneously acceleration ω-bar X (t) occurs with respect to the output axis. The necessary and sufficient conditions of stability and degeneracy conditions for the autonomous case, whose vehicle undergoes a steady rotation, were provided by Routh-Hurwitz theory. The stability of the nonlinear nonautonomous system was investigated by Liapunov stability and instability theorems. As the electrical time constant is much smaller than the mechanical time constant, the singularly perturbed system can be obtained by the singular perturbation theory. The Liapunov stability of this system by studying the reduced and boundary-layer systems was also analyzed. Using the Melinikov technique, we can give criteria for the existence of chaos in the gyro motion when the vehicle undergoes perturbed harmonic rotation about its spin and output axes

  5. A Nonlinear Adaptive Filter for Gyro Thermal Bias Error Cancellation

    Science.gov (United States)

    Galante, Joseph M.; Sanner, Robert M.

    2012-01-01

    Deterministic errors in angular rate gyros, such as thermal biases, can have a significant impact on spacecraft attitude knowledge. In particular, thermal biases are often the dominant error source in MEMS gyros after calibration. Filters, such as J\\,fEKFs, are commonly used to mitigate the impact of gyro errors and gyro noise on spacecraft closed loop pointing accuracy, but often have difficulty in rapidly changing thermal environments and can be computationally expensive. In this report an existing nonlinear adaptive filter is used as the basis for a new nonlinear adaptive filter designed to estimate and cancel thermal bias effects. A description of the filter is presented along with an implementation suitable for discrete-time applications. A simulation analysis demonstrates the performance of the filter in the presence of noisy measurements and provides a comparison with existing techniques.

  6. Regular self-oscillating and chaotic behaviour of a PID controlled gimbal suspension gyro

    International Nuclear Information System (INIS)

    Perez Polo, Manuel F.; Perez Molina, Manuel

    2004-01-01

    The dynamics of a gyro in gimbal with a PID controller to obtain steady state, self-oscillating and chaotic motion is considered in this paper. The mathematical model of the whole system is deduced from the gyroscope nutation theory and from a feedback control system formed by a PID controller with constrained integral action. The paper shows that the gyro and the associated PID feedback control system have multiple equilibrium points, and from the analysis of a Poincare-Andronov-Hopf bifurcation at the equilibrium points, it is possible to deduce the conditions, which give regular and self-oscillating behaviour. The calculation of the first Lyapunov value is used to predict the motion of the gyro in order to obtain a desired equilibrium point or self-oscillating behaviour. The mechanism of the stability loss of the gyro under small vibrations of the gyro platform and the appearance of chaotic motion is also presented. Numerical simulations are performed to verify the analytical results

  7. Nonlinear Adaptive Filter for MEMS Gyro Error Cancellation

    Data.gov (United States)

    National Aeronautics and Space Administration — Thermal biases are the dominate error in low-cost low-power small MEMS gyros. CubeSats often can't afford the power/mass to put a heater on their MEMS gyros and...

  8. Nonlinear chaotic model for predicting storm surges

    Directory of Open Access Journals (Sweden)

    M. Siek

    2010-09-01

    Full Text Available This paper addresses the use of the methods of nonlinear dynamics and chaos theory for building a predictive chaotic model from time series. The chaotic model predictions are made by the adaptive local models based on the dynamical neighbors found in the reconstructed phase space of the observables. We implemented the univariate and multivariate chaotic models with direct and multi-steps prediction techniques and optimized these models using an exhaustive search method. The built models were tested for predicting storm surge dynamics for different stormy conditions in the North Sea, and are compared to neural network models. The results show that the chaotic models can generally provide reliable and accurate short-term storm surge predictions.

  9. Controlling chaotic systems via nonlinear feedback control

    International Nuclear Information System (INIS)

    Park, Ju H.

    2005-01-01

    In this article, a new method to control chaotic systems is proposed. Using Lyapunov method, we design a nonlinear feedback controller to make the controlled system be stabilized. A numerical example is given to illuminate the design procedure and advantage of the result derived

  10. Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

    Science.gov (United States)

    Jeevarekha, A.; Paul Asir, M.; Philominathan, P.

    2016-06-01

    This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.

  11. Synchronization of two different chaotic systems via nonlinear ...

    African Journals Online (AJOL)

    ADOWIE PERE

    ABSTRACT: This work reports the synchronization of a pair of four chaotic systems via nonlinear control technique. This method has been found to be easy to implement and effective especially on two different chaotic systems. We paired four chaotic systems out of which one is new and we have six possible pairs.

  12. Chaotic synchronization of two complex nonlinear oscillators

    International Nuclear Information System (INIS)

    Mahmoud, Gamal M.; Mahmoud, Emad E.; Farghaly, Ahmed A.; Aly, Shaban A.

    2009-01-01

    Synchronization is an important phenomenon commonly observed in nature. It is also often artificially induced because it is desirable for a variety of applications in physics, applied sciences and engineering. In a recent paper [Mahmoud GM, Mohamed AA, Aly SA. Strange attractors and chaos control in periodically forced complex Duffing's oscillators. Physica A 2001;292:193-206], a system of periodically forced complex Duffing's oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. Their connection to solutions of the nonlinear Schroedinger equation has also been pointed out. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using active control and global synchronization techniques. We derive analytical expressions for control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.

  13. Hash function based on piecewise nonlinear chaotic map

    International Nuclear Information System (INIS)

    Akhavan, A.; Samsudin, A.; Akhshani, A.

    2009-01-01

    Chaos-based cryptography appeared recently in the early 1990s as an original application of nonlinear dynamics in the chaotic regime. In this paper, an algorithm for one-way hash function construction based on piecewise nonlinear chaotic map with a variant probability parameter is proposed. Also the proposed algorithm is an attempt to present a new chaotic hash function based on multithreaded programming. In this chaotic scheme, the message is connected to the chaotic map using probability parameter and other parameters of chaotic map such as control parameter and initial condition, so that the generated hash value is highly sensitive to the message. Simulation results indicate that the proposed algorithm presented several interesting features, such as high flexibility, good statistical properties, high key sensitivity and message sensitivity. These properties make the scheme a suitable choice for practical applications.

  14. Chaotic Motion of Nonlinearly Coupled Quintic Oscillators | Adeloye ...

    African Journals Online (AJOL)

    With a fixed energy, we investigate the motion of two nonlinearly coupled quintic oscillators for various values of the coupling strength with the aid of the Poincare surface of section. It is observed that chaotic motion sets in for coupling strength as low as 0.001. The degree of chaoticity generally increases as the coupling ...

  15. Nonlinear observer based phase synchronization of chaotic systems

    International Nuclear Information System (INIS)

    Meng Juan; Wang Xingyuan

    2007-01-01

    This Letter analyzes the phase synchronization problem of autonomous chaotic systems. Based on the nonlinear state observer algorithm and the pole placement technique, a phase synchronization scheme is designed. The phase synchronization of a new chaotic system is achieved by using this observer controller. Numerical simulations further demonstrate the effectiveness of the proposed phase synchronization scheme

  16. Chaos synchronization of a new chaotic system via nonlinear control

    International Nuclear Information System (INIS)

    Zhang Qunjiao; Lu Junan

    2008-01-01

    This paper investigates chaos synchronization of a new chaotic system [Lue J, Chen G, Cheng D. A new chaotic system and beyond: the generalized Lorenz-like system. Int J Bifurcat Chaos 2004;14:1507-37]. Two kinds of novel nonlinear controllers are designed based on the Lyapunov stability theory. It can be viewed as an improvement to the existing results of reference [Park JH. Chaos synchronization of a chaotic system via nonlinear control. Chaos, Solitons and Fractals 2005;25:579-84] because we use less controllers but realize a global and exponential asymptotical synchronization. Numerical simulations are provided to show the effectiveness and advantage of this method

  17. Nonlinear PI control of chaotic systems using singular perturbation theory

    International Nuclear Information System (INIS)

    Wang Jiang; Wang Jing; Li Huiyan

    2005-01-01

    In this paper, we develop the nonlinear PI controllers for a class of chaotic systems based on singular perturbation theory. The original system is decomposed into two reduced order systems, to which the nonlinear uncertain terms belongs. In order to alleviate the deterioration of these nonlinear uncertainties, the nonlinear PI controllers are applied to each subsystem and combined to construct the composite controller for the full order system. The effectiveness and feasibility of the proposed control scheme is demonstrated through numerical simulations on the chaotic Chua's circuit

  18. Experimental Observation of Chaotic Beats in Oscillators Sharing Nonlinearity

    Science.gov (United States)

    Paul Asir, M.; Jeevarekha, A.; Philominathan, P.

    This paper deals with the generation of chaotic beats in a system of two forced dissipative LCR oscillators sharing a nonlinear element. The presence of two external periodic excitations and a common nonlinear element in the chosen system enables the facile generation of chaotic beats. Thus rendered chaotic beats were characterized in both time domain and phase space. Lyapunov exponents and envelope of the beats were computed to diagnose the chaotic nature of the signals. The role of common nonlinearity on the complexity of the generated beats is discussed. Real-time experimental hardware implementation has also been done to confirm the subsistence of the phenomenon, for the first time. Extensive Multisim simulations were carried out to understand, a bit more about the shrinkage and revivals of state variables in phase space.

  19. Adaptive projective synchronization of different chaotic systems with nonlinearity inputs

    International Nuclear Information System (INIS)

    Niu Yu-Jun; Pei Bing-Nan; Wang Xing-Yuan

    2012-01-01

    We investigate the projective synchronization of different chaotic systems with nonlinearity inputs. Based on the adaptive technique, sliding mode control method and pole assignment technique, a novel adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor. (general)

  20. Chaos synchronization of a chaotic system via nonlinear control

    International Nuclear Information System (INIS)

    Park, Ju H.

    2005-01-01

    In this letter, the problem of chaos synchronization of a chaotic system which is proposed by Lue et al. [Int J Bifurcat Chaos 2004;14:1507] is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical example is given to illuminate the design procedure and advantage of the result derived

  1. Global chaos synchronization of new chaotic systems via nonlinear control

    International Nuclear Information System (INIS)

    Chen, H.-K.

    2005-01-01

    Nonlinear control is an effective method for making two identical chaotic systems or two different chaotic systems be synchronized. However, this method assumes that the Lyapunov function of error dynamic (e) of synchronization is always formed as V (e) = 1/2e T e. In this paper, modification based on Lyapunov stability theory to design a controller is proposed in order to overcome this limitation. The method has been applied successfully to make two identical new systems and two different chaotic systems (new system and Lorenz system) globally asymptotically synchronized. Since the Lyapunov exponents are not required for the calculation, this method is effective and convenient to synchronize two identical systems and two different chaotic systems. Numerical simulations are also given to validate the proposed synchronization approach

  2. Nonlinear mode conversion with chaotic soliton generation at plasma resonance

    International Nuclear Information System (INIS)

    Pietsch, H.; Laedke, E.W.; Spatschek, K.H.

    1993-01-01

    The resonant absorption of electromagnetic waves near the critical density in inhomogeneous plasmas is studied. A driven nonlinear Schroedinger equation for the mode-converted oscillations is derived by multiple-scaling techniques. The model is simulated numerically. The generic transition from a stationary to a time-dependent solution is investigated. Depending on the parameters, a time-chaotic behavior is found. By a nonlinear analysis, based on the inverse scattering transform, solitons of a corresponding integrable equation are identified as the dominant coherent structures of the chaotic dynamics. Finally, a map is presented which predicts chaotic soliton generation and emission at the critical density. Its qualitative behavior, concerning the bifurcation points, is in excellent agreement with the numerical simulations

  3. A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps

    International Nuclear Information System (INIS)

    Behnia, S.; Akhshani, A.; Ahadpour, S.; Mahmodi, H.; Akhavan, A.

    2007-01-01

    In recent years, a growing number of discrete chaotic cryptographic algorithms have been proposed. However, most of them encounter some problems such as the lack of robustness and security. In this Letter, we introduce a new image encryption algorithm based on one-dimensional piecewise nonlinear chaotic maps. The system is a measurable dynamical system with an interesting property of being either ergodic or having stable period-one fixed point. They bifurcate from a stable single periodic state to chaotic one and vice versa without having usual period-doubling or period-n-tippling scenario. Also, we present the KS-entropy of this maps with respect to control parameter. This algorithm tries to improve the problem of failure of encryption such as small key space, encryption speed and level of security

  4. A new chaotic attractor with two quadratic nonlinearities, its synchronization and circuit implementation

    Science.gov (United States)

    Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Gundara, G.; Mada Sanjaya, W. S.; Subiyanto

    2018-03-01

    A 3-D new chaotic attractor with two quadratic nonlinearities is proposed in this paper. The dynamical properties of the new chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new chaotic system has three unstable equilibrium points. The new chaotic attractor is dissipative in nature. As an engineering application, adaptive synchronization of identical new chaotic attractors is designed via nonlinear control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic attractor model.

  5. Nonlinear dynamics and chaotic phenomena an introduction

    CERN Document Server

    Shivamoggi, Bhimsen K

    2014-01-01

    This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics  -- integrable systems, Poincaré maps, chaos, fractals and strange attractors. The Baker’s transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-deVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painlevé property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special...

  6. Nonlinear Dynamics, Chaotic and Complex Systems

    Science.gov (United States)

    Infeld, E.; Zelazny, R.; Galkowski, A.

    2011-04-01

    Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet

  7. Color image encryption based on Coupled Nonlinear Chaotic Map

    International Nuclear Information System (INIS)

    Mazloom, Sahar; Eftekhari-Moghadam, Amir Masud

    2009-01-01

    Image encryption is somehow different from text encryption due to some inherent features of image such as bulk data capacity and high correlation among pixels, which are generally difficult to handle by conventional methods. The desirable cryptographic properties of the chaotic maps such as sensitivity to initial conditions and random-like behavior have attracted the attention of cryptographers to develop new encryption algorithms. Therefore, recent researches of image encryption algorithms have been increasingly based on chaotic systems, though the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. This paper proposes a Coupled Nonlinear Chaotic Map, called CNCM, and a novel chaos-based image encryption algorithm to encrypt color images by using CNCM. The chaotic cryptography technique which used in this paper is a symmetric key cryptography with a stream cipher structure. In order to increase the security of the proposed algorithm, 240 bit-long secret key is used to generate the initial conditions and parameters of the chaotic map by making some algebraic transformations to the key. These transformations as well as the nonlinearity and coupling structure of the CNCM have enhanced the cryptosystem security. For getting higher security and higher complexity, the current paper employs the image size and color components to cryptosystem, thereby significantly increasing the resistance to known/chosen-plaintext attacks. The results of several experimental, statistical analysis and key sensitivity tests show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission.

  8. On nonlinear control design for autonomous chaotic systems of integer and fractional orders

    International Nuclear Information System (INIS)

    Ahmad, Wajdi M.; Harb, Ahmad M.

    2003-01-01

    In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive 'backstepping' method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an electronic chaotic oscillator model, and a mechanical chaotic 'jerk' model. We demonstrate the robustness of the derived controllers against system order reduction arising from the use of fractional integrators in the system models. Our results are validated via numerical simulations

  9. Chaos synchronizations of chaotic systems via active nonlinear control

    International Nuclear Information System (INIS)

    Huang, J; Xiao, T J

    2008-01-01

    This paper not only investigates the chaos synchronization between two LCC chaotic systems, but also discusses the chaos synchronization between LCC system and Genesio system. Some novel active nonlinear controllers are designed to achieve synchronizations between drive and response systems effectively. Moreover, the sufficient conditions of synchronizations are derived by using Lyapunov stability theorem. Numerical simulations are presented to verify the theoretical analysis, which shows that the synchronization schemes are global effective

  10. Chaotic saddles in nonlinear modulational interactions in a plasma

    International Nuclear Information System (INIS)

    Miranda, Rodrigo A.; Rempel, Erico L.; Chian, Abraham C.-L.

    2012-01-01

    A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.

  11. Chaotic saddles in nonlinear modulational interactions in a plasma

    Energy Technology Data Exchange (ETDEWEB)

    Miranda, Rodrigo A. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); University of Brasilia (UnB), Gama Campus, and Plasma Physics Laboratory, Institute of Physics, Brasilia, DF 70910-900 (Brazil); Rempel, Erico L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Chian, Abraham C.-L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), Sao Jose dos Campos, SP 12228-900 (Brazil); National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, Sao Jose dos Campos, SP 12227-010 (Brazil); Observatoire de Paris, LESIA, CNRS, 92195 Meudon (France)

    2012-11-15

    A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.

  12. Nonlinear Time Series Prediction Using Chaotic Neural Networks

    Science.gov (United States)

    Li, Ke-Ping; Chen, Tian-Lun

    2001-06-01

    A nonlinear feedback term is introduced into the evaluation equation of weights of the backpropagation algorithm for neural network, the network becomes a chaotic one. For the purpose of that we can investigate how the different feedback terms affect the process of learning and forecasting, we use the model to forecast the nonlinear time series which is produced by Makey-Glass equation. By selecting the suitable feedback term, the system can escape from the local minima and converge to the global minimum or its approximate solutions, and the forecasting results are better than those of backpropagation algorithm. The project supported by National Basic Research Project "Nonlinear Science" and National Natural Science Foundation of China under Grant No. 60074020

  13. Chaotic dynamics and chaos control in nonlinear laser systems

    International Nuclear Information System (INIS)

    Fang Jinqing; Yao Weiguang

    2001-01-01

    Chaotic dynamics and chaos control have become a great challenge in nonlinear laser systems and its advances are reviewed mainly based on the ring cavity laser systems. The principle and stability conditions for time-delay feedback control are analyzed and applied to chaos control in the laser systems. Other advanced methods of chaos control, such as weak spatial perturbation and occasional proportional feedback technique, are discussed. Prospects of chaos control for application (such as improvement of laser power and performance, synchronized chaos secure communication and information processing) are pointed out finally

  14. Multisynchronization of Chaotic Oscillators via Nonlinear Observer Approach

    Directory of Open Access Journals (Sweden)

    Ricardo Aguilar-López

    2014-01-01

    Full Text Available The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves’ oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.

  15. Multisynchronization of chaotic oscillators via nonlinear observer approach.

    Science.gov (United States)

    Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Mata-Machuca, Juan L

    2014-01-01

    The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves' oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.

  16. Nonlinear dynamics and chaotic behaviour of spin wave instabilities

    Energy Technology Data Exchange (ETDEWEB)

    Rezende, S M; Aguiar, F.M. de.

    1986-09-01

    Recent experiments revealed that spin wave instabilities driven by microwave fields, either parallel or transverse to the static magnetic field, display chaotic dynamics similar to other physical systems. A theory based on the coupled nonlinear equations of motion for two spin wave modes is presented which explains most features of the experimental observations. The model predicts subharmonic routes to chaos that depend on the parameter values. For certain parameters the system exhibits a Feigenbaum scenario characteristic of one-dimensional maps. Other parameters lead to different subharmonic routes indicative of multidimensional behavior, as observed in some experiments.

  17. Nonlinear Time-Reversal in a Wave Chaotic System

    Science.gov (United States)

    Frazier, Matthew; Taddese, Biniyam; Ott, Edward; Antonsen, Thomas; Anlage, Steven

    2012-02-01

    Time reversal mirrors are particularly simple to implement in wave chaotic systems and form the basis for a new class of sensors [1-3]. These sensors work by applying the quantum mechanical concepts of Loschmidt echo and fidelity decay to classical waves. The sensors make explicit use of time-reversal invariance and spatial reciprocity in a wave chaotic system to remotely measure the presence of small perturbations to the system. The underlying ray chaos increases the sensitivity to small perturbations throughout the volume explored by the waves. We extend our time-reversal mirror to include a discrete element with a nonlinear dynamical response. The initially injected pulse interacts with the nonlinear element, generating new frequency components originating at the element. By selectively filtering for and applying the time-reversal mirror to the new frequency components, we focus a pulse only onto the element, without knowledge of its location. Furthermore, we demonstrate transmission of arbitrary patterns of pulses to the element, creating a targeted communication channel to the exclusion of 'eavesdroppers' at other locations in the system. [1] Appl. Phys. Lett. 95, 114103 (2009) [2] J. Appl. Phys. 108, 1 (2010) [3] Acta Physica Polonica A 112, 569 (2007)

  18. Observer-based design of set-point tracking adaptive controllers for nonlinear chaotic systems

    International Nuclear Information System (INIS)

    Khaki-Sedigh, A.; Yazdanpanah-Goharrizi, A.

    2006-01-01

    A gradient based approach for the design of set-point tracking adaptive controllers for nonlinear chaotic systems is presented. In this approach, Lyapunov exponents are used to select the controller gain. In the case of unknown or time varying chaotic plants, the Lyapunov exponents may vary during the plant operation. In this paper, an effective adaptive strategy is used for online identification of Lyapunov exponents and adaptive control of nonlinear chaotic plants. Also, a nonlinear observer for estimation of the states is proposed. Simulation results are provided to show the effectiveness of the proposed methodology

  19. Observer-based design of set-point tracking adaptive controllers for nonlinear chaotic systems

    Energy Technology Data Exchange (ETDEWEB)

    Khaki-Sedigh, A. [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran 16314 (Iran, Islamic Republic of)]. E-mail: sedigh@kntu.ac.ir; Yazdanpanah-Goharrizi, A. [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran 16314 (Iran, Islamic Republic of)]. E-mail: yazdanpanah@ee.kntu.ac.ir

    2006-09-15

    A gradient based approach for the design of set-point tracking adaptive controllers for nonlinear chaotic systems is presented. In this approach, Lyapunov exponents are used to select the controller gain. In the case of unknown or time varying chaotic plants, the Lyapunov exponents may vary during the plant operation. In this paper, an effective adaptive strategy is used for online identification of Lyapunov exponents and adaptive control of nonlinear chaotic plants. Also, a nonlinear observer for estimation of the states is proposed. Simulation results are provided to show the effectiveness of the proposed methodology.

  20. Explosion of limit cycles and chaotic waves in a simple nonlinear chemical system

    DEFF Research Database (Denmark)

    Brøns, Morten; Sturis, Jeppe

    2001-01-01

    A model of an autocatalytic chemical reaction was employed to study the explosion of limit cycles and chaotic waves in a nonlinear chemical system. The bifurcation point was determined using asymptotic analysis and perturbations. Scaling laws for amplitude and period were derived. A strong sensit...... sensitivity was introduced due to bifurcation to infinity resulting in chaotic dynamics on adding diffusion....

  1. Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

    International Nuclear Information System (INIS)

    Jia Li-Xin; Dai Hao; Hui Meng

    2010-01-01

    This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method

  2. A New Chaotic Attractor with Quadratic Exponential Nonlinear Term from Chen’s Attractor

    Directory of Open Access Journals (Sweden)

    Iftikhar Ahmed

    2014-02-01

    Full Text Available In this paper a new three-dimensional chaotic system is proposed, which relies on a nonlinear exponential term and a nonlinear quadratic cross term necessary for folding trajectories. Basic dynamical characteristics of the new system are analyzed. Compared with the Chen system, the equilibrium points of the new system does not contain the origin, and has a greater positive Lyapunov index, can produce more complex shaped chaotic attractor.

  3. Chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity

    International Nuclear Information System (INIS)

    Sun, Y.-J.

    2009-01-01

    In this Letter, the concept of practical synchronization is introduced and the chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity is investigated. Based on the time-domain approach, a tracking control is proposed to realize chaos synchronization for the uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity. Moreover, the guaranteed exponential convergence rate and convergence radius can be pre-specified. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained result.

  4. A nonlinear optimal control approach for chaotic finance dynamics

    Science.gov (United States)

    Rigatos, G.; Siano, P.; Loia, V.; Tommasetti, A.; Troisi, O.

    2017-11-01

    A new nonlinear optimal control approach is proposed for stabilization of the dynamics of a chaotic finance model. The dynamic model of the financial system, which expresses interaction between the interest rate, the investment demand, the price exponent and the profit margin, undergoes approximate linearization round local operating points. These local equilibria are defined at each iteration of the control algorithm and consist of the present value of the systems state vector and the last value of the control inputs vector that was exerted on it. The approximate linearization makes use of Taylor series expansion and of the computation of the associated Jacobian matrices. The truncation of higher order terms in the Taylor series expansion is considered to be a modelling error that is compensated by the robustness of the control loop. As the control algorithm runs, the temporary equilibrium is shifted towards the reference trajectory and finally converges to it. The control method needs to compute an H-infinity feedback control law at each iteration, and requires the repetitive solution of an algebraic Riccati equation. Through Lyapunov stability analysis it is shown that an H-infinity tracking performance criterion holds for the control loop. This implies elevated robustness against model approximations and external perturbations. Moreover, under moderate conditions the global asymptotic stability of the control loop is proven.

  5. Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control

    International Nuclear Information System (INIS)

    Fu Shi-Hui; Lu Qi-Shao; Du Ying

    2012-01-01

    Adaptive H ∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based on Lyapunov's stability theory, linear and nonlinear feedback control of adaptive H ∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an H ∞ -norm constraint. Adaptive H ∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems. Numerical simulations are also given to identify the effectiveness of the theoretical analysis. (general)

  6. Modeling of memristor-based chaotic systems using nonlinear Wiener adaptive filters based on backslash operator

    International Nuclear Information System (INIS)

    Zhao, Yibo; Jiang, Yi; Feng, Jiuchao; Wu, Lifu

    2016-01-01

    Highlights: • A novel nonlinear Wiener adaptive filters based on the backslash operator are proposed. • The identification approach to the memristor-based chaotic systems using the proposed adaptive filters. • The weight update algorithm and convergence characteristics for the proposed adaptive filters are derived. - Abstract: Memristor-based chaotic systems have complex dynamical behaviors, which are characterized as nonlinear and hysteresis characteristics. Modeling and identification of their nonlinear model is an important premise for analyzing the dynamical behavior of the memristor-based chaotic systems. This paper presents a novel nonlinear Wiener adaptive filtering identification approach to the memristor-based chaotic systems. The linear part of Wiener model consists of the linear transversal adaptive filters, the nonlinear part consists of nonlinear adaptive filters based on the backslash operator for the hysteresis characteristics of the memristor. The weight update algorithms for the linear and nonlinear adaptive filters are derived. Final computer simulation results show the effectiveness as well as fast convergence characteristics. Comparing with the adaptive nonlinear polynomial filters, the proposed nonlinear adaptive filters have less identification error.

  7. Nonlinear dynamics of drops and bubbles and chaotic phenomena

    Science.gov (United States)

    Trinh, Eugene H.; Leal, L. G.; Feng, Z. C.; Holt, R. G.

    1994-01-01

    Nonlinear phenomena associated with the dynamics of free drops and bubbles are investigated analytically, numerically and experimentally. Although newly developed levitation and measurement techniques have been implemented, the full experimental validation of theoretical predictions has been hindered by interfering artifacts associated with levitation in the Earth gravitational field. The low gravity environment of orbital space flight has been shown to provide a more quiescent environment which can be utilized to better match the idealized theoretical conditions. The research effort described in this paper is a closely coupled collaboration between predictive and guiding theoretical activities and a unique experimental program involving the ultrasonic and electrostatic levitation of single droplets and bubbles. The goal is to develop and to validate methods based on nonlinear dynamics for the understanding of the large amplitude oscillatory response of single drops and bubbles to both isotropic and asymmetric pressure stimuli. The first specific area on interest has been the resonant coupling between volume and shape oscillatory modes isolated gas or vapor bubbles in a liquid host. The result of multiple time-scale asymptotic treatment, combined with domain perturbation and bifurcation methods, has been the prediction of resonant and near-resonant coupling between volume and shape modes leading to stable as well as chaotic oscillations. Experimental investigations of the large amplitude shape oscillation modes of centimeter-size single bubbles trapped in water at 1 G and under reduced hydrostatic pressure, have suggested the possibility of a low gravity experiment to study the direct coupling between these low frequency shape modes and the volume pulsation, sound-radiating mode. The second subject of interest has involved numerical modeling, using the boundary integral method, of the large amplitude shape oscillations of charged and uncharged drops in the presence

  8. Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperbolic Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters

    Directory of Open Access Journals (Sweden)

    S. Vaidyanathan

    2013-09-01

    Full Text Available This research work describes the modelling of two novel 3-D chaotic systems, the first with a hyperbolic sinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (A and the second with a hyperbolic cosinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (B. In this work, a detailed qualitative analysis of the novel chaotic systems (A and (B has been presented, and the Lyapunov exponents and Kaplan-Yorke dimension of these chaotic systems have been obtained. It is found that the maximal Lyapunov exponent (MLE for the novel chaotic systems (A and (B has a large value, viz. for the system (A and for the system (B. Thus, both the novel chaotic systems (A and (B display strong chaotic behaviour. This research work also discusses the problem of finding adaptive controllers for the global chaos synchronization of identical chaotic systems (A, identical chaotic systems (B and nonidentical chaotic systems (A and (B with unknown system parameters. The adaptive controllers for achieving global chaos synchronization of the novel chaotic systems (A and (B have been derived using adaptive control theory and Lyapunov stability theory. MATLAB simulations have been shown to illustrate the novel chaotic systems (A and (B, and also the adaptive synchronization results derived for the novel chaotic systems (A and (B.

  9. Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control

    International Nuclear Information System (INIS)

    Cui Baotong; Lou Xuyang

    2009-01-01

    In this paper, a new method to synchronize two identical chaotic recurrent neural networks is proposed. Using the drive-response concept, a nonlinear feedback control law is derived to achieve the state synchronization of the two identical chaotic neural networks. Furthermore, based on the Lyapunov method, a delay independent sufficient synchronization condition in terms of linear matrix inequality (LMI) is obtained. A numerical example with graphical illustrations is given to illuminate the presented synchronization scheme

  10. Chaos synchronization of uncertain chaotic systems using composite nonlinear feedback based integral sliding mode control.

    Science.gov (United States)

    Mobayen, Saleh

    2018-06-01

    This paper proposes a combination of composite nonlinear feedback and integral sliding mode techniques for fast and accurate chaos synchronization of uncertain chaotic systems with Lipschitz nonlinear functions, time-varying delays and disturbances. The composite nonlinear feedback method allows accurate following of the master chaotic system and the integral sliding mode control provides invariance property which rejects the perturbations and preserves the stability of the closed-loop system. Based on the Lyapunov- Krasovskii stability theory and linear matrix inequalities, a novel sufficient condition is offered for the chaos synchronization of uncertain chaotic systems. This method not only guarantees the robustness against perturbations and time-delays, but also eliminates reaching phase and avoids chattering problem. Simulation results demonstrate that the suggested procedure leads to a great control performance. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

  11. Sliding mode control for uncertain unified chaotic systems with input nonlinearity

    International Nuclear Information System (INIS)

    Chiang, T.-Y.; Hung, M.-L.; Yan, J.-J.; Yang, Y.-S.; Chang, J.-F.

    2007-01-01

    This paper investigates the stabilization problem for a class of unified chaotic systems subject to uncertainties and input nonlinearity. Using the sliding mode control technique, a robust control law is established which stabilizes the uncertain unified chaotic systems even when the nonlinearity in the actuators is present. A novel adaptive switching surface is introduced to simplify the task of assigning the stability of the closed-loop system in the sliding mode motion. An illustrative example is given to demonstrate the effectiveness of the proposed sliding mode control design

  12. Einstein-Friedmann equation, nonlinear dynamics and chaotic behaviours

    International Nuclear Information System (INIS)

    Tanaka, Yosuke; Nakano, Shingo; Ohta, Shigetoshi; Mori, Keisuke; Horiuchi, Tanji

    2009-01-01

    We have studied the Einstein-Friedmann equation [Case 1] on the basis of the bifurcation theory and shown that the chaotic behaviours in the Einstein-Friedmann equation [Case 1] are reduced to the pitchfork bifurcation and the homoclinic bifurcation. We have obtained the following results: (i) 'The chaos region diagram' (the p-λ plane) in the Einstein-Friedmann equation [Case 1]. (ii) 'The chaos inducing chart' of the homoclinic orbital systems in the unforced differential equations. We have discussed the non-integrable conditions in the Einstein-Friedmann equation and proposed the chaotic model: p=p 0 ρ n (n≥0). In case n≠0,1, the Einstein-Friedmann equation is not integrable and there may occur chaotic behaviours. The cosmological constant (λ) turns out to play important roles for the non-integrable condition in the Einstein-Friedmann equation and also for the pitchfork bifurcation and the homoclinic bifurcation in the relativistic field equation. With the use of the E-infinity theory, we have also discussed the physical quantities in the gravitational field equations, and obtained the formula logκ=-10(1/φ) 2 [1+(φ) 8 ]=-26.737, which is in nice agreement with the experiment (-26.730).

  13. Chaotic synchronization of symbolic information in the discrete nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Pando L, C.L.

    2003-08-01

    We have studied the discrete nonlinear Schrodinger equation (DNLSE) with on-site defects and periodic boundary conditions. When the array dynamics becomes chaotic, the otherwise quasiperiodic amplitude correlations between the oscillators are destroyed. However, we show that synchronization of symbolic information of suitable amplitude signals is possible in this hamiltonian system. (author)

  14. Adaptive control of nonlinear in parameters chaotic system via Lyapunov exponents placement

    Energy Technology Data Exchange (ETDEWEB)

    Ayati, Moosa [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran (Iran, Islamic Republic of)], E-mail: Ayati@dena.kntu.ac.ir; Khaki-Sedigh, Ali [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran (Iran, Islamic Republic of)], E-mail: sedigh@kntu.ac.ir

    2009-08-30

    This paper proposes a new method for the adaptive control of nonlinear in parameters (NLP) chaotic systems. A method based on Lagrangian of a cost function is used to identify the parameters of the system. Estimation results are used to calculate the Lyapunov exponents adaptively. Finally, the Lyapunov exponents placement method is used to assign the desired Lyapunov exponents of the closed loop system.

  15. Adaptive control of nonlinear in parameters chaotic system via Lyapunov exponents placement

    International Nuclear Information System (INIS)

    Ayati, Moosa; Khaki-Sedigh, Ali

    2009-01-01

    This paper proposes a new method for the adaptive control of nonlinear in parameters (NLP) chaotic systems. A method based on Lagrangian of a cost function is used to identify the parameters of the system. Estimation results are used to calculate the Lyapunov exponents adaptively. Finally, the Lyapunov exponents placement method is used to assign the desired Lyapunov exponents of the closed loop system.

  16. Evidence for bifurcation and universal chaotic behavior in nonlinear semiconducting devices

    International Nuclear Information System (INIS)

    Testa, J.; Perez, J.; Jeffries, C.

    1982-01-01

    Bifurcations, chaos, and extensive periodic windows in the chaotic regime are observed for a driven LRC circuit, the capacitive element being a nonlinear varactor diode. Measurements include power spectral analysis; real time amplitude data; phase portraits; and a bifurcation diagram, obtained by sampling methods. The effects of added external noise are studied. These data yield experimental determinations of several of the universal numbers predicted to characterize nonlinear systems having this route to chaos

  17. Nonlinear observer for synchronization of chaotic systems with application to secure data transmission

    Science.gov (United States)

    Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Perez-Pinacho, Claudia A.

    2014-06-01

    The main issue of this work is related with the design of a class of nonlinear observer in order to synchronize chaotic dynamical systems in a master-slave scheme, considering different initial conditions. The oscillator of Chen is proposed as a benchmark model and a bounded-type observer is proposed to reach synchronicity between both two chaotic systems. The proposed observer contains a proportional and sigmoid form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Some numerical simulations were carrying out in order to show the operation of the proposed methodology, with possible applications to secure data communications issues.

  18. Nonlinear unknown input sliding mode observer based chaotic system synchronization and message recovery scheme with uncertainty

    International Nuclear Information System (INIS)

    Sharma, Vivek; Sharma, B.B.; Nath, R.

    2017-01-01

    In the present manuscript, observer based synchronization and message recovery scheme is discussed for a system with uncertainties. LMI conditions are analytically derived solution of which gives the observer design matrices. Earlier approaches have used adaptive laws to address the uncertainties, however in present work, decoupling approach is used to make observer robust against uncertainties. The methodology requires upper bounds on nonlinearity and the message signal and estimates for these bounds are generated adaptively. Thus no information about the nature of nonlinearity and associated Lipschitz constant is needed in proposed approach. Message signal is recovered using equivalent output injection which is a low pass filtered equivalent of the discontinuous effort required to maintain the sliding motion. Finally, the efficacy of proposed Nonlinear Unknown Input Sliding Mode Observer (NUISMO) for chaotic communication is verified by conducting simulation studies on two chaotic systems i.e. third order Chua circuit and Rossler system.

  19. Adaptive variable structure control for uncertain chaotic systems containing dead-zone nonlinearity

    International Nuclear Information System (INIS)

    Yan, J.-J.; Shyu, K.-K.; Lin, J.-S.

    2005-01-01

    This paper addresses a practical tracking problem for a class of uncertain chaotic systems with dead-zone nonlinearity in the input function. Based on the Lyapunov stability theorem and Barbalat lemma, an adaptive variable structure controller (AVSC) is proposed to ensure the occurrence of the sliding mode even though the control input contains a dead-zone. Also it is worthy of note that the proposed AVSC involves no information of the upper bound of uncertainty. Thus, the limitation of knowing the bound of uncertainty in advance is certainly released. Furthermore, in the sliding mode, the investigated uncertain chaotic system remains insensitive to the uncertainty, and behaves like a linear system. Finally, a well-known Duffing-Holmes chaotic system is used to demonstrate the feasibility of the proposed AVSC

  20. Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator

    KAUST Repository

    Mansingka, Abhinav S.

    2012-07-29

    This paper introduces the first fully digital implementation of a 3rd order ODE-based chaotic oscillator with signum nonlinearity. A threshold bus width of 12-bits for reliable chaotic behavior is observed, below which the system output becomes periodic. Beyond this threshold, the maximum Lyapunov exponent (MLE) is shown to improve up to a peak value at 16-bits and subsequently decrease with increasing bus width. The MLE is also shown to gradually increase with number of introduced internal delay cycles until a peak value at 14 cycles, after which the system loses chaotic properties. Introduced external delay cycles are shown to rotate the attractors in 3-D phase space. Bus width and delay elements can be independently modulated to optimize the system to suit specifications. The experimental results of the system show low area and high performance on a Xilinx Virtex 4 FPGA with throughput of 13.35 Gbits/s for a 32-bit implementation.

  1. Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator

    KAUST Repository

    Mansingka, Abhinav S.; Radwan, Ahmed G.; Salama, Khaled N.; Zidan, Mohammed A.

    2012-01-01

    This paper introduces the first fully digital implementation of a 3rd order ODE-based chaotic oscillator with signum nonlinearity. A threshold bus width of 12-bits for reliable chaotic behavior is observed, below which the system output becomes periodic. Beyond this threshold, the maximum Lyapunov exponent (MLE) is shown to improve up to a peak value at 16-bits and subsequently decrease with increasing bus width. The MLE is also shown to gradually increase with number of introduced internal delay cycles until a peak value at 14 cycles, after which the system loses chaotic properties. Introduced external delay cycles are shown to rotate the attractors in 3-D phase space. Bus width and delay elements can be independently modulated to optimize the system to suit specifications. The experimental results of the system show low area and high performance on a Xilinx Virtex 4 FPGA with throughput of 13.35 Gbits/s for a 32-bit implementation.

  2. Chaotic Dynamics-Based Analysis of Broadband Piezoelectric Vibration Energy Harvesting Enhanced by Using Nonlinearity

    Directory of Open Access Journals (Sweden)

    Zhongsheng Chen

    2016-01-01

    Full Text Available Nonlinear magnetic forces are always used to enlarge resonant bandwidth of vibration energy harvesting systems with piezoelectric cantilever beams. However, how to determine properly the distance between two magnets is one of the key engineering problems. In this paper, the Melnikov theory is introduced to overcome it. Firstly, the Melnikov state-space model of the nonlinear piezoelectric vibration energy harvesting (PVEH system is built. Based on it, chaotic dynamics mechanisms of achieving broadband PVEH by nonlinearity are exposed by potential function of the unperturbed nonlinear PVEH system. Then the corresponding Melnikov function of the nonlinear PVEH system is defined, based on which two Melnikov necessary conditions of determining the distance are obtained. Finally, numerical simulations are done to testify the theoretic results. The results demonstrate that the distance is closely related to the excitation amplitude and frequency once geometric and material parameters are fixed. Under a single-frequency excitation, the nonlinear PVEH system can generate a periodic vibration around a stable point, a large-amplitude vibration around two stable points, or a chaotic vibration. The proposed method is very valuable for optimally designing and utilizing nonlinear broadband PVEH devices in engineering applications.

  3. Localization of Stable and Chaotic Nonpropagating Structures in Nonlinear Mesoscopic Lattices.

    Science.gov (United States)

    Greenfield, Alan Barry

    Recent developments in the study of non-linear localized states, especially non-propagating ones, are outlined. Theoretical models of linear and nonlinear states in a lattice of coupled pendulums and related systems are reviewed. Particular attention is paid to those states which can be described by the Nonlinear Schrodinger equation as well as states where two modes can coexist and states exhibiting chaos. Measurement of localized stable and chaotic states in a 35 site physical pendulum lattice is reported. Various measurement techniques that were used are explained. States that were measured include the tanh profile or kink soliton, and the corresponding uniform state in the wavelength 2 mode, a similar soliton and uniform state in the wavelength 4 mode, a domain wall between the wavelength 2 and 4 modes and a domain wall between a chaotic state and the wavelength 2 mode. Amplitude profiles were measured for the stable kink and domain wall states and smooth curves were obtained by dividing the kink states by the corresponding uniform states. Return maps were measured for two sites in the chaotic domain wall. Simulation of a chaotic domain wall in a 50 site numerical lattice is reported. This system has the advantage that its parameters can be modified much more easily than those of the physical lattice. An attempt is made at quantifying the level of chaos as a function of lattice site with fractal dimension calculations on return maps embedded in a three dimensional space. The drive plane of the chaotic domain wall is mapped out in the drive amplitude - drive frequency plane. Transitions to various stable and quasiperiodic domain walls are noted.

  4. Chaotic behaviour of nonlinear coupled reaction–diffusion system in ...

    Indian Academy of Sciences (India)

    chaos in four-dimensional space by the generalized definitions of spatial ... according to nonlinear noise in the real physical world, f(φ(x),ψ(x)) and g(φ(x) ... tion in ecological system, where φm,n(s) is the host density in generations s and s + 1,.

  5. Chaotic dynamics with high complexity in a simplified new nonautonomous nonlinear electronic circuit

    International Nuclear Information System (INIS)

    Arulgnanam, A.; Thamilmaran, K.; Daniel, M.

    2009-01-01

    A two dimensional nonautonomous dissipative forced series LCR circuit with a simple nonlinear element exhibiting an immense variety of dynamical features is proposed for the first time. Unlike the usual cases of nonlinear element, the nonlinear element used here possesses three segment piecewise linear character with one positive and one negative slope. This nonlinearity is verified to be sufficient to produce chaos with high complexity in many established nonautonomous nonlinear circuits, such as MLC, MLCV, driven Chua, etc., thus indicating an universal behavior similar to the familiar Chua's diode. The dynamics of the proposed circuit is studied experimentally, confirmed numerically, simulated through PSPICE and proved mathematically. An important feature of the circuit is its ability to show dual chaotic behavior.

  6. A non-linear discrete transform for pattern recognition of discrete chaotic systems

    International Nuclear Information System (INIS)

    Karanikas, C.; Proios, G.

    2003-01-01

    It is shown, by an invertible non-linear discrete transform that any finite sequence or any collection of strings of any length can be presented as a random walk on trees. These transforms create the mathematical background for coding any information, for exploring its local variability and diversity. With the underlying computational algorithms, with several examples and applications we propose that these transforms can be used for pattern recognition of immune type. In other words we propose a mathematical platform for detecting self and non-self strings of any alphabet, based on a negative selection algorithms, for scouting data's periodicity and self-similarity and for measuring the diversity of chaotic strings with fractal dimension methods. In particular we estimate successfully the entropy and the ratio of chaotic data with self similarity. Moreover we give some applications of a non-linear denoising filter

  7. A non-linear discrete transform for pattern recognition of discrete chaotic systems

    CERN Document Server

    Karanikas, C

    2003-01-01

    It is shown, by an invertible non-linear discrete transform that any finite sequence or any collection of strings of any length can be presented as a random walk on trees. These transforms create the mathematical background for coding any information, for exploring its local variability and diversity. With the underlying computational algorithms, with several examples and applications we propose that these transforms can be used for pattern recognition of immune type. In other words we propose a mathematical platform for detecting self and non-self strings of any alphabet, based on a negative selection algorithms, for scouting data's periodicity and self-similarity and for measuring the diversity of chaotic strings with fractal dimension methods. In particular we estimate successfully the entropy and the ratio of chaotic data with self similarity. Moreover we give some applications of a non-linear denoising filter.

  8. Nonlinear Time Series Prediction Using LS-SVM with Chaotic Mutation Evolutionary Programming for Parameter Optimization

    International Nuclear Information System (INIS)

    Xu Ruirui; Chen Tianlun; Gao Chengfeng

    2006-01-01

    Nonlinear time series prediction is studied by using an improved least squares support vector machine (LS-SVM) regression based on chaotic mutation evolutionary programming (CMEP) approach for parameter optimization. We analyze how the prediction error varies with different parameters (σ, γ) in LS-SVM. In order to select appropriate parameters for the prediction model, we employ CMEP algorithm. Finally, Nasdaq stock data are predicted by using this LS-SVM regression based on CMEP, and satisfactory results are obtained.

  9. Nonlinear dynamics non-integrable systems and chaotic dynamics

    CERN Document Server

    Borisov, Alexander

    2017-01-01

    This monograph reviews advanced topics in the area of nonlinear dynamics. Starting with theory of integrable systems – including methods to find and verify integrability – the remainder of the book is devoted to non-integrable systems with an emphasis on dynamical chaos. Topics include structural stability, mechanisms of emergence of irreversible behaviour in deterministic systems as well as chaotisation occurring in dissipative systems.

  10. A new two-scroll chaotic attractor with three quadratic nonlinearities, its adaptive control and circuit design

    Science.gov (United States)

    Lien, C.-H.; Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Sanjaya, W. S. M.; Subiyanto

    2018-03-01

    A 3-D new two-scroll chaotic attractor with three quadratic nonlinearities is investigated in this paper. First, the qualitative and dynamical properties of the new two-scroll chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new two-scroll dissipative chaotic system has three unstable equilibrium points. As an engineering application, global chaos control of the new two-scroll chaotic system with unknown system parameters is designed via adaptive feedback control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic two-scroll attractor model.

  11. Chaotic synchronization via adaptive sliding mode observers subject to input nonlinearity

    International Nuclear Information System (INIS)

    Lin Juisheng; Yan Junjuh; Liao Tehlu

    2005-01-01

    This paper is concerned with the state reconstruction of nonlinear chaotic systems with uncertainty having unknown bounds. An adaptive output feedback sliding mode observer (AOFSMO) is established from the available output measurement. Unlike most works we further consider the presence of input nonlinearity due to physical limitations and no restrictive assumption is imposed on the system. Thus, the range of applicability of the proposed method becomes broad. Finally, a hyperchaotic Roessler system is used as an illustrative example to demonstrate the effectiveness of the proposed AOFSMO design method

  12. Chaotic dynamics in nonlinear duopoly Stackelberg game with heterogeneous players

    Science.gov (United States)

    Xiao, Yue; Peng, Yu; Lu, Qian; Wu, Xue

    2018-02-01

    In this paper, a nonlinear duopoly Stackelberg game of competition on output is concerned. In consideration of the effects of difference between plan products and actual products, the two heterogeneous players always adopt suitable strategies which can improve their benefits most. In general, status of each firm is unequal. As the firms take strategies sequentially and produce simultaneously, complex behaviors are brought about. Numerical simulation presents period doubling bifurcation, maximal Lyapunov exponent and chaos. Moreover, an appropriate method of chaos controlling is applied and fractal dimension is analyzed as well.

  13. Electricity demand and spot price forecasting using evolutionary computation combined with chaotic nonlinear dynamic model

    International Nuclear Information System (INIS)

    Unsihuay-Vila, C.; Zambroni de Souza, A.C.; Marangon-Lima, J.W.; Balestrassi, P.P.

    2010-01-01

    This paper proposes a new hybrid approach based on nonlinear chaotic dynamics and evolutionary strategy to forecast electricity loads and prices. The main idea is to develop a new training or identification stage in a nonlinear chaotic dynamic based predictor. In the training stage five optimal parameters for a chaotic based predictor are searched through an optimization model based on evolutionary strategy. The objective function of the optimization model is the mismatch minimization between the multi-step-ahead forecasting of predictor and observed data such as it is done in identification problems. The first contribution of this paper is that the proposed approach is capable of capturing the complex dynamic of demand and price time series considered resulting in a more accuracy forecasting. The second contribution is that the proposed approach run on-line manner, i.e. the optimal set of parameters and prediction is executed automatically which can be used to prediction in real-time, it is an advantage in comparison with other models, where the choice of their input parameters are carried out off-line, following qualitative/experience-based recipes. A case study of load and price forecasting is presented using data from New England, Alberta, and Spain. A comparison with other methods such as autoregressive integrated moving average (ARIMA) and artificial neural network (ANN) is shown. The results show that the proposed approach provides a more accurate and effective forecasting than ARIMA and ANN methods. (author)

  14. Suppression of chaotic vibrations in a nonlinear half-car model

    Energy Technology Data Exchange (ETDEWEB)

    Tusset, Ângelo Marcelo, E-mail: tusset@utfpr.edu.br, E-mail: piccirillo@utfpr.edu.br, E-mail: fcjanzen@utfpr.edu.br, E-mail: wagner-barth@hotmail.com; Piccirillo, Vinícius, E-mail: tusset@utfpr.edu.br, E-mail: piccirillo@utfpr.edu.br, E-mail: fcjanzen@utfpr.edu.br, E-mail: wagner-barth@hotmail.com; Janzen, Frederic Conrad, E-mail: tusset@utfpr.edu.br, E-mail: piccirillo@utfpr.edu.br, E-mail: fcjanzen@utfpr.edu.br, E-mail: wagner-barth@hotmail.com; Lenz, Wagner Barth, E-mail: tusset@utfpr.edu.br, E-mail: piccirillo@utfpr.edu.br, E-mail: fcjanzen@utfpr.edu.br, E-mail: wagner-barth@hotmail.com [UTFPR- PONTA GROSSA, PR (Brazil); Balthazar, José Manoel, E-mail: jmbaltha@rc.unesp.br [UNESP-BAURU, SP (Brazil); Fonseca Brasil, Reyolando M. L. R. da, E-mail: reyolando.brasil@ufabc.edu.br [UFABC-SANTO ANDRE, SP (Brazil)

    2014-12-10

    The present work investigates the nonlinear response of a half-car model. The disturbances of the road are assumed to be sinusoidal. After constructing the bifurcation diagram, we using the 0-1 test for identify the chaotic motion. The principal objective of this study is to eliminate the chaotic behaviour of the chassis and reduce its vibration, and for this reason a control system for semi-active vehicle suspension with magnetorheological damper is proposed. The control mechanism is designed based on SDRE technique, where the control parameter is the voltage applied to the coil of the damper. Numerical results show that the proposed control method is effective in significantly reducing of the chassis vibration, increasing therefore, passenger comfort.

  15. An Eight-Term Novel Four-Scroll Chaotic System with Cubic Nonlinearity and its Circuit Simulation

    Directory of Open Access Journals (Sweden)

    S. Sampath

    2014-11-01

    Full Text Available This research work proposes an eight-term novel four-scroll chaotic system with cubic nonlinearity and analyses its fundamental properties such as dissipativity, equilibria, symmetry and invariance, Lyapunov exponents and KaplanYorke dimension. The phase portraits of the novel chaotic system, which are obtained in this work by using MATLAB, depict the four-scroll attractor of the system. For the parameter values and initial conditions chosen in this work, the Lyapunov exponents of the novel four-scroll chaotic system are obtained as L1 = 0.75335, L2 = 0 and L3 = −22.43304. Also, the Kaplan-Yorke dimension of the novel four-scroll chaotic system is obtained as DKY = 2.0336. Finally, an electronic circuit realization of the novel four-scroll chaotic system is presented by using SPICE to confirm the feasibility of the theoretical model.

  16. Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

    Science.gov (United States)

    Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A

    2012-03-01

    We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

  17. Assessment of Effects of a Delay Block and a Nonlinear Block in Systems with Chaotic Behavior Using Lyapunov Exponents

    Directory of Open Access Journals (Sweden)

    Pablo César Rodríguez Gómez

    2017-05-01

    Full Text Available Context: Because feedback systems are very common and widely used, studies of the structural characteristics under which chaotic behavior is generated have been developed. These can be separated into a nonlinear system and a linear system at least of the third order. Methods such as the descriptive function have been used for analysis. Method: A feedback system is proposed comprising a linear system, a nonlinear system and a delay block, in order to assess his behavior using Lyapunov exponents. It is evaluated with three different linear systems, different delay values and different values for parameters of nonlinear characteristic, aiming to reach chaotic behavior. Results: One hundred experiments were carried out for each of the three linear systems, by changing the value of some parameters, assessing their influence on the dynamics of the system. Contour plots that relate these parameters to the Largest Lyapunov exponent were obtained and analyzed. Conclusions: In spite non-linearity is a condition for the existence of chaos, this does not imply that any nonlinear characteristic generates a chaotic system, it is reflected by the contour plots showing the transitions between chaotic and no chaotic behavior of the feedback system. Language: English

  18. The Chaotic Prediction for Aero-Engine Performance Parameters Based on Nonlinear PLS Regression

    Directory of Open Access Journals (Sweden)

    Chunxiao Zhang

    2012-01-01

    Full Text Available The prediction of the aero-engine performance parameters is very important for aero-engine condition monitoring and fault diagnosis. In this paper, the chaotic phase space of engine exhaust temperature (EGT time series which come from actual air-borne ACARS data is reconstructed through selecting some suitable nearby points. The partial least square (PLS based on the cubic spline function or the kernel function transformation is adopted to obtain chaotic predictive function of EGT series. The experiment results indicate that the proposed PLS chaotic prediction algorithm based on biweight kernel function transformation has significant advantage in overcoming multicollinearity of the independent variables and solve the stability of regression model. Our predictive NMSE is 16.5 percent less than that of the traditional linear least squares (OLS method and 10.38 percent less than that of the linear PLS approach. At the same time, the forecast error is less than that of nonlinear PLS algorithm through bootstrap test screening.

  19. Robust intelligent sliding model control using recurrent cerebellar model articulation controller for uncertain nonlinear chaotic systems

    International Nuclear Information System (INIS)

    Peng Yafu

    2009-01-01

    In this paper, a robust intelligent sliding model control (RISMC) scheme using an adaptive recurrent cerebellar model articulation controller (RCMAC) is developed for a class of uncertain nonlinear chaotic systems. This RISMC system offers a design approach to drive the state trajectory to track a desired trajectory, and it is comprised of an adaptive RCMAC and a robust controller. The adaptive RCMAC is used to mimic an ideal sliding mode control (SMC) due to unknown system dynamics, and a robust controller is designed to recover the residual approximation error for guaranteeing the stable characteristic. Moreover, the Taylor linearization technique is employed to derive the linearized model of the RCMAC. The all adaptation laws of the RISMC system are derived based on the Lyapunov stability analysis and projection algorithm, so that the stability of the system can be guaranteed. Finally, the proposed RISMC system is applied to control a Van der Pol oscillator, a Genesio chaotic system and a Chua's chaotic circuit. The effectiveness of the proposed control scheme is verified by some simulation results with unknown system dynamics and existence of external disturbance. In addition, the advantages of the proposed RISMC are indicated in comparison with a SMC system

  20. Robust intelligent backstepping tracking control for uncertain non-linear chaotic systems using H∞ control technique

    International Nuclear Information System (INIS)

    Peng, Y.-F.

    2009-01-01

    The cerebellar model articulation controller (CMAC) is a non-linear adaptive system with built-in simple computation, good generalization capability and fast learning property. In this paper, a robust intelligent backstepping tracking control (RIBTC) system combined with adaptive CMAC and H ∞ control technique is proposed for a class of chaotic systems with unknown system dynamics and external disturbance. In the proposed control system, an adaptive backstepping cerebellar model articulation controller (ABCMAC) is used to mimic an ideal backstepping control (IBC), and a robust H ∞ controller is designed to attenuate the effect of the residual approximation errors and external disturbances with desired attenuation level. Moreover, the all adaptation laws of the RIBTC system are derived based on the Lyapunov stability analysis, the Taylor linearization technique and H ∞ control theory, so that the stability of the closed-loop system and H ∞ tracking performance can be guaranteed. Finally, three application examples, including a Duffing-Holmes chaotic system, a Genesio chaotic system and a Sprott circuit system, are used to demonstrate the effectiveness and performance of proposed robust control technique.

  1. Chaotic behavior of earthquakes induced by a nonlinear magma up flow

    International Nuclear Information System (INIS)

    Pelap, F.B.; Kagho, L.Y.; Fogang, C.F.

    2016-01-01

    This paper considers the dynamics of a modified 1D nonlinear spring-block model for earthquake subjected to the strengths induced by the motion of the tectonic plates and the up flow of magma during volcanism. Based on the multiple time scales method, we establish that after the slip, the fault remains active and the frictions increase with the power of the earthquake. We also obtain in the non-resonance case that the appearing probability of an event decreases with these frictions. In the resonance case, the dynamics of harmonic oscillations show that the rocks constituting the block will fracture or resist to the effects induced by the magma motion. Our analytical investigations are complemented by numerical simulations from which it appears that, for given values of the magma thrust strength magnitude, the friction coefficient, the quadratic and cubic nonlinear parameters, the system exhibits chaotic behavior.

  2. Analysis, Adaptive Control and Adaptive Synchronization of a Nine-Term Novel 3-D Chaotic System with Four Quadratic Nonlinearities and its Circuit Simulation

    Directory of Open Access Journals (Sweden)

    S. Vaidyanathan

    2014-11-01

    Full Text Available This research work describes a nine-term novel 3-D chaotic system with four quadratic nonlinearities and details its qualitative properties. The phase portraits of the 3-D novel chaotic system simulated using MATLAB, depict the strange chaotic attractor of the system. For the parameter values chosen in this work, the Lyapunov exponents of the novel chaotic system are obtained as L1 = 6.8548, L2 = 0 and L3 = −32.8779. Also, the Kaplan-Yorke dimension of the novel chaotic system is obtained as DKY = 2.2085. Next, an adaptive controller is design to achieve global stabilization of the 3-D novel chaotic system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global chaos synchronization of two identical novel chaotic systems with unknown system parameters. Finally, an electronic circuit realization of the novel chaotic system is presented using SPICE to confirm the feasibility of the theoretical model.

  3. Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy

    Directory of Open Access Journals (Sweden)

    Shih-Yu Li

    2015-01-01

    Full Text Available A novel bioinspired control strategy design is proposed for generalized synchronization of nonlinear chaotic systems, combining the bioinspired stability theory, fuzzy modeling, and a novel, simple-form Lyapunov control function design of derived high efficient, heuristic and bioinspired controllers. Three main contributions are concluded: (1 apply the bioinspired stability theory to further analyze the stability of fuzzy error systems; the high performance of controllers has been shown in previous study by Li and Ge 2009, (2 a new Lyapunov control function based on bioinspired stability theory is designed to achieve synchronization without using traditional LMI method, which is a simple linear homogeneous function of states and the process of designing controller to synchronize two fuzzy chaotic systems becomes much simpler, and (3 three different situations of synchronization are proposed; classical master and slave Lorenz systems, slave Chen’s system, and Rossler’s system as functional system are illustrated to further show the effectiveness and feasibility of our novel strategy. The simulation results show that our novel control strategy can be applied to different and complicated control situations with high effectiveness.

  4. A novel joint-processing adaptive nonlinear equalizer using a modular recurrent neural network for chaotic communication systems.

    Science.gov (United States)

    Zhao, Haiquan; Zeng, Xiangping; Zhang, Jiashu; Liu, Yangguang; Wang, Xiaomin; Li, Tianrui

    2011-01-01

    To eliminate nonlinear channel distortion in chaotic communication systems, a novel joint-processing adaptive nonlinear equalizer based on a pipelined recurrent neural network (JPRNN) is proposed, using a modified real-time recurrent learning (RTRL) algorithm. Furthermore, an adaptive amplitude RTRL algorithm is adopted to overcome the deteriorating effect introduced by the nesting process. Computer simulations illustrate that the proposed equalizer outperforms the pipelined recurrent neural network (PRNN) and recurrent neural network (RNN) equalizers. Copyright © 2010 Elsevier Ltd. All rights reserved.

  5. Chaotic behaviour in the non-linear optimal control of unilaterally contacting building systems during earthquakes

    CERN Document Server

    Liolios, A

    2003-01-01

    The paper presents a new numerical approach for a non-linear optimal control problem arising in earthquake civil engineering. This problem concerns the elastoplastic softening-fracturing unilateral contact between neighbouring buildings during earthquakes when Coulomb friction is taken into account under second-order instabilizing effects. So, the earthquake response of the adjacent structures can appear instabilities and chaotic behaviour. The problem formulation presented here leads to a set of equations and inequalities, which is equivalent to a dynamic hemivariational inequality in the way introduced by Panagiotopoulos [Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer-Verlag, Berlin, 1993]. The numerical procedure is based on an incremental problem formulation and on a double discretization, in space by the finite element method and in time by the Wilson-theta method. The generally non-convex constitutive contact laws are piecewise linearized, and in each time-step a non-c...

  6. A new reduced-order observer for the synchronization of nonlinear chaotic systems: An application to secure communications

    Energy Technology Data Exchange (ETDEWEB)

    Castro-Ramírez, Joel, E-mail: ingcastro.7@gmail.com [Universidad Politécnica de Tlaxcala Av. Universidad Politecnica de Tlaxcala No.1, San Pedro Xalcaltzinco, Tepeyanco, Tlaxcala, C.P. 90180 (Mexico); Martínez-Guerra, Rafael, E-mail: rguerra@ctrl.cinvestav.mx [Departamento de Control Automático CINVESTAV-IPN, A.P. 14-740, D.F., México C.P. 07360 (Mexico); Cruz-Victoria, Juan Crescenciano, E-mail: juancrescenciano.cruz@uptlax.edu.mx [Universidad Politécnica de Tlaxcala Av. Universidad Politécnica de Tlaxcala No.1, San Pedro Xalcaltzinco, Tepeyanco, Tlaxcala, C.P. 90180 (Mexico)

    2015-10-15

    This paper deals with the master-slave synchronization scheme for partially known nonlinear chaotic systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown states. It introduced a new reduced order observer, using the concept of Algebraic Observability; we applied the results to a Sundarapandian chaotic system, and by means of some numerical simulations we show the effectiveness of the suggested approach. Finally, the proposed observer is utilized for encryption, where encryption key is the master system and decryption key is the slave system.

  7. A new reduced-order observer for the synchronization of nonlinear chaotic systems: An application to secure communications

    International Nuclear Information System (INIS)

    Castro-Ramírez, Joel; Martínez-Guerra, Rafael; Cruz-Victoria, Juan Crescenciano

    2015-01-01

    This paper deals with the master-slave synchronization scheme for partially known nonlinear chaotic systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown states. It introduced a new reduced order observer, using the concept of Algebraic Observability; we applied the results to a Sundarapandian chaotic system, and by means of some numerical simulations we show the effectiveness of the suggested approach. Finally, the proposed observer is utilized for encryption, where encryption key is the master system and decryption key is the slave system

  8. Non-linear thermal engineering, chaotic advection and mixing; Thermique non-lineaire, melange et advection chaotique

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1999-12-31

    This conference day was jointly organized by the `university group of thermal engineering (GUT)` and the French association of thermal engineers. This book of proceedings contains 7 papers entitled: `energy spectra of a passive scalar undergoing advection by a chaotic flow`; `analysis of chaotic behaviours: from topological characterization to modeling`; `temperature homogeneity by Lagrangian chaos in a direct current flow heat exchanger: numerical approach`; ` thermal instabilities in a mixed convection phenomenon: nonlinear dynamics`; `experimental characterization study of the 3-D Lagrangian chaos by thermal analogy`; `influence of coherent structures on the mixing of a passive scalar`; `evaluation of the performance index of a chaotic advection effect heat exchanger for a wide range of Reynolds numbers`. (J.S.)

  9. Non-linear thermal engineering, chaotic advection and mixing; Thermique non-lineaire, melange et advection chaotique

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1998-12-31

    This conference day was jointly organized by the `university group of thermal engineering (GUT)` and the French association of thermal engineers. This book of proceedings contains 7 papers entitled: `energy spectra of a passive scalar undergoing advection by a chaotic flow`; `analysis of chaotic behaviours: from topological characterization to modeling`; `temperature homogeneity by Lagrangian chaos in a direct current flow heat exchanger: numerical approach`; ` thermal instabilities in a mixed convection phenomenon: nonlinear dynamics`; `experimental characterization study of the 3-D Lagrangian chaos by thermal analogy`; `influence of coherent structures on the mixing of a passive scalar`; `evaluation of the performance index of a chaotic advection effect heat exchanger for a wide range of Reynolds numbers`. (J.S.)

  10. Chaotic behaviour in the non-linear optimal control of unilaterally contacting building systems during earthquakes

    International Nuclear Information System (INIS)

    Liolios, A.A.; Boglou, A.K.

    2003-01-01

    The paper presents a new numerical approach for a non-linear optimal control problem arising in earthquake civil engineering. This problem concerns the elastoplastic softening-fracturing unilateral contact between neighbouring buildings during earthquakes when Coulomb friction is taken into account under second-order instabilizing effects. So, the earthquake response of the adjacent structures can appear instabilities and chaotic behaviour. The problem formulation presented here leads to a set of equations and inequalities, which is equivalent to a dynamic hemivariational inequality in the way introduced by Panagiotopoulos [Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer-Verlag, Berlin, 1993]. The numerical procedure is based on an incremental problem formulation and on a double discretization, in space by the finite element method and in time by the Wilson-θ method. The generally non-convex constitutive contact laws are piecewise linearized, and in each time-step a non-convex linear complementarity problem is solved with a reduced number of unknowns

  11. Adaptive fuzzy observer-based stabilization of a class of uncertain time-delayed chaotic systems with actuator nonlinearities

    International Nuclear Information System (INIS)

    Shahnazi, Reza; Haghani, Adel; Jeinsch, Torsten

    2015-01-01

    An observer-based output feedback adaptive fuzzy controller is proposed to stabilize a class of uncertain chaotic systems with unknown time-varying time delays, unknown actuator nonlinearities and unknown external disturbances. The actuator nonlinearity can be backlash-like hysteresis or dead-zone. Based on universal approximation property of fuzzy systems the unknown nonlinear functions are approximated by fuzzy systems, where the consequent parts of fuzzy rules are tuned with adaptive schemes. The proposed method does not need the availability of the states and an observer based output feedback approach is proposed to estimate the states. To have more robustness and at the same time to alleviate chattering an adaptive discontinuous structure is suggested. Semi-global asymptotic stability of the overall system is ensured by proposing a suitable Lyapunov–Krasovskii functional candidate. The approach is applied to stabilize the time-delayed Lorenz chaotic system with uncertain dynamics amid significant disturbances. Analysis of simulations reveals the effectiveness of the proposed method in terms of coping well with the modeling uncertainties, nonlinearities in actuators, unknown time-varying time-delays and unknown external disturbances while maintaining asymptotic convergence

  12. Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system

    Science.gov (United States)

    Mobayen, Saleh; Kingni, Sifeu Takougang; Pham, Viet-Thanh; Nazarimehr, Fahimeh; Jafari, Sajad

    2018-02-01

    This paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behaviour of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicity, periodic oscillations and double-scroll chaotic attractor. Basin of attraction of the proposed system shows that the chaotic attractor is self-excited. Furthermore, feasibility of double-scroll chaotic attractor in the real word is investigated by using the OrCAD-PSpice software via an electronic implementation of the proposed system. A good qualitative agreement is illustrated between the numerical simulations and the OrCAD-PSpice results. Finally, a finite-time control method based on dynamic sliding surface for the synchronisation of master and slave chaotic systems in the presence of external disturbances is performed. Using the suggested control technique, the superior master-slave synchronisation is attained. Illustrative simulation results on the studied chaotic system are presented to indicate the effectiveness of the suggested scheme.

  13. Analysis, Adaptive Control and Anti-Synchronization of a Six-Term Novel Jerk Chaotic System with two Exponential Nonlinearities and its Circuit Simulation

    Directory of Open Access Journals (Sweden)

    S. Vaidyanathan

    2014-11-01

    Full Text Available This research work proposes a six-term novel 3-D jerk chaotic system with two exponential nonlinearities. This work also analyses system’s fundamental properties such as dissipativity, equilibria, Lyapunov exponents and Kaplan-Yorke dimension. The phase portraits of the jerk chaotic system simulated using MATLAB, depict the strange chaotic attractor of the system. For the parameter values and initial conditions chosen in this work, the Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0.24519, L2 = 0 and L3 = −0.84571. Also, the Kaplan-Yorke dimension of the novel jerk chaotic system is obtained as DKY = 2.2899. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system having two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve global chaos anti-synchronization of two identical novel jerk chaotic systems with two unknown system parameters. Finally, an electronic circuit realization of the novel jerk chaotic system is presented using SPICE to confirm the feasibility of the theoretical model.

  14. Symposium Gyro Technology 1997

    Energy Technology Data Exchange (ETDEWEB)

    Sorg, H [ed.; Stuttgart Univ. (Germany). Inst. A fuer Mechanik

    1997-10-01

    This volume includes the twenty papers which were presented at the Symposium Gyro Technology 1997. The subjects that have been treated during the symposium were as follows: Performance and design of silicon micromachined gyro; improved rate gyroscope designs designated for fabrication by modern deep silicon etching; micromechanical vibratory rate gyroscopes fabricated in conventional CMOS; error modelling of silicon angular rate sensor; a capacitive accelerometer as an example for surface micromachined inertial sensors; initial production results of a new family of fiber optic gyroscopes; dual-axis multiplexed open loop fiber optic gyroscope; flattely supported vibratory gyro-sensor using a Trident-type tuning fork resonator; innovative mechanizations to optimize inertial sensors for high or low rate operations; design of a planar vibratory gyroscope using electrostatic actuation and electromanetic detection; fiber optic gyro based land navigation system; FOG AHRS and AHRS/GPS navigation system: the low cost solution; GPS/GLONASS/INS-navigation (GLOGINAV); small-sized integrated system of the sea mobile objects attitude and navigation; concepts for hybrid positioning; preliminary results from a large ring laser gyroscope for fundamental physics and geophysics; a `sense of balance` - AHRS with low-cost vibrating-gyroscopes for medical diagnostics; application of strapdown inertial systems of orientation and navigation in intrapipe moving diagnostic apparatus; investigation of a digital readout system for laser gyro; the use of angular rate multiple integrals as input signals for strapdown attitude algorithms. (AKF)

  15. Chaotic examination

    Science.gov (United States)

    Bildirici, Melike; Sonustun, Fulya Ozaksoy; Sonustun, Bahri

    2018-01-01

    In the regards of chaos theory, new concepts such as complexity, determinism, quantum mechanics, relativity, multiple equilibrium, complexity, (continuously) instability, nonlinearity, heterogeneous agents, irregularity were widely questioned in economics. It is noticed that linear models are insufficient for analyzing unpredictable, irregular and noncyclical oscillations of economies, and for predicting bubbles, financial crisis, business cycles in financial markets. Therefore, economists gave great consequence to use appropriate tools for modelling non-linear dynamical structures and chaotic behaviors of the economies especially in macro and the financial economy. In this paper, we aim to model the chaotic structure of exchange rates (USD-TL and EUR-TL). To determine non-linear patterns of the selected time series, daily returns of the exchange rates were tested by BDS during the period from January 01, 2002 to May 11, 2017 which covers after the era of the 2001 financial crisis. After specifying the non-linear structure of the selected time series, it was aimed to examine the chaotic characteristic for the selected time period by Lyapunov Exponents. The findings verify the existence of the chaotic structure of the exchange rate returns in the analyzed time period.

  16. A simple chaotic delay differential equation

    International Nuclear Information System (INIS)

    Sprott, J.C.

    2007-01-01

    The simplest chaotic delay differential equation with a sinusoidal nonlinearity is described, including the route to chaos, Lyapunov exponent spectrum, and chaotic diffusion. It is prototypical of many other high-dimensional chaotic systems

  17. Nonlinear feedback control of chaotic pendulum in presence of saturation effect

    Energy Technology Data Exchange (ETDEWEB)

    Alasty, Aria [Center of Excellence in Design, Robotics, and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran 1458889694 (Iran, Islamic Republic of)]. E-mail: aalasti@sharif.edu; Salarieh, Hassan [Center of Excellence in Design, Robotics, and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran 1458889694 (Iran, Islamic Republic of)]. E-mail: salarieh@mehr.sharif.edu

    2007-01-15

    In present paper, a feedback linearization control is applied to control a chaotic pendulum system. Tracking the desired periodic orbits such as period-one, period-two, and period-four orbits is efficiently achieved. Due to the presence of saturation in real world control signals, the stability of controller is investigated in presence of saturation and sufficient stability conditions are obtained. At first feedback linearization control law is designed, then to avoid the singularity condition, a saturating constraint is applied to the control signal. The stability conditions are obtained analytically. These conditions must be investigated for each specific case numerically. Simulation results show the effectiveness and robustness of proposed controller. A major advantage of this method is its shorter chaotic transient time in compare to other methods such as OGY and Pyragas controllers.

  18. Synchronization of chaotic systems and identification of nonlinear systems by using recurrent hierarchical type-2 fuzzy neural networks.

    Science.gov (United States)

    Mohammadzadeh, Ardashir; Ghaemi, Sehraneh

    2015-09-01

    This paper proposes a novel approach for training of proposed recurrent hierarchical interval type-2 fuzzy neural networks (RHT2FNN) based on the square-root cubature Kalman filters (SCKF). The SCKF algorithm is used to adjust the premise part of the type-2 FNN and the weights of defuzzification and the feedback weights. The recurrence property in the proposed network is the output feeding of each membership function to itself. The proposed RHT2FNN is employed in the sliding mode control scheme for the synchronization of chaotic systems. Unknown functions in the sliding mode control approach are estimated by RHT2FNN. Another application of the proposed RHT2FNN is the identification of dynamic nonlinear systems. The effectiveness of the proposed network and its learning algorithm is verified by several simulation examples. Furthermore, the universal approximation of RHT2FNNs is also shown. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

  19. Cumulative effect of structural nonlinearities: chaotic dynamics of cantilever beam system with impacts

    International Nuclear Information System (INIS)

    Emans, Joseph; Wiercigroch, Marian; Krivtsov, Anton M.

    2005-01-01

    The nonlinear analysis of a common beam system was performed, and the method for such, outlined and presented. Nonlinear terms for the governing dynamic equations were extracted and the behaviour of the system was investigated. The analysis was carried out with and without physically realistic parameters, to show the characteristics of the system, and the physically realistic responses. Also, the response as part of a more complex system was considered, in order to investigate the cumulative effects of nonlinearities. Chaos, as well as periodic motion was found readily for the physically unrealistic parameters. In addition, nonlinear behaviour such as co-existence of attractors was found even at modest oscillation levels during investigations with realistic parameters. When considered as part of a more complex system with further nonlinearities, comparisons with linear beam theory show the classical approach to be lacking in accuracy of qualitative predictions, even at weak oscillations

  20. Transient and chaotic low-energy transfers in a system with bistable nonlinearity

    Energy Technology Data Exchange (ETDEWEB)

    Romeo, F., E-mail: francesco.romeo@uniroma1.it [Department of Structural and Geotechnical Engineering, SAPIENZA University of Rome, Rome (Italy); Manevitch, L. I. [Institute of Chemical Physics, RAS, Moscow (Russian Federation); Bergman, L. A.; Vakakis, A. [College of Engineering, University of Illinois at Urbana–Champaign, Champaign, Illinois 61820 (United States)

    2015-05-15

    The low-energy dynamics of a two-dof system composed of a grounded linear oscillator coupled to a lightweight mass by means of a spring with both cubic nonlinear and negative linear components is investigated. The mechanisms leading to intense energy exchanges between the linear oscillator, excited by a low-energy impulse, and the nonlinear attachment are addressed. For lightly damped systems, it is shown that two main mechanisms arise: Aperiodic alternating in-well and cross-well oscillations of the nonlinear attachment, and secondary nonlinear beats occurring once the dynamics evolves solely in-well. The description of the former dissipative phenomenon is provided in a two-dimensional projection of the phase space, where transitions between in-well and cross-well oscillations are associated with sequences of crossings across a pseudo-separatrix. Whereas the second mechanism is described in terms of secondary limiting phase trajectories of the nonlinear attachment under certain resonance conditions. The analytical treatment of the two aformentioned low-energy transfer mechanisms relies on the reduction of the nonlinear dynamics and consequent analysis of the reduced dynamics by asymptotic techniques. Direct numerical simulations fully validate our analytical predictions.

  1. Nonlinear generalized synchronization of chaotic systems by pure error dynamics and elaborate nondiagonal Lyapunov function

    International Nuclear Information System (INIS)

    Ge Zhengming; Chang Chingming

    2009-01-01

    By applying pure error dynamics and elaborate nondiagonal Lyapunov function, the nonlinear generalized synchronization is studied in this paper. Instead of current mixed error dynamics in which master state variables and slave state variables are presented, the nonlinear generalized synchronization can be obtained by pure error dynamics without auxiliary numerical simulation. The elaborate nondiagonal Lyapunov function is applied rather than current monotonous square sum Lyapunov function deeply weakening the powerfulness of Lyapunov direct method. Both autonomous and nonautonomous double Mathieu systems are used as examples with numerical simulations.

  2. Elementary chaotic snap flows

    International Nuclear Information System (INIS)

    Munmuangsaen, Buncha; Srisuchinwong, Banlue

    2011-01-01

    Highlights: → Five new elementary chaotic snap flows and a generalization of an existing chaotic snap flow have been presented. → Three of all are conservative systems whilst three others are dissipative systems. → Four cases need only a single control parameter and a single nonlinearity. → A cubic case in a jerk representation requires only two terms and a single nonlinearity. - Abstract: Hyperjerk systems with 4th-order derivative of the form x .... =f(x ... ,x .. ,x . ,x) have been referred to as snap systems. Five new elementary chaotic snap flows and a generalization of an existing flow are presented through an extensive numerical search. Four of these flows demonstrate elegant simplicity of a single control parameter based on a single nonlinearity of a quadratic, a piecewise-linear or an exponential type. Two others demonstrate elegant simplicity of all unity-in-magnitude parameters based on either a single cubic nonlinearity or three cubic nonlinearities. The chaotic snap flow with a single cubic nonlinearity requires only two terms and can be transformed to its equivalent dynamical form of only five terms which have a single nonlinearity. An advantage is that such a chaotic flow offers only five terms even though the (four) dimension is high. Three of the chaotic snap flows are characterized as conservative systems whilst three others are dissipative systems. Basic dynamical properties are described.

  3. Stages of chaotic synchronization.

    Science.gov (United States)

    Tang, D. Y.; Dykstra, R.; Hamilton, M. W.; Heckenberg, N. R.

    1998-09-01

    In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (c) 1998 American Institute of Physics.

  4. Multi-piecewise quadratic nonlinearity memristor and its 2N-scroll and 2N + 1-scroll chaotic attractors system.

    Science.gov (United States)

    Wang, Chunhua; Liu, Xiaoming; Xia, Hu

    2017-03-01

    In this paper, two kinds of novel ideal active flux-controlled smooth multi-piecewise quadratic nonlinearity memristors with multi-piecewise continuous memductance function are presented. The pinched hysteresis loop characteristics of the two memristor models are verified by building a memristor emulator circuit. Using the two memristor models establish a new memristive multi-scroll Chua's circuit, which can generate 2N-scroll and 2N+1-scroll chaotic attractors without any other ordinary nonlinear function. Furthermore, coexisting multi-scroll chaotic attractors are found in the proposed memristive multi-scroll Chua's circuit. Phase portraits, Lyapunov exponents, bifurcation diagrams, and equilibrium point analysis have been used to research the basic dynamics of the memristive multi-scroll Chua's circuit. The consistency of circuit implementation and numerical simulation verifies the effectiveness of the system design.

  5. Intermittently chaotic oscillations for a differential-delay equation with Gaussian nonlinearity

    Science.gov (United States)

    Hamilton, Ian

    1992-01-01

    For a differential-delay equation the time dependence of the variable is a function of the variable at a previous time. We consider a differential-delay equation with Gaussian nonlinearity that displays intermittent chaos. Although not the first example of a differential-delay equation that displays such behavior, for this example the intermittency is classified as type III, and the origin of the intermittent chaos may be qualitatively understood from the limiting forms of the equation for large and small variable magnitudes.

  6. Chaotic properties between the nonintegrable discrete nonlinear Schroedinger equation and a nonintegrable discrete Heisenberg model

    International Nuclear Information System (INIS)

    Ding Qing

    2007-01-01

    We prove that the integrable-nonintegrable discrete nonlinear Schroedinger equation (AL-DNLS) introduced by Cai, Bishop and Gronbech-Jensen (Phys. Rev. Lett. 72 591(1994)) is the discrete gauge equivalent to an integrable-nonintegrable discrete Heisenberg model from the geometric point of view. Then we study whether the transmission and bifurcation properties of the AL-DNLS equation are preserved under the action of discrete gauge transformations. Our results reveal that the transmission property of the AL-DNLS equation is completely preserved and the bifurcation property is conditionally preserved to those of the integrable-nonintegrable discrete Heisenberg model

  7. A novel sort of adaptive complex synchronizations of two indistinguishable chaotic complex nonlinear models with uncertain parameters and its applications in secure communications

    Science.gov (United States)

    Mahmoud, Emad E.; Abood, Fatimah S.

    In this paper, we will demonstrate the adaptive complex anti-lag synchronization (CALS) of two indistinguishable complex chaotic nonlinear systems with the parameters which are uncertain. The significance of CALS is not advised well in the literature yet. The CALS contains or consolidate two sorts of synchronizations (anti-lag synchronization ALS and lag synchronization LS). The state variable of the master system synchronizes with an alternate state variable of the slave system. Depending on the function of Lyapunov, a plan is orchestrated to achieve CALS of chaotic attractors of complex systems with unverifiable parameters. CALS of two indistinguishable complexes of Lü systems is viewed as, for example, an occasion for affirming the likelihood of the plan exhibited. In physics, we can see complex chaotic systems in numerous different applications, for example, applied sciences or engineering. With a specific end goal to affirm the proposed synchronization plan viability and demonstrate the hypothetical outcomes, we can compute the numerical simulation. The above outcomes will give the hypothetical establishment to the secure communication applications. CALS of complex chaotic systems in which a state variable of the master system synchronizes with an alternate state variable of the slave system is an encouraging sort of synchronization as it contributes excellent security in secure communication. Amid this secure communication, the synchronization between transmitter and collector is shut and message signals are recouped. The encryption and restoration of the signals are simulated numerically.

  8. Developing a local least-squares support vector machines-based neuro-fuzzy model for nonlinear and chaotic time series prediction.

    Science.gov (United States)

    Miranian, A; Abdollahzade, M

    2013-02-01

    Local modeling approaches, owing to their ability to model different operating regimes of nonlinear systems and processes by independent local models, seem appealing for modeling, identification, and prediction applications. In this paper, we propose a local neuro-fuzzy (LNF) approach based on the least-squares support vector machines (LSSVMs). The proposed LNF approach employs LSSVMs, which are powerful in modeling and predicting time series, as local models and uses hierarchical binary tree (HBT) learning algorithm for fast and efficient estimation of its parameters. The HBT algorithm heuristically partitions the input space into smaller subdomains by axis-orthogonal splits. In each partitioning, the validity functions automatically form a unity partition and therefore normalization side effects, e.g., reactivation, are prevented. Integration of LSSVMs into the LNF network as local models, along with the HBT learning algorithm, yield a high-performance approach for modeling and prediction of complex nonlinear time series. The proposed approach is applied to modeling and predictions of different nonlinear and chaotic real-world and hand-designed systems and time series. Analysis of the prediction results and comparisons with recent and old studies demonstrate the promising performance of the proposed LNF approach with the HBT learning algorithm for modeling and prediction of nonlinear and chaotic systems and time series.

  9. Chaos control and generalized projective synchronization of heavy symmetric chaotic gyroscope systems via Gaussian radial basis adaptive variable structure control

    International Nuclear Information System (INIS)

    Farivar, Faezeh; Aliyari Shoorehdeli, Mahdi; Nekoui, Mohammad Ali; Teshnehlab, Mohammad

    2012-01-01

    Highlights: ► A systematic procedure for GPS of unknown heavy chaotic gyroscope systems. ► Proposed methods are based on Lyapunov stability theory. ► Without calculating Lyapunov exponents and Eigen values of the Jacobian matrix. ► Capable to extend for a variety of chaotic systems. ► Useful for practical applications in the future. - Abstract: This paper proposes the chaos control and the generalized projective synchronization methods for heavy symmetric gyroscope systems via Gaussian radial basis adaptive variable structure control. Because of the nonlinear terms of the gyroscope system, the system exhibits chaotic motions. Occasionally, the extreme sensitivity to initial states in a system operating in chaotic mode can be very destructive to the system because of unpredictable behavior. In order to improve the performance of a dynamic system or avoid the chaotic phenomena, it is necessary to control a chaotic system with a periodic motion beneficial for working with a particular condition. As chaotic signals are usually broadband and noise like, synchronized chaotic systems can be used as cipher generators for secure communication. This paper presents chaos synchronization of two identical chaotic motions of symmetric gyroscopes. In this paper, the switching surfaces are adopted to ensure the stability of the error dynamics in variable structure control. Using the neural variable structure control technique, control laws are established which guarantees the chaos control and the generalized projective synchronization of unknown gyroscope systems. In the neural variable structure control, Gaussian radial basis functions are utilized to on-line estimate the system dynamic functions. Also, the adaptation laws of the on-line estimator are derived in the sense of Lyapunov function. Thus, the unknown gyro systems can be guaranteed to be asymptotically stable. Also, the proposed method can achieve the control objectives. Numerical simulations are presented to

  10. Forecasting nonlinear chaotic time series with function expression method based on an improved genetic-simulated annealing algorithm.

    Science.gov (United States)

    Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

    2015-01-01

    The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.

  11. Nonlinear forecasting of stream flows using a chaotic approach and artificial neural networks

    Directory of Open Access Journals (Sweden)

    Hakan Tongal

    2013-07-01

    Full Text Available This paper evaluates the forecasting performance of two nonlinear models, k-nearest neighbor (kNN and feed-forward neural networks (FFNN, using stream flow data of the Kızılırmak River, the longest river in Turkey. For the kNN model, the required parameters are delay time, number of nearest neigh- bors and embedding dimension. The optimal delay time was obtained with the mutual information function; the number of nearest neighbors was obtained with the optimization process that minimi- zes RMSE as a function of the neighbor number and the embedding dimension was obtained with the correlation dimension method. The correlation dimension of the Kızılırmak River was d = 2.702, which was used in forming the input structure of the FFNN. The nearest integer above the correlation dimension (i.e., 3 provided the minimal number of required variables to characterize the system, and the maximum number of required variables was obtained with the nearest integer above the value 2d + 1 (Takens, 1981 (i.e., 7. Two FFNN models were developed that incorporate 3 and 7 lagged discharge values and the predicted performance compared to that of the kNN model. The results showed that the kNN model was superior to the FFNN model in stream flow forecasting. However, as a result from the kNN model structure, the model failed in the prediction of peak values. Additionally, it was found that the correlation dimension (if it existed could successfully be used in time series where the determina- tion of the input structure is difficult because of high inter-dependency, as in stream flow time series.  Resumen Este trabajo evalúa el desempeño de pronóstico de dos modelos no lineares, de método de clasificación no paramétrico kNN y de redes neuronales con alimentación avanzada (FNNN, usando datos de flujo del río Kizilirmak, el mayor de Turquía. Para el modelo kNN, los parámetros requeridos son tiempo de retraso, número de vecindarios cercanos y dimensión de

  12. Chaotic Boltzmann machines

    Science.gov (United States)

    Suzuki, Hideyuki; Imura, Jun-ichi; Horio, Yoshihiko; Aihara, Kazuyuki

    2013-01-01

    The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented. PMID:23558425

  13. On the New Scenario of Annihilation of the Cross-Well Chaotic Attractor in a Nonlinear Oscillator

    International Nuclear Information System (INIS)

    Szemplinska, W.; Zubrzycki, A.; Tyrkiel, E.

    1999-01-01

    The twin-well potential Duffing oscillator is considered and the investigations are focused on a new scenario of destruction of the cross-well chaotic attractor. The new phenomenon belongs to the category of subduction bifurcation and consists in replacement of the cross-well chaotic attractor by a pair of unsymmetric 2T-periodic attractors. It is shown that the new scenario forms a transition zone in the system control parameter plane, the zone, which separates the two known scenarios of annihilation of the cross-well chaotic attractor: the boundary crisis, and the subduction in which the two single-well T-periodic attractors are born in a saddle-node bifurcation. (author)

  14. The chaotic dynamical aperture

    International Nuclear Information System (INIS)

    Lee, S.Y.; Tepikian, S.

    1985-01-01

    Nonlinear magnetic forces become more important for particles in the modern large accelerators. These nonlinear elements are introduced either intentionally to control beam dynamics or by uncontrollable random errors. Equations of motion in the nonlinear Hamiltonian are usually non-integrable. Because of the nonlinear part of the Hamiltonian, the tune diagram of accelerators is a jungle. Nonlinear magnet multipoles are important in keeping the accelerator operation point in the safe quarter of the hostile jungle of resonant tunes. Indeed, all the modern accelerator design have taken advantages of nonlinear mechanics. On the other hand, the effect of the uncontrollable random multipoles should be evaluated carefully. A powerful method of studying the effect of these nonlinear multipoles is using a particle tracking calculation, where a group of test particles are tracing through these magnetic multipoles in the accelerator hundreds to millions of turns in order to test the dynamical aperture of the machine. These methods are extremely useful in the design of a large accelerator such as SSC, LEP, HERA and RHIC. These calculations unfortunately take tremendous amount of computing time. In this paper, we try to apply the existing method in the nonlinear dynamics to study the possible alternative solution. When the Hamiltonian motion becomes chaotic, the tune of the machine becomes undefined. The aperture related to the chaotic orbit can be identified as chaotic dynamical aperture. We review the method of determining chaotic orbit and apply the method to nonlinear problems in accelerator physics. We then discuss the scaling properties and effect of random sextupoles

  15. Using Chaotic System in Encryption

    Science.gov (United States)

    Findik, Oğuz; Kahramanli, Şirzat

    In this paper chaotic systems and RSA encryption algorithm are combined in order to develop an encryption algorithm which accomplishes the modern standards. E.Lorenz's weather forecast' equations which are used to simulate non-linear systems are utilized to create chaotic map. This equation can be used to generate random numbers. In order to achieve up-to-date standards and use online and offline status, a new encryption technique that combines chaotic systems and RSA encryption algorithm has been developed. The combination of RSA algorithm and chaotic systems makes encryption system.

  16. Chaotic phenomena in plasmas

    International Nuclear Information System (INIS)

    Kawai, Y.

    1991-08-01

    It has recently been recognized that the research on various aspects of chaotic dynamics grows rapidly as one of some areas in nonlinear science. On the other hands, the plasma has long been called a treasure-house of nonlinear phenomena, so it is easy to imagine that the plasma is abundant in chaotic phenomena. In fact, the research on plasma chaos is going on, such as the research on the stochastic magnetic field and the chaotic orbit in the toroidal helical system, as well as the research in other experiments. To review the present status of the research on plasma chaos and to make clear the basic common physics, a working group was organized in 1990 as a collaboration research of National Institute for Fusion Science. This is the report on its activity in 1990, with a stress on experimental data obtained in basic plasma experiments and RFP, and on the relaxed theories and computer simulations. (author)

  17. Gyro precession and Mach's principle

    International Nuclear Information System (INIS)

    Eby, P.

    1979-01-01

    The precession of a gyroscope is calculated in a nonrelativistic theory due to Barbour which satisfies Mach's principle. It is shown that the theory predicts both the geodetic and motional precession of general relativity to within factors of order 1. The significance of the gyro experiment is discussed from the point of view of metric theories of gravity and this is contrasted with its significance from the point of view of Mach's principle. (author)

  18. Multi-step ahead nonlinear identification of Lorenz's chaotic system using radial basis neural network with learning by clustering and particle swarm optimization

    International Nuclear Information System (INIS)

    Guerra, Fabio A.; Coelho, Leandro dos S.

    2008-01-01

    An important problem in engineering is the identification of nonlinear systems, among them radial basis function neural networks (RBF-NN) using Gaussian activation functions models, which have received particular attention due to their potential to approximate nonlinear behavior. Several design methods have been proposed for choosing the centers and spread of Gaussian functions and training the RBF-NN. The selection of RBF-NN parameters such as centers, spreads, and weights can be understood as a system identification problem. This paper presents a hybrid training approach based on clustering methods (k-means and c-means) to tune the centers of Gaussian functions used in the hidden layer of RBF-NNs. This design also uses particle swarm optimization (PSO) for centers (local clustering search method) and spread tuning, and the Penrose-Moore pseudoinverse for the adjustment of RBF-NN weight outputs. Simulations involving this RBF-NN design to identify Lorenz's chaotic system indicate that the performance of the proposed method is superior to that of the conventional RBF-NN trained for k-means and the Penrose-Moore pseudoinverse for multi-step ahead forecasting

  19. Hypogenetic chaotic jerk flows

    International Nuclear Information System (INIS)

    Li, Chunbiao; Sprott, Julien Clinton; Xing, Hongyan

    2016-01-01

    Removing the amplitude or polarity information in the feedback loop of a jerk structure shows that special nonlinearities with partial information in the variable can also lead to chaos. Some striking properties are found for this kind of hypogenetic chaotic jerk flow, including multistability of symmetric coexisting attractors from an asymmetric structure, hidden attractors with respect to equilibria but with global attraction, easy amplitude control, and phase reversal which is convenient for chaos applications. - Highlights: • Hypogenetic chaotic jerk flows with incomplete feedback of amplitude or polarity are obtained. • Multistability of symmetric coexisting attractors from an asymmetric structure is found. • Some jerk systems have hidden attractors with respect to equilibria but have global attraction. • These chaotic jerk flows have the properties of amplitude control and phase reversal.

  20. Study of chaotic oscillations in practical work on radio physics

    International Nuclear Information System (INIS)

    Ezdov, A.A.; Il'in, V.A.; Petrova, E.B.

    1995-01-01

    A description is given of a laboratory study of chaotic oscillations in deterministic dynamical systems. This work utilizes mathematical modeling and a computer experiment, as well as a direct study of the chaotic behavior of nonlinear electrical circuits

  1. Modeling of Coupled Chaotic Oscillators

    International Nuclear Information System (INIS)

    Lai, Y.; Grebogi, C.

    1999-01-01

    Chaotic dynamics may impose severe limits to deterministic modeling by dynamical equations of natural systems. We give theoretical argument that severe modeling difficulties may occur for high-dimensional chaotic systems in the sense that no model is able to produce reasonably long solutions that are realized by nature. We make these ideas concrete by investigating systems of coupled chaotic oscillators. They arise in many situations of physical and biological interests, and they also arise from discretization of nonlinear partial differential equations. copyright 1999 The American Physical Society

  2. Chaotic solar oscillations

    Energy Technology Data Exchange (ETDEWEB)

    Blacher, S; Perdang, J [Institut d' Astrophysique, B-4200 Cointe-Ougree (Belgium)

    1981-09-01

    A numerical experiment on Hamiltonian oscillations demonstrates the existence of chaotic motions which satisfy the property of phase coherence. It is observed that the low-frequency end of the power spectrum of such motions is remarkably similar in structure to the low-frequency SCLERA spectra. Since the smallness of the observed solar amplitudes is not a sufficient mathematical ground for inefficiency of non-linear effects the possibility of chaos among solar oscillations cannot be discarded a priori.

  3. Chaotic spectroscopy

    International Nuclear Information System (INIS)

    Doron, E.; Smilanski, U.

    1991-11-01

    We discuss the spectra of quantized chaotic billiards from the point of view of scattering theory. We show that the spectral and resonance density functions both fluctuate about a common mean. A semiclassical treatment explains this in terms of classical scattering trajectories and periodic orbits of the poincare scattering map. This formalism is used to interpret recent experiments where the spectra of chaotic cavities where measured by microwave scattering. (author)

  4. Lectures on chaotic dynamical systems

    CERN Document Server

    Afraimovich, Valentin

    2002-01-01

    This book is devoted to chaotic nonlinear dynamics. It presents a consistent, up-to-date introduction to the field of strange attractors, hyperbolic repellers, and nonlocal bifurcations. The authors keep the highest possible level of "physical" intuition while staying mathematically rigorous. In addition, they explain a variety of important nonstandard algorithms and problems involving the computation of chaotic dynamics. The book will help readers who are not familiar with nonlinear dynamics to understand and appreciate sophisticated modern dynamical systems and chaos. Intended for courses in either mathematics, physics, or engineering, prerequisites are calculus, differential equations, and functional analysis.

  5. Reconfigurable chaotic logic gates based on novel chaotic circuit

    International Nuclear Information System (INIS)

    Behnia, S.; Pazhotan, Z.; Ezzati, N.; Akhshani, A.

    2014-01-01

    Highlights: • A novel method for implementing logic gates based on chaotic maps is introduced. • The logic gates can be implemented without any changes in the threshold voltage. • The chaos-based logic gates may serve as basic components of future computing devices. - Abstract: The logical operations are one of the key issues in today’s computer architecture. Nowadays, there is a great interest in developing alternative ways to get the logic operations by chaos computing. In this paper, a novel implementation method of reconfigurable logic gates based on one-parameter families of chaotic maps is introduced. The special behavior of these chaotic maps can be utilized to provide same threshold voltage for all logic gates. However, there is a wide interval for choosing a control parameter for all reconfigurable logic gates. Furthermore, an experimental implementation of this nonlinear system is presented to demonstrate the robustness of computing capability of chaotic circuits

  6. Dynamics and control of the GyroPTO wave energy point absorber under sea waves

    DEFF Research Database (Denmark)

    Zhang, Zili; Nielsen, Søren R.K.; Basu, Biswajit

    2017-01-01

    The Gyroscopic Power Take-Off (GyroPTO) wave energy point absorber has the operational principle somewhat similar to the so-called gyroscopic hand wrist exerciser. Inside the float of GyroPTO, there is a mechanical system made up of a spinning flywheel with its spin axis in rolling contact...... to a ring. At certain conditions, the ring starts to rotate at a frequency equal to the excitation angular frequency. In this synchronized state, the generator is running at almost constant speed and the generated power becomes constant. In this paper, theoretical modeling of the GyroPTO device is carried...... out based on analytical rigid body dynamics, and a 3-DOF nonlinear model is established. Simulation results show that synchronization of the device is maintained under harmonic sea wave, but is lost easily under non-harmonic sea waves.To overcome this problem, a magnetic coupling mechanism is added...

  7. Repetitive learning control of continuous chaotic systems

    International Nuclear Information System (INIS)

    Chen Maoyin; Shang Yun; Zhou Donghua

    2004-01-01

    Combining a shift method and the repetitive learning strategy, a repetitive learning controller is proposed to stabilize unstable periodic orbits (UPOs) within chaotic attractors in the sense of least mean square. If nonlinear parts in chaotic systems satisfy Lipschitz condition, the proposed controller can be simplified into a simple proportional repetitive learning controller

  8. Coexisting chaotic attractors in a single neuron model with adapting feedback synapse

    International Nuclear Information System (INIS)

    Li Chunguang; Chen Guanrong

    2005-01-01

    In this paper, we consider the nonlinear dynamical behavior of a single neuron model with adapting feedback synapse, and show that chaotic behaviors exist in this model. In some parameter domain, we observe two coexisting chaotic attractors, switching from the coexisting chaotic attractors to a connected chaotic attractor, and then switching back to the two coexisting chaotic attractors. We confirm the chaoticity by simulations with phase plots, waveform plots, and power spectra

  9. Design of secure digital communication systems using chaotic modulation, cryptography and chaotic synchronization

    International Nuclear Information System (INIS)

    Chien, T.-I.; Liao, T.-L.

    2005-01-01

    This paper presents a secure digital communication system based on chaotic modulation, cryptography, and chaotic synchronization techniques. The proposed system consists of a Chaotic Modulator (CM), a Chaotic Secure Transmitter (CST), a Chaotic Secure Receiver (CSR) and a Chaotic Demodulator (CDM). The CM module incorporates a chaotic system and a novel Chaotic Differential Peaks Keying (CDPK) modulation scheme to generate analog patterns corresponding to the input digital bits. The CST and CSR modules are designed such that a single scalar signal is transmitted in the public channel. Furthermore, by giving certain structural conditions of a particular class of chaotic system, the CST and the nonlinear observer-based CSR with an appropriate observer gain are constructed to synchronize with each other. These two slave systems are driven simultaneously by the transmitted signal and are designed to synchronize and generate appropriate cryptography keys for encryption and decryption purposes. In the CDM module, a nonlinear observer is designed to estimate the chaotic modulating system in the CM. A demodulation mechanism is then applied to decode the transmitted input digital bits. The effectiveness of the proposed scheme is demonstrated through the numerical simulation of an illustrative communication system. Synchronization between the chaotic circuits of the transmitter and receiver modules is guaranteed through the Lyapunov stability theorem. Finally, the security features of the proposed system in the event of attack by an intruder in either the time domain or the frequency domain are discussed

  10. Bidirectional communication using delay coupled chaotic directly ...

    Indian Academy of Sciences (India)

    Corresponding author. ... 30 September 2009. Abstract. Chaotic synchronization of two directly modulated semiconductor lasers with ... For InGaAsP lasers used in optical communication systems, the nonlinear gain re- duction is very strong and its ...

  11. Bifurcation Control of Chaotic Dynamical Systems

    National Research Council Canada - National Science Library

    Wang, Hua O; Abed, Eyad H

    1992-01-01

    A nonlinear system which exhibits bifurcations, transient chaos, and fully developed chaos is considered, with the goal of illustrating the role of two ideas in the control of chaotic dynamical systems...

  12. Design of Threshold Controller Based Chaotic Circuits

    DEFF Research Database (Denmark)

    Mohamed, I. Raja; Murali, K.; Sinha, Sudeshna

    2010-01-01

    We propose a very simple implementation of a second-order nonautonomous chaotic oscillator, using a threshold controller as the only source of nonlinearity. We demonstrate the efficacy and simplicity of our design through numerical and experimental results. Further, we show that this approach...... of using a threshold controller as a nonlinear element, can be extended to obtain autonomous and multiscroll chaotic attractor circuits as well....

  13. Aging in a Chaotic System

    OpenAIRE

    Barkai, E.

    2002-01-01

    We demonstrate aging behavior in a simple non-linear system. Our model is a chaotic map which generates deterministically sub-diffusion. Asymptotic behaviors of the diffusion process are described using aging continuous time random walks, introduced previously to model diffusion in glasses.

  14. Autonomous estimation of Allan variance coefficients of onboard fiber optic gyro

    International Nuclear Information System (INIS)

    Song Ningfang; Yuan Rui; Jin Jing

    2011-01-01

    Satellite motion included in gyro output disturbs the estimation of Allan variance coefficients of fiber optic gyro on board. Moreover, as a standard method for noise analysis of fiber optic gyro, Allan variance has too large offline computational effort and data storages to be applied to online estimation. In addition, with the development of deep space exploration, it is urged that satellite requires more autonomy including autonomous fault diagnosis and reconfiguration. To overcome the barriers and meet satellite autonomy, we present a new autonomous method for estimation of Allan variance coefficients including rate ramp, rate random walk, bias instability, angular random walk and quantization noise coefficients. In the method, we calculate differences between angle increments of star sensor and gyro to remove satellite motion from gyro output, and propose a state-space model using nonlinear adaptive filter technique for quantities previously measured from offline data techniques such as the Allan variance method. Simulations show the method correctly estimates Allan variance coefficients, R = 2.7965exp-4 0 /h 2 , K = 1.1714exp-3 0 /h 1.5 , B = 1.3185exp-3 0 /h, N = 5.982exp-4 0 /h 0.5 and Q = 5.197exp-7 0 in real time, and tracks degradation of gyro performance from initail values, R = 0.651 0 /h 2 , K = 0.801 0 /h 1.5 , B = 0.385 0 /h, N = 0.0874 0 /h 0.5 and Q = 8.085exp-5 0 , to final estimations, R = 9.548 0 /h 2 , K = 9.524 0 /h 1.5 , B = 2.234 0 /h, N = 0.5594 0 /h 0.5 and Q = 5.113exp-4 0 , due to gamma radiation in space. The technique proposed here effectively isolates satellite motion, and requires no data storage and any supports from the ground.

  15. Predicting chaotic time series

    International Nuclear Information System (INIS)

    Farmer, J.D.; Sidorowich, J.J.

    1987-01-01

    We present a forecasting technique for chaotic data. After embedding a time series in a state space using delay coordinates, we ''learn'' the induced nonlinear mapping using local approximation. This allows us to make short-term predictions of the future behavior of a time series, using information based only on past values. We present an error estimate for this technique, and demonstrate its effectiveness by applying it to several examples, including data from the Mackey-Glass delay differential equation, Rayleigh-Benard convection, and Taylor-Couette flow

  16. Autonomous third-order duffing-holmes type chaotic oscillator

    DEFF Research Database (Denmark)

    Lindberg, Erik; Tamaseviciute, E; Mykolaitis, G

    2009-01-01

    feedback loop. In contrast to many other autonomous chaotic oscillators, including linear unstable resonators and nonlinear damping loops, the novel circuit is based on nonlinear resonator and linear damping loop in the negative feedback. SPICE simulation and hardware experimental investigations...

  17. Chaotic structure of oil prices

    Science.gov (United States)

    Bildirici, Melike; Sonustun, Fulya Ozaksoy

    2018-01-01

    The fluctuations in oil prices are very complicated and therefore, it is unable to predict its effects on economies. For modelling complex system of oil prices, linear economic models are not sufficient and efficient tools. Thus, in recent years, economists attached great attention to non-linear structure of oil prices. For analyzing this relationship, GARCH types of models were used in some papers. Distinctively from the other papers, in this study, we aimed to analyze chaotic pattern of oil prices. Thus, it was used the Lyapunov Exponents and Hennon Map to determine chaotic behavior of oil prices for the selected time period.

  18. Statistical properties of the gyro-averaged standard map

    Science.gov (United States)

    da Fonseca, Julio D.; Sokolov, Igor M.; Del-Castillo-Negrete, Diego; Caldas, Ibere L.

    2015-11-01

    A statistical study of the gyro-averaged standard map (GSM) is presented. The GSM is an area preserving map model proposed in as a simplified description of finite Larmor radius (FLR) effects on ExB chaotic transport in magnetized plasmas with zonal flows perturbed by drift waves. The GSM's effective perturbation parameter, gamma, is proportional to the zero-order Bessel function of the particle's Larmor radius. In the limit of zero Larmor radius, the GSM reduces to the standard, Chirikov-Taylor map. We consider plasmas in thermal equilibrium and assume a Larmor radius' probability density function (pdf) resulting from a Maxwell-Boltzmann distribution. Since the particles have in general different Larmor radii, each orbit is computed using a different perturbation parameter, gamma. We present analytical and numerical computations of the pdf of gamma for a Maxwellian distribution. We also compute the pdf of global chaos, which gives the probability that a particle with a given Larmor radius exhibits global chaos, i.e. the probability that Kolmogorov-Arnold-Moser (KAM) transport barriers do not exist.

  19. Failure of GIMBAL bearing in directional GYRO

    International Nuclear Information System (INIS)

    Pervaiz, R.; Baig, N.A.; Shahid, M.; Ahmad, A.; Chohan, G.Y.

    2003-01-01

    This paper relates to the directional gyro of a sensing device used in indigenously developed surface-to-surface missile. The assembling of more than one thousand components in the form of several sub assemblies including hundreds of silver solders of this device was done in the hundred-thousands-class clean room according to assembly procedure. Whereas more than twenty bearings including gimbals bearings were assembled in the ten-thousands-class clean room after inspection/ testing them on beating testing system as per routine. The device was entered in testing and adjustment phase after successful completion of assembly work. The directional gyro qualified all the tests except the most critical one, the drift-rate. The drift-rate of outer gimbal was 60% more than permissible limit whereas drift-rate of inner gimbal was found O.K. It was diagnosed that at least one inner gimbal bearing out of two had some problem. The results were same after rebalancing of gimbals three times. The directional gyro was disassembled in clean room and the radial-thrust-bearing was recovered and flange bearing which are inner gimbal bearings. They were checked on bearing testing system and it was found that flange-bearing had more friction than permissible limit and hence rejected but radial thrust bearing were declared O.K. The gyro was reassembled with new O.K. flange bearing and the assembly work was completed in all respects. The sensing device qualified all the tests including the drift-rate. This case study is being presented to emphasize the importance of careful assembly of gyro in clean environment. (author)

  20. Design studies of the Ku-band, wide-band Gyro-TWT amplifier

    Science.gov (United States)

    Jung, Sang Wook; Lee, Han Seul; Jang, Kwong Ho; Choi, Jin Joo; Hong, Yong Jun; Shin, Jin Woo; So, Jun Ho; Won, Jong Hyo

    2014-02-01

    This paper reports a Ku-band, wide band Gyrotron-Traveling-wave-tube(Gyro-TWT) that is currently being developed at Kwangwoon University. The Gyro-TWT has a two stage linear tapered interaction circuit to obtain a wide operating bandwidth. The linearly-tapered interaction circuit and nonlinearly-tapered magnetic field gives the Gyro-TWT a wide operating bandwidth. The Gyro-TWT bandwidth is 23%. The 2d-Particle-in-cell(PIC) and MAGIC2d code simulation results are 17.3 dB and 24.34 kW, respectively for the maximum saturated output power. A double anode MIG was simulated with E-Gun code. The results were 0.7 for the transvers to the axial beam velocity ratio (=alpha) and a 2.3% axial velocity spread at 50 kV and 4 A. A magnetic field profile simulation was performed by using the Poisson code to obtain the grazing magnetic field of the entire interaction circuit with Poisson code.

  1. Chaotic dynamics of respiratory sounds

    International Nuclear Information System (INIS)

    Ahlstrom, C.; Johansson, A.; Hult, P.; Ask, P.

    2006-01-01

    There is a growing interest in nonlinear analysis of respiratory sounds (RS), but little has been done to justify the use of nonlinear tools on such data. The aim of this paper is to investigate the stationarity, linearity and chaotic dynamics of recorded RS. Two independent data sets from 8 + 8 healthy subjects were recorded and investigated. The first set consisted of lung sounds (LS) recorded with an electronic stethoscope and the other of tracheal sounds (TS) recorded with a contact accelerometer. Recurrence plot analysis revealed that both LS and TS are quasistationary, with the parts corresponding to inspiratory and expiratory flow plateaus being stationary. Surrogate data tests could not provide statistically sufficient evidence regarding the nonlinearity of the data. The null hypothesis could not be rejected in 4 out of 32 LS cases and in 15 out of 32 TS cases. However, the Lyapunov spectra, the correlation dimension (D 2 ) and the Kaplan-Yorke dimension (D KY ) all indicate chaotic behavior. The Lyapunov analysis showed that the sum of the exponents was negative in all cases and that the largest exponent was found to be positive. The results are partly ambiguous, but provide some evidence of chaotic dynamics of RS, both concerning LS and TS. The results motivate continuous use of nonlinear tools for analysing RS data

  2. Chaotic dynamics of respiratory sounds

    Energy Technology Data Exchange (ETDEWEB)

    Ahlstrom, C. [Department of Biomedical Engineering, Linkoepings Universitet, IMT/LIU, Universitetssjukhuset, S-58185 Linkoeping (Sweden) and Biomedical Engineering, Orebro University Hospital, S-70185 Orebro (Sweden)]. E-mail: christer@imt.liu.se; Johansson, A. [Department of Biomedical Engineering, Linkoepings Universitet, IMT/LIU, Universitetssjukhuset, S-58185 Linkoeping (Sweden); Hult, P. [Department of Biomedical Engineering, Linkoepings Universitet, IMT/LIU, Universitetssjukhuset, S-58185 Linkoeping (Sweden); Biomedical Engineering, Orebro University Hospital, S-70185 Orebro (Sweden); Ask, P. [Department of Biomedical Engineering, Linkoepings Universitet, IMT/LIU, Universitetssjukhuset, S-58185 Linkoeping (Sweden); Biomedical Engineering, Orebro University Hospital, S-70185 Orebro (Sweden)

    2006-09-15

    There is a growing interest in nonlinear analysis of respiratory sounds (RS), but little has been done to justify the use of nonlinear tools on such data. The aim of this paper is to investigate the stationarity, linearity and chaotic dynamics of recorded RS. Two independent data sets from 8 + 8 healthy subjects were recorded and investigated. The first set consisted of lung sounds (LS) recorded with an electronic stethoscope and the other of tracheal sounds (TS) recorded with a contact accelerometer. Recurrence plot analysis revealed that both LS and TS are quasistationary, with the parts corresponding to inspiratory and expiratory flow plateaus being stationary. Surrogate data tests could not provide statistically sufficient evidence regarding the nonlinearity of the data. The null hypothesis could not be rejected in 4 out of 32 LS cases and in 15 out of 32 TS cases. However, the Lyapunov spectra, the correlation dimension (D {sub 2}) and the Kaplan-Yorke dimension (D {sub KY}) all indicate chaotic behavior. The Lyapunov analysis showed that the sum of the exponents was negative in all cases and that the largest exponent was found to be positive. The results are partly ambiguous, but provide some evidence of chaotic dynamics of RS, both concerning LS and TS. The results motivate continuous use of nonlinear tools for analysing RS data.

  3. Chaotic universe model.

    Science.gov (United States)

    Aydiner, Ekrem

    2018-01-15

    In this study, we consider nonlinear interactions between components such as dark energy, dark matter, matter and radiation in the framework of the Friedman-Robertson-Walker space-time and propose a simple interaction model based on the time evolution of the densities of these components. By using this model we show that these interactions can be given by Lotka-Volterra type equations. We numerically solve these coupling equations and show that interaction dynamics between dark energy-dark matter-matter or dark energy-dark matter-matter-radiation has a strange attractor for 0 > w de  >-1, w dm  ≥ 0, w m  ≥ 0 and w r  ≥ 0 values. These strange attractors with the positive Lyapunov exponent clearly show that chaotic dynamics appears in the time evolution of the densities. These results provide that the time evolution of the universe is chaotic. The present model may have potential to solve some of the cosmological problems such as the singularity, cosmic coincidence, big crunch, big rip, horizon, oscillation, the emergence of the galaxies, matter distribution and large-scale organization of the universe. The model also connects between dynamics of the competing species in biological systems and dynamics of the time evolution of the universe and offers a new perspective and a new different scenario for the universe evolution.

  4. Empirically characteristic analysis of chaotic PID controlling particle swarm optimization.

    Science.gov (United States)

    Yan, Danping; Lu, Yongzhong; Zhou, Min; Chen, Shiping; Levy, David

    2017-01-01

    Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic community and industry society throughout the world. To improve the performance of particle swarm optimization (PSO), we herein propose a chaotic proportional integral derivative (PID) controlling PSO algorithm by the hybridization of chaotic logistic dynamics and hierarchical inertia weight. The hierarchical inertia weight coefficients are determined in accordance with the present fitness values of the local best positions so as to adaptively expand the particles' search space. Moreover, the chaotic logistic map is not only used in the substitution of the two random parameters affecting the convergence behavior, but also used in the chaotic local search for the global best position so as to easily avoid the particles' premature behaviors via the whole search space. Thereafter, the convergent analysis of chaotic PID controlling PSO is under deep investigation. Empirical simulation results demonstrate that compared with other several chaotic PSO algorithms like chaotic PSO with the logistic map, chaotic PSO with the tent map and chaotic catfish PSO with the logistic map, chaotic PID controlling PSO exhibits much better search efficiency and quality when solving the optimization problems. Additionally, the parameter estimation of a nonlinear dynamic system also further clarifies its superiority to chaotic catfish PSO, genetic algorithm (GA) and PSO.

  5. Anti-synchronization between different chaotic complex systems

    International Nuclear Information System (INIS)

    Liu Ping; Liu Shutang

    2011-01-01

    Many studies on the anti-synchronization of nonlinear real dynamic systems have been carried out, whereas the anti-synchronization of chaotic complex systems has not been studied extensively. In this work, the anti-synchronization between a new chaotic complex system and a complex Lorenz system and that between a new chaotic complex system and a complex Lue system were separately investigated by active control and nonlinear control methods, and explicit expressions were derived for the controllers that are used to achieve the anti-synchronization of chaotic complex systems. These expressions were tested numerically and excellent agreement was found. Concerning the new chaotic complex system, we discuss its dynamical properties including dissipation, chaotic behavior, fixed points, and their stability and invariance.

  6. Chaotic Patterns in Aeroelastic Signals

    Directory of Open Access Journals (Sweden)

    F. D. Marques

    2009-01-01

    patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincaré mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.

  7. 280 GHz Gyro-BWO design study: Final report

    International Nuclear Information System (INIS)

    1988-07-01

    This report summarizes the results of a design study of a 280 GHz Gyro-BWO tunable source. The purpose of this study is to identify and propose viable design alternatives for any significant technological risk associated with building an operational BWO system. The tunable Gyro-BWO system will have three major components: a Gyro-BWO microwave tube, a superconducting magnet, and a power supply/modulator. The design tasks for this study in order of decreasing importance are: design and specification of the superconducting magnet; preliminary design and layout of a Gyro-BWO microwave tube; and specification for the power supply/modulator. 2 refs., 4 figs

  8. On analytical justification of phase synchronization in different chaotic systems

    International Nuclear Information System (INIS)

    Erjaee, G.H.

    2009-01-01

    In analytical or numerical synchronizations studies of coupled chaotic systems the phase synchronizations have less considered in the leading literatures. This article is an attempt to find a sufficient analytical condition for stability of phase synchronization in some coupled chaotic systems. The method of nonlinear feedback function and the scheme of matrix measure have been used to justify this analytical stability, and tested numerically for the existence of the phase synchronization in some coupled chaotic systems.

  9. Searching of Chaotic Elements in Hydrology

    Directory of Open Access Journals (Sweden)

    Sorin VLAD

    2014-03-01

    Full Text Available Chaos theory offers new means of understanding and prediction of phenomena otherwise considered random and unpredictable. The signatures of chaos can be isolated by performing nonlinear analysis of the time series available. The paper presents the results obtained by conducting a nonlinear analysis of the time series of daily Siret river flow (located in the North-Eastern part of Romania. The time series analysis is recorded starting with January 1999 to July 2009. The attractor is embedded in the reconstructed phase space then the chaotic dynamics is revealed computing the chaotic invariants - correlation dimension and the maximum Lyapunov Exponent.

  10. A new chaotic cryptosystem

    International Nuclear Information System (INIS)

    Wei Jun; Liao Xiaofeng; Wong, Kwok-wo; Xiang Tao

    2006-01-01

    Based on the study of some previously proposed chaotic encryption algorithms, we found that it is dangerous to mix chaotic state or iteration number of the chaotic system with ciphertext. In this paper, a new chaotic cryptosystem is proposed. Instead of simply mixing the chaotic signal of the proposed chaotic cryptosystem with the ciphertext, a noise-like variable is utilized to govern the encryption and decryption processes. This adds statistical sense to the new cryptosystem. Numerical simulations show that the new cryptosystem is practical whenever efficiency, ciphertext length or security is concerned

  11. Implementation of chaotic secure communication systems based on OPA circuits

    International Nuclear Information System (INIS)

    Huang, C.-K.; Tsay, S.-C.; Wu, Y.-R.

    2005-01-01

    In this paper, we proposed a novel three-order autonomous circuit to construct a chaotic circuit with double scroll characteristic. The design idea is to use RLC elements and a nonlinear resistor. The one of salient features of the chaotic circuit is that the circuit with two flexible breakpoints of nonlinear element, and the advantage of the flexible breakpoint is that it increased complexity of the dynamical performance. Here, if we take a large and suitable breakpoint value, then the chaotic state can masking a large input signal in the circuit. Furthermore, we proposed a secure communication hyperchaotic system based on the proposed chaotic circuits, where the chaotic communication system is constituted by a chaotic transmitter and a chaotic receiver. To achieve the synchronization between the transmitter and the receiver, we are using a suitable Lyapunov function and Lyapunov theorem to design the feedback control gain. Thus, the transmitting message masked by chaotic state in the transmitter can be guaranteed to perfectly recover in the receiver. To achieve the systems performance, some basic components containing OPA, resistor and capacitor elements are used to implement the proposed communication scheme. From the viewpoints of circuit implementation, this proposed chaotic circuit is superior to the Chua chaotic circuits. Finally, the test results containing simulation and the circuit measurement are shown to demonstrate that the proposed method is correct and feasible

  12. Detection of chaotic dynamics in human gait signals from mobile devices

    Science.gov (United States)

    DelMarco, Stephen; Deng, Yunbin

    2017-05-01

    The ubiquity of mobile devices offers the opportunity to exploit device-generated signal data for biometric identification, health monitoring, and activity recognition. In particular, mobile devices contain an Inertial Measurement Unit (IMU) that produces acceleration and rotational rate information from the IMU accelerometers and gyros. These signals reflect motion properties of the human carrier. It is well-known that the complexity of bio-dynamical systems gives rise to chaotic dynamics. Knowledge of chaotic properties of these systems has shown utility, for example, in detecting abnormal medical conditions and neurological disorders. Chaotic dynamics has been found, in the lab, in bio-dynamical systems data such as electrocardiogram (heart), electroencephalogram (brain), and gait data. In this paper, we investigate the following question: can we detect chaotic dynamics in human gait as measured by IMU acceleration and gyro data from mobile phones? To detect chaotic dynamics, we perform recurrence analysis on real gyro and accelerometer signal data obtained from mobile devices. We apply the delay coordinate embedding approach from Takens' theorem to reconstruct the phase space trajectory of the multi-dimensional gait dynamical system. We use mutual information properties of the signal to estimate the appropriate delay value, and the false nearest neighbor approach to determine the phase space embedding dimension. We use a correlation dimension-based approach together with estimation of the largest Lyapunov exponent to make the chaotic dynamics detection decision. We investigate the ability to detect chaotic dynamics for the different one-dimensional IMU signals, across human subject and walking modes, and as a function of different phone locations on the human carrier.

  13. Alternative implementation of the chaotic Chen-Lee system

    International Nuclear Information System (INIS)

    Sheu, L.-J.; Tam, L.-M.; Chen, H.-K.; Lao, S.-K.

    2009-01-01

    The chaotic Chen-Lee system was developed with a formalism based on the Euler equations for the motion of a rigid body. It was proved that this system is the governing set of equations for gyro motion with feedback control. Recently, studies were conducted to explore the dynamic behavior of this system, including fractional order behavior, the generation of hyperchaos and perturbation analysis, control and anti-control of chaos, synchronization, etc. In this study, we further explore (1) the stability of the equilibrium points and (2) the implementation of an electronic circuit using the Chen-Lee system. It is shown that not only is this system related to gyro motion but can also be applied to electronic circuits for encryption purposes.

  14. Modelling chaotic Hamiltonian systems as a Markov Chain ...

    African Journals Online (AJOL)

    The behaviour of chaotic Hamiltonian system has been characterised qualitatively in recent times by its appearance on the Poincaré section and quantitatively by the Lyapunov exponent. Studying the dynamics of the two chaotic Hamiltonian systems: the Henon-Heiles system and non-linearly coupled oscillators as their ...

  15. Chaotic neoclassical separatrix dissipation in parametric drift-wave decay.

    Science.gov (United States)

    Kabantsev, A A; Tsidulko, Yu A; Driscoll, C F

    2014-02-07

    Experiments and theory characterize a parametric decay instability between plasma drift waves when the nonlinear coupling is modified by an electrostatic barrier. Novel mode coupling terms representing enhanced dissipation and mode phase shifts are caused by chaotic separatrix crossings on the wave-ruffled separatrix. Experimental determination of these coupling terms is in broad agreement with new chaotic neoclassical transport analyses.

  16. Transition to a pair of chaotic symmetric flows

    International Nuclear Information System (INIS)

    Chen Zhimin; Price, W.G.

    2006-01-01

    The complexity of transition to chaotic flow is discussed. It is shown that many different bifurcation processes may coexist and join together to excite the chaotic flow. The profile of this nonlinear dynamical behaviour is developed on the basis of a four-mode truncation model

  17. Chaos synchronization between two different chaotic dynamical systems

    International Nuclear Information System (INIS)

    Park, Ju H.

    2006-01-01

    This work presents chaos synchronization between two different chaotic systems by nonlinear control laws. First, synchronization problem between Genesio system and Rossler system has been investigated, and then the similar approach is applied to the synchronization problem between Genesio system and a new chaotic system developed recently in the literature. The control performances are verified by two numerical examples

  18. Indirect adaptive control of discrete chaotic systems

    International Nuclear Information System (INIS)

    Salarieh, Hassan; Shahrokhi, Mohammad

    2007-01-01

    In this paper an indirect adaptive control algorithm is proposed to stabilize the fixed points of discrete chaotic systems. It is assumed that the functionality of the chaotic dynamics is known but the system parameters are unknown. This assumption is usually applicable to many chaotic systems, such as the Henon map, logistic and many other nonlinear maps. Using the recursive-least squares technique, the system parameters are identified and based on the feedback linearization method an adaptive controller is designed for stabilizing the fixed points, or unstable periodic orbits of the chaotic maps. The stability of the proposed scheme has been shown and the effectiveness of the control algorithm has been demonstrated through computer simulations

  19. Autonomous estimation of Allan variance coefficients of onboard fiber optic gyro

    Energy Technology Data Exchange (ETDEWEB)

    Song Ningfang; Yuan Rui; Jin Jing, E-mail: rayleing@139.com [School of Instrumentation Science and Opto-electronics Engineering, Beihang University, Beijing 100191 (China)

    2011-09-15

    Satellite motion included in gyro output disturbs the estimation of Allan variance coefficients of fiber optic gyro on board. Moreover, as a standard method for noise analysis of fiber optic gyro, Allan variance has too large offline computational effort and data storages to be applied to online estimation. In addition, with the development of deep space exploration, it is urged that satellite requires more autonomy including autonomous fault diagnosis and reconfiguration. To overcome the barriers and meet satellite autonomy, we present a new autonomous method for estimation of Allan variance coefficients including rate ramp, rate random walk, bias instability, angular random walk and quantization noise coefficients. In the method, we calculate differences between angle increments of star sensor and gyro to remove satellite motion from gyro output, and propose a state-space model using nonlinear adaptive filter technique for quantities previously measured from offline data techniques such as the Allan variance method. Simulations show the method correctly estimates Allan variance coefficients, R = 2.7965exp-4 {sup 0}/h{sup 2}, K = 1.1714exp-3 {sup 0}/h{sup 1.5}, B = 1.3185exp-3 {sup 0}/h, N = 5.982exp-4 {sup 0}/h{sup 0.5} and Q = 5.197exp-7 {sup 0} in real time, and tracks degradation of gyro performance from initail values, R = 0.651 {sup 0}/h{sup 2}, K = 0.801 {sup 0}/h{sup 1.5}, B = 0.385 {sup 0}/h, N = 0.0874 {sup 0}/h{sup 0.5} and Q = 8.085exp-5 {sup 0}, to final estimations, R = 9.548 {sup 0}/h{sup 2}, K = 9.524 {sup 0}/h{sup 1.5}, B = 2.234 {sup 0}/h, N = 0.5594 {sup 0}/h{sup 0.5} and Q = 5.113exp-4 {sup 0}, due to gamma radiation in space. The technique proposed here effectively isolates satellite motion, and requires no data storage and any supports from the ground.

  20. Dither Gyro Scale Factor Calibration: GOES-16 Flight Experience

    Science.gov (United States)

    Reth, Alan D.; Freesland, Douglas C.; Krimchansky, Alexander

    2018-01-01

    This poster is a sequel to a paper presented at the 34th Annual AAS Guidance and Control Conference in 2011, which first introduced dither-based calibration of gyro scale factors. The dither approach uses very small excitations, avoiding the need to take instruments offline during gyro scale factor calibration. In 2017, the dither calibration technique was successfully used to estimate gyro scale factors on the GOES-16 satellite. On-orbit dither calibration results were compared to more traditional methods using large angle spacecraft slews about each gyro axis, requiring interruption of science. The results demonstrate that the dither technique can estimate gyro scale factors to better than 2000 ppm during normal science observations.

  1. The chaotic environment

    International Nuclear Information System (INIS)

    Cook, A.

    1990-09-01

    An elementary account of the origin of chaotic behaviour in classical dynamics is given with examples from geophysics, and in conclusion some thoughts about what can be predicted of chaotic behaviour and what sorts of arguments can be used to guide human behaviour in chaotic conditions are presented. 4 refs

  2. Chaotic evolution of arms races

    Science.gov (United States)

    Tomochi, Masaki; Kono, Mitsuo

    1998-12-01

    A new set of model equations is proposed to describe the evolution of the arms race, by extending Richardson's model with special emphases that (1) power dependent defensive reaction or historical enmity could be a motive force to promote armaments, (2) a deterrent would suppress the growth of armaments, and (3) the defense reaction of one nation against the other nation depends nonlinearly on the difference in armaments between two. The set of equations is numerically solved to exhibit stationary, periodic, and chaotic behavior depending on the combinations of parameters involved. The chaotic evolution is realized when the economic situation of each country involved in the arms race is quite different, which is often observed in the real world.

  3. Comportamiento no lineal y caótico en una bomba centrífuga operando en estado de cavitación//Nonlinear and chaotic behavior in a centrifugal pump operating in state of cavitation

    Directory of Open Access Journals (Sweden)

    Juan E. Álvarez Naranjo

    2015-05-01

    Full Text Available Mejorar la precisión en el diagnóstico y pronóstico del mantenimiento industrial ha sido una tarea de constante investigación debido a la necesidad de preservar el continuo funcionamiento de las máquinas de producción. En el presentetrabajo se estudió la bomba centrífuga en estado de cavitación. Se construyó un banco de pruebas y mediante obstrucción del fluido hacia el rodete del equipo por medio de la válvula de succión, se registraron las señales temporales mediante un acelerómetro. Posteriormente, se empleó un estudio no lineal y caótico para representar la geometría en el espacio de fases y su validación se realizó con el registro de datos de la bomba centrífuga operando sin cavitación y con máxima eficiencia. Los resultados mostraron que la dinámica del sistema actúa de forma no lineal y caótica, representado el fenómeno de cavitación con una geometría característica.Palabras claves: bomba centrífuga, cavitación, caos, dinámica no lineal, espacio de fases, serie temporal.______________________________________________________________________________AbstractImproving accuracy in the diagnosis and prognosis of industrial maintenance has been a constant task of research to preserve the continuous operation of machines. Today is necessary to improve this technique for avoiding reductionism that the traditional linear techniques employ. In this paper it is studied the centrifugal pump cavitation state. To simulate the phenomenon, a test bed is constructed and the fluid is blocked toward the impeller of pump by the suction valve, the time signals were recorded using an accelerometer. Subsequently, a chaotic nonlinear study was used to represent the geometry in the phase space and validation was performed with the data recording operation of the centrifugal pump without cavitation and with maximum efficiency. The results showed that the system dynamics is non-linear and chaotic, and the cavitation is represented

  4. A novel double-convection chaotic attractor, its adaptive control and circuit simulation

    Science.gov (United States)

    Mamat, M.; Vaidyanathan, S.; Sambas, A.; Mujiarto; Sanjaya, W. S. M.; Subiyanto

    2018-03-01

    A 3-D novel double-convection chaotic system with three nonlinearities is proposed in this research work. The dynamical properties of the new chaotic system are described in terms of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, stability analysis of equilibria, etc. Adaptive control and synchronization of the new chaotic system with unknown parameters are achieved via nonlinear controllers and the results are established using Lyapunov stability theory. Furthermore, an electronic circuit realization of the new 3-D novel chaotic system is presented in detail. Finally, the circuit experimental results of the 3-D novel chaotic attractor show agreement with the numerical simulations.

  5. Complex economic dynamics: Chaotic saddle, crisis and intermittency

    International Nuclear Information System (INIS)

    Chian, Abraham C.-L.; Rempel, Erico L.; Rogers, Colin

    2006-01-01

    Complex economic dynamics is studied by a forced oscillator model of business cycles. The technique of numerical modeling is applied to characterize the fundamental properties of complex economic systems which exhibit multiscale and multistability behaviors, as well as coexistence of order and chaos. In particular, we focus on the dynamics and structure of unstable periodic orbits and chaotic saddles within a periodic window of the bifurcation diagram, at the onset of a saddle-node bifurcation and of an attractor merging crisis, and in the chaotic regions associated with type-I intermittency and crisis-induced intermittency, in non-linear economic cycles. Inside a periodic window, chaotic saddles are responsible for the transient motion preceding convergence to a periodic or a chaotic attractor. The links between chaotic saddles, crisis and intermittency in complex economic dynamics are discussed. We show that a chaotic attractor is composed of chaotic saddles and unstable periodic orbits located in the gap regions of chaotic saddles. Non-linear modeling of economic chaotic saddle, crisis and intermittency can improve our understanding of the dynamics of financial intermittency observed in stock market and foreign exchange market. Characterization of the complex dynamics of economic systems is a powerful tool for pattern recognition and forecasting of business and financial cycles, as well as for optimization of management strategy and decision technology

  6. Gyro-fluid and two-fluid theory and simulations of edge-localized-modes

    Energy Technology Data Exchange (ETDEWEB)

    Xu, X. Q.; Dimits, A.; Joseph, I.; Umansky, M. V. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States); Xi, P. W. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States); School of Physics, Peking University, Beijing (China); Xia, T. Y.; Gui, B. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States); Institute of Plasma Physics, Chinese Academy of Sciences, Hefei (China); Kim, S. S.; Park, G. Y.; Rhee, T.; Jhang, H. [WCI Center for Fusion Theory, National Fusion Research Institute, Daejon 305-333 (Korea, Republic of); Diamond, P. H. [WCI Center for Fusion Theory, National Fusion Research Institute, Daejon 305-333 (Korea, Republic of); Center for Astrophysics and Space Sciences and Department of Physics, University of California, San Diego, La Jolla, California 92093-0424 (United States); Dudson, B. [University of York, Heslington, York YO10 5DD (United Kingdom); Snyder, P. B. [General Atomics, San Diego, California 92186 (United States)

    2013-05-15

    This paper reports on the theoretical and simulation results of a gyro-Landau-fluid extension of the BOUT++ code, which contributes to increasing the physics understanding of edge-localized-modes (ELMs). Large ELMs with low-to-intermediate-n peeling-ballooning (P-B) modes are significantly suppressed due to finite Larmor radius (FLR) effects when the ion temperature increases. For type-I ELMs, it is found from linear simulations that retaining complete first order FLR corrections as resulting from the incomplete “gyroviscous cancellation” in Braginskii's two-fluid model is necessary to obtain good agreement with gyro-fluid results for high ion temperature cases (T{sub i}≽3 keV) when the ion density has a strong radial variation, which goes beyond the simple local model of ion diamagnetic stabilization of ideal ballooning modes. The maximum growth rate is inversely proportional to T{sub i} because the FLR effect is proportional to T{sub i}. The FLR effect is also proportional to toroidal mode number n, so for high n cases, the P-B mode is stabilized by FLR effects. Nonlinear gyro-fluid simulations show results that are similar to those from the two-fluid model, namely that the P-B modes trigger magnetic reconnection, which drives the collapse of the pedestal pressure. Due to the additional FLR-corrected nonlinear E × B convection of the ion gyro-center density, for a ballooning-dominated equilibrium the gyro-fluid model further limits the radial spreading of ELMs. In six-field two fluid simulations, the parallel thermal diffusivity is found to prevent the ELM encroachment further into core plasmas and therefore leads to steady state L-mode profiles. The simulation results show that most energy is lost via ion channel during an ELM event, followed by particle loss and electron energy loss. Because edge plasmas have significant spatial inhomogeneities and complicated boundary conditions, we have developed a fast non-Fourier method for the computation of

  7. Verification of GENE and GYRO with L-mode and I-mode plasmas in Alcator C-Mod

    Science.gov (United States)

    Mikkelsen, D. R.; Howard, N. T.; White, A. E.; Creely, A. J.

    2018-04-01

    Verification comparisons are carried out for L-mode and I-mode plasma conditions in Alcator C-Mod. We compare linear and nonlinear ion-scale calculations by the gyrokinetic codes GENE and GYRO to each other and to the experimental power balance analysis. The two gyrokinetic codes' linear growth rates and real frequencies are in good agreement throughout all the ion temperature gradient mode branches and most of the trapped electron mode branches of the kyρs spectra at r/a = 0.65, 0.7, and 0.8. The shapes of the toroidal mode spectra of heat fluxes in nonlinear simulations are very similar for kyρs ≤ 0.5, but in most cases GENE has a relatively higher heat flux than GYRO at higher mode numbers. The ratio of ion to electron heat flux is similar in the two codes' simulations, but the heat fluxes themselves do not agree in almost all cases. In the I-mode regime, GENE's heat fluxes are ˜3 times those from GYRO, and they are ˜60%-100% higher than GYRO in the L-mode conditions. The GYRO under-prediction of Qe is much reduced in GENE's L-mode simulations, and it is eliminated in the I-mode simulations. This largely improved agreement with the experimental electron heat flux is offset, however, by the large overshoot of GENE's ion heat fluxes, which are 2-3 times the experimental level, and its electron heat flux overshoot at r/a = 0.80 in the I-mode. Rotation effects can explain part of the difference between the two codes' predictions, but very significant differences remain in simulations without any rotation effects.

  8. Method to restore images from chaotic frequency-down-converted light using phase matching

    International Nuclear Information System (INIS)

    Andreoni, Alessandra; Puddu, Emiliano; Bondani, Maria

    2006-01-01

    We present an optical frequency-down-conversion process of the image of an object illuminated with chaotic light in which also the low-frequency field entering the second-order nonlinear crystal is chaotic. We show that the fulfillment of the phase-matching conditions by the chaotic interacting fields provides the rules to retrieve the object image by calculating suitable correlations of the local intensity fluctuations even if a single record of down-converted chaotic image is available

  9. Quantum Statistical Operator and Classically Chaotic Hamiltonian ...

    African Journals Online (AJOL)

    Quantum Statistical Operator and Classically Chaotic Hamiltonian System. ... Journal of the Nigerian Association of Mathematical Physics ... In a Hamiltonian system von Neumann Statistical Operator is used to tease out the quantum consequence of (classical) chaos engendered by the nonlinear coupling of system to its ...

  10. Adaptive projective synchronization between different chaotic ...

    Indian Academy of Sciences (India)

    Numerical simulation results are performed to explain the effectiveness and feasibility of ... analysis of nonlinear dynamics have gained immense popularity during the last few ... applications of projective synchronization is in secure communication [31] due to ... of uncertain chaotic systems using adaptive control method.

  11. Two-Gyro Pointing Stability of HST measured with ACS

    Science.gov (United States)

    Koekemoer, Anton M.; Kozhurina-Platais, Vera; Riess, Adam; Sirianni, Marco; Biretta, John; Pavlovsky

    2005-06-01

    We present the results of the pointing stability tests for HST, as measured with the ACS/ HRC during the Two-Gyro test program conducted in February 2005. We measure the shifts of 185 exposures of the globular clusters NGC6341 and Omega Centauri, obtained over a total of 13 orbits, and compare the measured pointings to those that were commanded in the observing program. We find in all cases that the measured shifts and rotations have the same level of accuracy as those that were commanded in three-gyro mode. Specifically, the pointing offsets during an orbit relative to the first exposure can be characterized with distributions having a dispersion of 2.3 milliarcseconds for shifts and 0.00097 degrees for rotations, thus less than 0.1 HRC pixels, and agree extremely well with similar values measured for comparable exposures obtained in three-gyro mode. In addition, we successfully processed these two-gyro test data through the MultiDrizzle software which is used in the HST pipeline to perform automated registration, cosmic ray rejection and image combination for multiple exposure sequences, and we find excellent agreement with similar exposures obtained in three-gyro mode. In summary, we find no significant difference between the quality of HST pointing as measured from these two-gyro test data, relative to the nominal behavior of HST in regular three-gyro operations.

  12. Comparisons of 'Identical' Simulations by the Eulerian Gyrokinetic Codes GS2 and GYRO

    Science.gov (United States)

    Bravenec, R. V.; Ross, D. W.; Candy, J.; Dorland, W.; McKee, G. R.

    2003-10-01

    A major goal of the fusion program is to be able to predict tokamak transport from first-principles theory. To this end, the Eulerian gyrokinetic code GS2 was developed years ago and continues to be improved [1]. Recently, the Eulerian code GYRO was developed [2]. These codes are not subject to the statistical noise inherent to particle-in-cell (PIC) codes, and have been very successful in treating electromagnetic fluctuations. GS2 is fully spectral in the radial coordinate while GYRO uses finite-differences and ``banded" spectral schemes. To gain confidence in nonlinear simulations of experiment with these codes, ``apples-to-apples" comparisons (identical profile inputs, flux-tube geometry, two species, etc.) are first performed. We report on a series of linear and nonlinear comparisons (with overall agreement) including kinetic electrons, collisions, and shaped flux surfaces. We also compare nonlinear simulations of a DIII-D discharge to measurements of not only the fluxes but also the turbulence parameters. [1] F. Jenko, et al., Phys. Plasmas 7, 1904 (2000) and refs. therein. [2] J. Candy, J. Comput. Phys. 186, 545 (2003).

  13. Flight suspension for the relativity gyro

    International Nuclear Information System (INIS)

    Patten, R.A. van

    1983-01-01

    A suspension system for levitation and precision positioning of the niobium coated spherical quartz gyro rotor during orbital flight has been simulated. The system employs multiple controllers and estimators with microprocessor (Z80) controlled range switching. The resulting system handles external accelerations up to 1 g in the highest range yet in the lowest range, below 10 -6 g the sensor noise power spectral density produces only 10 -10 g rms in the rotor. The system is capable of automatic emergency switch up within 100 μsec. Switch down is automatic to expected flight levels of ± 5 x 10 -8 g. Positioning accuracy in all ranges including emergency switch up is ± 5 μin. static, and ± 50 μin. dynamic. The average acceleration during the mission should be 10 -10 g to attain the science data accuracy goal. (Auth.)

  14. On robust control of uncertain chaotic systems: a sliding-mode synthesis via chaotic optimization

    International Nuclear Information System (INIS)

    Lu Zhao; Shieh Leangsan; Chen GuanRong

    2003-01-01

    This paper presents a novel Lyapunov-based control approach which utilizes a Lyapunov function of the nominal plant for robust tracking control of general multi-input uncertain nonlinear systems. The difficulty of constructing a control Lyapunov function is alleviated by means of predefining an optimal sliding mode. The conventional schemes for constructing sliding modes of nonlinear systems stipulate that the system of interest is canonical-transformable or feedback-linearizable. An innovative approach that exploits a chaotic optimizing algorithm is developed thereby obtaining the optimal sliding manifold for the control purpose. Simulations on the uncertain chaotic Chen's system illustrate the effectiveness of the proposed approach

  15. Fiber optic gyro development at the Jet Propulsion Laboratory

    Science.gov (United States)

    Goss, Willis C.

    1987-01-01

    A low-level, but continuing, fiber-gyro development activity has been carried on at the Jet Propulsion Laboratory since 1977. The activity was originated because of a recognition of the potential for low-cost high-performance gyros suitable for interplanetary spacecraft. An early decision was made to concentrate available resources on supporting the development of electrooptically active channel waveguide components which could be fabricated by mask diffusion processes. Titanium-indiffused lithium niobate waveguide components used at 0.83 micron wavelength were first tested and then abandoned because of instabilities caused by so-called optical damage. Components fabricated for use at 1.3-micron wavelength have proven to be stable. A gyro configuration concept based upon 1.3 micron channel waveguide components has evolved, and a baseline 1.3-micron all-fiber gyro has been assembled and tested.

  16. Quantum-chaotic cryptography

    Science.gov (United States)

    de Oliveira, G. L.; Ramos, R. V.

    2018-03-01

    In this work, it is presented an optical scheme for quantum key distribution employing two synchronized optoelectronic oscillators (OEO) working in the chaotic regime. The produced key depends on the chaotic dynamic, and the synchronization between Alice's and Bob's OEOs uses quantum states. An attack on the synchronization signals will disturb the synchronization of the chaotic systems increasing the error rate in the final key.

  17. Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it, E-mail: lminati@istituto-besta.it [Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy); Center for Mind/Brain Sciences, University of Trento, Trento (Italy); Chiesa, Pietro; Tabarelli, Davide; Jovicich, Jorge [Center for Mind/Brain Sciences, University of Trento, Trento (Italy); D' Incerti, Ludovico [Neuroradiology Unit, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)

    2015-03-15

    In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D{sub 2}), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.

  18. Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

    International Nuclear Information System (INIS)

    Minati, Ludovico; Chiesa, Pietro; Tabarelli, Davide; Jovicich, Jorge; D'Incerti, Ludovico

    2015-01-01

    In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D 2 ), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes

  19. Implementation of an integrated op-amp based chaotic neuron model and observation of its chaotic dynamics

    International Nuclear Information System (INIS)

    Jung, Jinwoo; Lee, Jewon; Song, Hanjung

    2011-01-01

    This paper presents a fully integrated circuit implementation of an operational amplifier (op-amp) based chaotic neuron model with a bipolar output function, experimental measurements, and analyses of its chaotic behavior. The proposed chaotic neuron model integrated circuit consists of several op-amps, sample and hold circuits, a nonlinear function block for chaotic signal generation, a clock generator, a nonlinear output function, etc. Based on the HSPICE (circuit program) simulation results, approximated empirical equations for analyses were formulated. Then, the chaotic dynamical responses such as bifurcation diagrams, time series, and Lyapunov exponent were calculated using these empirical equations. In addition, we performed simulations about two chaotic neuron systems with four synapses to confirm neural network connections and got normal behavior of the chaotic neuron such as internal state bifurcation diagram according to the synaptic weight variation. The proposed circuit was fabricated using a 0.8-μm single poly complementary metal-oxide semiconductor technology. Measurements of the fabricated single chaotic neuron with ±2.5 V power supplies and a 10 kHz sampling clock frequency were carried out and compared with the simulated results.

  20. A new chaotic algorithm for image encryption

    International Nuclear Information System (INIS)

    Gao Haojiang; Zhang Yisheng; Liang Shuyun; Li Dequn

    2006-01-01

    Recent researches of image encryption algorithms have been increasingly based on chaotic systems, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. This paper presents a new nonlinear chaotic algorithm (NCA) which uses power function and tangent function instead of linear function. Its structural parameters are obtained by experimental analysis. And an image encryption algorithm in a one-time-one-password system is designed. The experimental results demonstrate that the image encryption algorithm based on NCA shows advantages of large key space and high-level security, while maintaining acceptable efficiency. Compared with some general encryption algorithms such as DES, the encryption algorithm is more secure

  1. Gravity Probe B Number 4 Gyro Inspected

    Science.gov (United States)

    2000-01-01

    The Gravity Probe B (GP-B) is the relativity experiment developed at Stanford University to test two extraordinary predictions of Albert Einstein's general theory of relativity. The experiment will measure, very precisely, the expected tiny changes in the direction of the spin axes of four gyroscopes contained in an Earth-orbiting satellite at a 400-mile altitude. So free are the gyroscopes from disturbance that they will provide an almost perfect space-time reference system. They will measure how space and time are very slightly warped by the presence of the Earth, and, more profoundly, how the Earth's rotation very slightly drags space-time around with it. These effects, though small for the Earth, have far-reaching implications for the nature of matter and the structure of the Universe. In this photograph, Stanford engineer, Chris Gray, is inspecting the number 4 gyro under monochromatic light. GP-B is among the most thoroughly researched programs ever undertaken by NASA. This is the story of a scientific quest in which physicists and engineers have collaborated closely over many years. Inspired by their quest, they have invented a whole range of technologies that are already enlivening other branches of science and engineering. Launched April 20, 2004 , the GP-B program was managed for NASA by the Marshall Space Flight Center. Development of the GP-B is the responsibility of Stanford University along with major subcontractor Lockheed Martin Corporation. (Image credit to Russ Leese, Stanford University.)

  2. Empirically characteristic analysis of chaotic PID controlling particle swarm optimization

    Science.gov (United States)

    Yan, Danping; Lu, Yongzhong; Zhou, Min; Chen, Shiping; Levy, David

    2017-01-01

    Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic community and industry society throughout the world. To improve the performance of particle swarm optimization (PSO), we herein propose a chaotic proportional integral derivative (PID) controlling PSO algorithm by the hybridization of chaotic logistic dynamics and hierarchical inertia weight. The hierarchical inertia weight coefficients are determined in accordance with the present fitness values of the local best positions so as to adaptively expand the particles’ search space. Moreover, the chaotic logistic map is not only used in the substitution of the two random parameters affecting the convergence behavior, but also used in the chaotic local search for the global best position so as to easily avoid the particles’ premature behaviors via the whole search space. Thereafter, the convergent analysis of chaotic PID controlling PSO is under deep investigation. Empirical simulation results demonstrate that compared with other several chaotic PSO algorithms like chaotic PSO with the logistic map, chaotic PSO with the tent map and chaotic catfish PSO with the logistic map, chaotic PID controlling PSO exhibits much better search efficiency and quality when solving the optimization problems. Additionally, the parameter estimation of a nonlinear dynamic system also further clarifies its superiority to chaotic catfish PSO, genetic algorithm (GA) and PSO. PMID:28472050

  3. Empirically characteristic analysis of chaotic PID controlling particle swarm optimization.

    Directory of Open Access Journals (Sweden)

    Danping Yan

    Full Text Available Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic community and industry society throughout the world. To improve the performance of particle swarm optimization (PSO, we herein propose a chaotic proportional integral derivative (PID controlling PSO algorithm by the hybridization of chaotic logistic dynamics and hierarchical inertia weight. The hierarchical inertia weight coefficients are determined in accordance with the present fitness values of the local best positions so as to adaptively expand the particles' search space. Moreover, the chaotic logistic map is not only used in the substitution of the two random parameters affecting the convergence behavior, but also used in the chaotic local search for the global best position so as to easily avoid the particles' premature behaviors via the whole search space. Thereafter, the convergent analysis of chaotic PID controlling PSO is under deep investigation. Empirical simulation results demonstrate that compared with other several chaotic PSO algorithms like chaotic PSO with the logistic map, chaotic PSO with the tent map and chaotic catfish PSO with the logistic map, chaotic PID controlling PSO exhibits much better search efficiency and quality when solving the optimization problems. Additionally, the parameter estimation of a nonlinear dynamic system also further clarifies its superiority to chaotic catfish PSO, genetic algorithm (GA and PSO.

  4. Disordered chaotic strings

    DEFF Research Database (Denmark)

    Schäfer, Mirko; Greiner, Martin

    2011-01-01

    to chaotic strings. Inhomogeneous coupling weights as well as small-world perturbations of the ring-network structure are discussed. It is found that certain combinations of coupling and network disorder preserve the empirical relationship between chaotic strings and the weak and strong sector...

  5. Synchronization of chaotic systems

    International Nuclear Information System (INIS)

    Pecora, Louis M.; Carroll, Thomas L.

    2015-01-01

    We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators

  6. Low-dimensional chaotic attractors in drift wave turbulence

    International Nuclear Information System (INIS)

    Persson, M.; Nordman, H.

    1991-01-01

    Simulation results of toroidal η i -mode turbulence are analyzed using mathematical tools of nonlinear dynamics. Low-dimensional chaotic attractors are found in the strongly nonlinear regime while in the weakly interacting regime the dynamics is high dimensional. In both regimes, the solutions are found to display sensitive dependence on initial conditions, characterized by a positive largest Liapunov exponent. (au)

  7. Robust control of time-delay chaotic systems

    International Nuclear Information System (INIS)

    Hua Changchun; Guan Xinping

    2003-01-01

    Robust control problem of nonlinear time-delay chaotic systems is investigated. For such uncertain systems, we propose adaptive feedback controller and novel nonlinear feedback controller. They are both independent of the time delay and can render the corresponding closed-loop systems globally uniformly ultimately bounded stable. The simulations on controlling logistic system are made and the results show the controllers are feasible

  8. CARM and harmonic gyro-amplifier experiments at 17 GHz

    International Nuclear Information System (INIS)

    Menninger, W.L.; Danly, B.G.; Alberti, S.; Chen, C.; Rullier, J.L.; Temkin, R.J.

    1993-01-01

    Cyclotron resonance maser amplifiers are possible sources for applications such as electron cyclotron resonance heating of fusion plasmas and driving high-gradient rf linear accelerators. For accelerator drivers, amplifiers or phase locked-oscillators are required. A 17 GHz cyclotron autoresonance maser (CARM) amplifier experiment and a 17 GHz third harmonic gyro-amplifier experiment are presently underway at the MIT Plasma Fusion Center. Using the SRL/MIT SNOMAD II introduction accelerator to provide a 380 kV, 180 A, 30 ns flat top electron beam, the gyro-amplifier experiment has produced 5 MW of rf power with over 50 dB of gain at 17 GHz. The gyro-amplifier operates in the TE 31 mode using a third harmonic interaction. Because of its high power output, the gyro-amplifier will be used as the rf source for a photocathode rf electron gun experiment also taking place at MIT. Preliminary gyro-amplifier results are presented, including measurement of rf power, gain versus interaction length, and the far-field pattern. A CARM experiment designed to operate in the TE 11 mode is also discussed

  9. Experimental observations of EMI effects in autonomous Chua's chaotic circuit

    International Nuclear Information System (INIS)

    Kilic, Recai; Saracoglu, O. Galip; Yildirim, Fatma

    2007-01-01

    This paper deals with the experimentally investigation of EMI effects in autonomous Chua's chaotic circuit. We realized this experimental investigation by constructing an experimental setup subject to a Chua's circuit and applying a 5-30 MHz/100-200 mV EMI signal to the input pins of voltage Op-Amps used for realizing nonlinear resistor in Chua's circuit. In addition, we also experimentally investigated whether EMI signals affect the chaos synchronization between two Chua's chaotic circuits or not

  10. CMAC-based adaptive backstepping synchronization of uncertain chaotic systems

    International Nuclear Information System (INIS)

    Lin, C.-M.; Peng, Y.-F.; Lin, M.-H.

    2009-01-01

    This study proposes an adaptive backstepping control system for synchronizing uncertain chaotic system by using cerebellar model articulation controller (CMAC). CMAC is a nonlinear network with simple computation, good generalization capability and fast learning property. The proposed CMAC-based adaptive backstepping control (CABC) system uses backstepping method and adaptive cerebellar model articulation controller (ACMAC) for synchronizing uncertain chaotic system. Finally, simulation results for the Genesio system are presented to illustrate the effectiveness of the proposed control system.

  11. Response to "Comment on `Solitonic and chaotic behaviors for the nonlinear dust-acoustic waves in a magnetized dusty plasma'" [Phys. Plasmas 24, 094701 (2017)

    Science.gov (United States)

    Zhen, Hui-Ling; Tian, Bo; Xie, Xi-Yang; Wu, Xiao-Yu; Wen, Xiao-Yong

    2018-02-01

    On our previous construction [H. L. Zhen et al., Phys. Plasmas 23, 052301 (2016)] of the soliton solutions of a model describing the dynamics of the dust particles in a weakly ionized, collisional dusty plasma comprised of the negatively charged cold dust particles, hot ions, hot electrons, and stationary neutrals in the presence of an external static magnetic field, Ali et al. [Phys. Plasmas 24, 094701 (2017)] have commented that there exists a different form of Eq. (4) from that shown in Zhen et al. [Phys. Plasmas 23, 052301 (2016)] and that certain interesting phenomena with the dust neutral collision frequency ν0>0 are ignored in Zhen et al. [Phys. Plasmas 23, 052301 (2016)]. In this Reply, according to the transformation given by the Ali et al. [Phys. Plasmas 24, 094701 (2017)] comment, we present some one-, two-, and N-soliton solutions which have not been obtained in the Ali et al. [Phys. Plasmas 24, 094701 (2017)] comment. We point out that our previous solutions in Zhen et al. [Phys. Plasmas 23, 052301 (2016)] are still valid because of the similarity between the two dispersion relations of previous solutions in Zhen et al. [Phys. Plasmas 23, 052301 (2016)] and the solutions presented in this Reply. Based on our soliton solutions in this Reply, it is found that the soliton amplitude is inversely related to Zd and B0, but positively related to md and α, where α refers to the coefficient of the nonlinear term, Zd and md are the charge number and mass of a dust particle, respectively, B0 represents the strength of the external static magnetic field. We also find that the two solitons are always in parallel during the propagation.

  12. Don't bleach chaotic data

    International Nuclear Information System (INIS)

    Theiler, J.; Eubank, S.

    1993-01-01

    A common first step in time series signal analysis involves digitally filtering the data to remove linear correlations. The residual data is spectrally white (it is ''bleached''), but in principle retains the nonlinear structure of the original time series. It is well known that simple linear autocorrelation can give rise to spurious results in algorithms for estimating nonlinear invariants, such as fractal dimension and Lyapunov exponents. In theory, bleached data avoids these pitfalls. But in practice, bleaching obscures the underlying deterministic structure of a low-dimensional chaotic process. This appears to be a property of the chaos itself, since nonchaotic data are not similarly affected. The adverse effects of bleaching are demonstrated in a series of numerical experiments on known chaotic data. Some theoretical aspects are also discussed

  13. Combined spacecraft orbit and attitude control through extended Kalman filtering of magnetometer, gyro, and GPS measurements

    Directory of Open Access Journals (Sweden)

    Tamer Mekky Ahmed Habib

    2014-06-01

    Full Text Available The main goal of this research is to establish spacecraft orbit and attitude control algorithms based on extended Kalman filter which provides estimates of spacecraft orbital and attitude states. The control and estimation algorithms must be capable of dealing with the spacecraft conditions during the detumbling and attitude acquisition modes of operation. These conditions are characterized by nonlinearities represented by large initial attitude angles, large initial angular velocities, large initial attitude estimation error, and large initial position estimation error. All of the developed estimation and control algorithms are suitable for application to the next Egyptian scientific satellite, EGYPTSAT-2. The parameters of the case-study spacecraft are similar but not identical to the former Egyptian satellite EGYPTSAT-1. This is done because the parameters of EGYPTSAT-2 satellite have not been consolidated yet. The sensors utilized are gyro, magnetometer, and GPS. Gyro and magnetometer are utilized to provide measurements for the estimates of spacecraft attitude state vector where as magnetometer and GPS are utilized to provide measurements for the estimates of spacecraft orbital state vector.

  14. Dynamics and Control of a Chaotic Electromagnetic System

    OpenAIRE

    Shun-Chang Chang

    2012-01-01

    In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simula...

  15. Introduction to nonlinear science

    CERN Document Server

    Nicolis, G

    1995-01-01

    One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...

  16. NARX prediction of some rare chaotic flows: Recurrent fuzzy functions approach

    Energy Technology Data Exchange (ETDEWEB)

    Goudarzi, Sobhan [Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413 (Iran, Islamic Republic of); Jafari, Sajad, E-mail: sajadjafari@aut.ac.ir [Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413 (Iran, Islamic Republic of); Moradi, Mohammad Hassan [Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413 (Iran, Islamic Republic of); Sprott, J.C. [Department of Physics, University of Wisconsin–Madison, Madison, WI 53706 (United States)

    2016-02-15

    The nonlinear and dynamic accommodating capability of time domain models makes them a useful representation of chaotic time series for analysis, modeling and prediction. This paper is devoted to the modeling and prediction of chaotic time series with hidden attractors using a nonlinear autoregressive model with exogenous inputs (NARX) based on a novel recurrent fuzzy functions (RFFs) approach. Case studies of recently introduced chaotic systems with hidden attractors plus classical chaotic systems demonstrate that the proposed modeling methodology exhibits better prediction performance from different viewpoints (short term and long term) compared to some other existing methods. - Highlights: • A new method is proposed for prediction of chaotic time series. • This method is based on novel recurrent fuzzy functions (RFFs) approach. • Some rare chaotic flows are used as test systems. • The new method shows proper performance in short-term prediction. • It also shows proper performance in prediction of attractor's topology.

  17. NARX prediction of some rare chaotic flows: Recurrent fuzzy functions approach

    International Nuclear Information System (INIS)

    Goudarzi, Sobhan; Jafari, Sajad; Moradi, Mohammad Hassan; Sprott, J.C.

    2016-01-01

    The nonlinear and dynamic accommodating capability of time domain models makes them a useful representation of chaotic time series for analysis, modeling and prediction. This paper is devoted to the modeling and prediction of chaotic time series with hidden attractors using a nonlinear autoregressive model with exogenous inputs (NARX) based on a novel recurrent fuzzy functions (RFFs) approach. Case studies of recently introduced chaotic systems with hidden attractors plus classical chaotic systems demonstrate that the proposed modeling methodology exhibits better prediction performance from different viewpoints (short term and long term) compared to some other existing methods. - Highlights: • A new method is proposed for prediction of chaotic time series. • This method is based on novel recurrent fuzzy functions (RFFs) approach. • Some rare chaotic flows are used as test systems. • The new method shows proper performance in short-term prediction. • It also shows proper performance in prediction of attractor's topology.

  18. Security analysis of chaotic communication systems based on Volterra-Wiener-Korenberg model

    International Nuclear Information System (INIS)

    Lei Min; Meng Guang; Feng Zhengjin

    2006-01-01

    Pseudo-randomicity is an important cryptological characteristic for proof of encryption algorithms. This paper proposes a nonlinear detecting method based on Volterra-Wiener-Korenberg model and suggests an autocorrelation function to analyze the pseudo-randomicity of chaotic secure systems under different sampling interval. The results show that: (1) the increase of the order of the chaotic transmitter will not necessarily result in a high degree of security; (2) chaotic secure systems have higher and stronger pseudo-randomicity at sparse sampling interval due to the similarity of chaotic time series to the noise; (3) Volterra-Wiener-Korenberg method can also give a further appropriate sparse sampling interval for improving the security of chaotic secure communication systems. For unmasking chaotic communication systems, the Volterra-Wiener-Korenberg technique can be applied to analyze the chaotic time series with surrogate data

  19. Generation and control of multi-scroll chaotic attractors in fractional order systems

    International Nuclear Information System (INIS)

    Ahmad, Wajdi M.

    2005-01-01

    The objective of this paper is twofold: on one hand we demonstrate the generation of multi-scroll attractors in fractional order chaotic systems. Then, we design state feedback controllers to eliminate chaos from the system trajectories. It is demonstrated that modifying the underlying nonlinearity of the fractional chaotic system results in the birth of multiple chaotic attractors, thus forming the so called multi-scroll attractors. The presence of chaotic behavior is evidenced by a positive largest Lyapunov exponent computed for the output time series. We investigate generation and control of multi-scroll attractors in two different models, both of which are fractional order and chaotic: an electronic oscillator, and a mechanical 'jerk' model. The current findings extend previously reported results on generation of n-scroll attractors from the domain of integer order to the domain of fractional order chaotic systems, and addresses the issue of controlling such chaotic behaviors. Our investigations are validated through numerical simulations

  20. Synchronization of identical chaotic systems through external chaotic driving

    International Nuclear Information System (INIS)

    Patidar, V.; Sud, K.K.

    2005-11-01

    In recent years, the study of synchronization of identical chaotic systems subjected to a common fluctuating random driving signal has drawn considerable interest. In this communication, we report that it is possible to achieve synchronization between two identical chaotic systems, which are not coupled directly but subjected to an external chaotic signal. The external chaotic signal may be obtained from any chaotic system identical or non-identical to both identical chaotic systems. Results of numerical simulations on well known Roessler and jerk dynamical systems have been presented. (author)

  1. Cascade Chaotic System With Applications.

    Science.gov (United States)

    Zhou, Yicong; Hua, Zhongyun; Pun, Chi-Man; Chen, C L Philip

    2015-09-01

    Chaotic maps are widely used in different applications. Motivated by the cascade structure in electronic circuits, this paper introduces a general chaotic framework called the cascade chaotic system (CCS). Using two 1-D chaotic maps as seed maps, CCS is able to generate a huge number of new chaotic maps. Examples and evaluations show the CCS's robustness. Compared with corresponding seed maps, newly generated chaotic maps are more unpredictable and have better chaotic performance, more parameters, and complex chaotic properties. To investigate applications of CCS, we introduce a pseudo-random number generator (PRNG) and a data encryption system using a chaotic map generated by CCS. Simulation and analysis demonstrate that the proposed PRNG has high quality of randomness and that the data encryption system is able to protect different types of data with a high-security level.

  2. Chaotic hydrodynamics of fluidized beds

    Energy Technology Data Exchange (ETDEWEB)

    Van der Stappen, M.L.M. [Unit Process and Systems Engineering, Advanced Manufacturing Technology Group, Unilever Research Laboratorium, Vlaardingen (Netherlands)

    1996-12-31

    The major goals of this thesis are: (1) to develop and evaluate an analysis method based on techniques from non-linear chaos theory to characterize the nonlinear hydrodynamics of gas-solids fluidized beds quantitatively; and (2) to determine the dependence of the chaotic invariants on the operating conditions and investigate how the chaos analysis method can be profitably applied to improve scale-up and design of gas-solids fluidized bed reactors. Chaos theory is introduced in chapter 2 with emphasis on analysis techniques for (experimental) time series, known from literature at the start of this work (1990-1991). In chapter 3, the testing of existing and newly developed techniques on both model and fluidized bed data is described. This leads to the development of the chaos analysis method to analyze measured pressure fluctuations time series of a fluidized bed. Following, in chapter 4, this method is tested and all choices for the parameters are evaluated. The influence of the experimental parameters and external disturbances on the measurements and analysis results is discussed and quantified. The result is a chaos measurement and analysis protocol, which is further used in this work. In chapter 5, the applications to fluidized beds are discussed. It is shown that the entropy is a good measure for the characterization of the dynamical behavior of gas-solids bubbling/slugging fluidized beds. Entropy is applied to characterize the influence of the operating conditions, to assess regime transitions and to analyze dimensionless similar beds of different scale. Quantitative design correlations that relate entropy to the operating parameters (including the bed diameter) are described. Finally, it is discussed how the results of this work might be used in scaling up the chaotic dynamics of fluidized beds. The overall conclusions and outlook from this work are presented in chapter 6. 182 refs.

  3. Chaotic behaviour of a fourth-order autonomous electric circuit

    International Nuclear Information System (INIS)

    Koliopanos, Ch.L.; Kyprianidis, I.M.; Stouboulos, I.N.; Anagnostopoulos, A.N.; Magafas, L.

    2003-01-01

    The chaotic dynamics of a fourth-order autonomous nonlinear electric circuit was studied by measuring its response in the form of chaotic time series. The circuit consists of two active elements, one linear negative conductance and one nonlinear resistor exhibiting a symmetrical piecewise-linear v-i characteristic and two capacitances C 1 and C 2 , which serve as the control parameters of the system. From the experimental time series the minimum embedding dimensions m min =4, correlation dimensions ν, with positive noninteger values, and Kolmogorov entropies, tending to constant positive values, were determined by numerical evaluation for the examined states of the system

  4. Synchronization of uncertain chaotic systems using a single transmission channel

    International Nuclear Information System (INIS)

    Feng Yong; Yu Xinghuo; Sun Lixia

    2008-01-01

    This paper proposes a robust sliding mode observer for synchronization of uncertain chaotic systems with multi-nonlinearities. A new control strategy is proposed for the construction of the robust sliding mode observer, which can avoid the strict conditions in the design process of Walcott-Zak observer. A new method of multi-dimensional signal transmission via single transmission channel is proposed and applied to chaos synchronization of uncertain chaotic systems with multi-nonlinearities. The simulation results are presented to validate the method

  5. Precision pointing of imaging spacecraft using gyro-based attitude ...

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    three-axis attitude of the spacecraft is required continuously for the controller. Gyros provide .... Right ascension of ascending node ( ). 78·1290476 ... U = {ω1 + ω0X,ω2 + ω0Y ,ω3 + ω0Z,} are the process inputs and the matrices A, B and G.

  6. Economic dispatch using chaotic bat algorithm

    International Nuclear Information System (INIS)

    Adarsh, B.R.; Raghunathan, T.; Jayabarathi, T.; Yang, Xin-She

    2016-01-01

    This paper presents the application of a new metaheuristic optimization algorithm, the chaotic bat algorithm for solving the economic dispatch problem involving a number of equality and inequality constraints such as power balance, prohibited operating zones and ramp rate limits. Transmission losses and multiple fuel options are also considered for some problems. The chaotic bat algorithm, a variant of the basic bat algorithm, is obtained by incorporating chaotic sequences to enhance its performance. Five different example problems comprising 6, 13, 20, 40 and 160 generating units are solved to demonstrate the effectiveness of the algorithm. The algorithm requires little tuning by the user, and the results obtained show that it either outperforms or compares favorably with several existing techniques reported in literature. - Highlights: • The chaotic bat algorithm, a new metaheuristic optimization algorithm has been used. • The problem solved – the economic dispatch problem – is nonlinear, discontinuous. • It has number of equality and inequality constraints. • The algorithm has been demonstrated to be applicable on high dimensional problems.

  7. Discrete Model Reference Adaptive Control for Gimbal Servosystem of Control Moment Gyro with Harmonic Drive

    Directory of Open Access Journals (Sweden)

    Bangcheng Han

    2013-01-01

    Full Text Available The double-gimbal control moment gyro (DGCMG demands that the gimbal servosystem should have fast response and small overshoot. But due to the low and nonlinear torsional stiffness of harmonic drive, the gimbal servo-system has poor dynamic performance with large overshoot and low bandwidth. In order to improve the dynamic performance of gimbal servo-system, a model reference adaptive control (MRAC law is introduced in this paper. The model of DGCMG gimbal servo-system with harmonic drive is established, and the adaptive control law based on POPOV super stable theory is designed. The MATLAB simulation results are provided to verify the effectiveness of the proposed control algorithm. The experimental results indicate that the MRAC could increase the bandwidth of gimbal servo-system to 3 Hz and improve the dynamic performance with small overshoot.

  8. Nonlinear chaos control in a permanent magnet reluctance machine

    International Nuclear Information System (INIS)

    Harb, Ahmad M.

    2004-01-01

    The dynamics of a permanent magnet synchronous machine (PMSM) is analyzed. The study shows that under certain conditions the PMSM is experiencing chaotic behavior. To control these unwanted chaotic oscillations, a nonlinear controller based on the backstepping nonlinear control theory is designed. The objective of the designed control is to stabilize the output chaotic trajectory by forcing it to the nearest constant solution in the basin of attraction. The result is compared with a nonlinear sliding mode controller. The designed controller that based on backstepping nonlinear control was able to eliminate the chaotic oscillations. Also the study shows that the designed controller is mush better than the sliding mode control

  9. Chaotic secure communication based on strong tracking filtering

    International Nuclear Information System (INIS)

    Li Xiongjie; Xu Zhengguo; Zhou Donghua

    2008-01-01

    A scheme for implementing secure communication based on chaotic maps and strong tracking filter (STF) is presented, and a modified STF algorithm with message estimation is developed for the special requirement of chaotic secure communication. At the emitter, the message symbol is modulated by chaotic mapping and is output through a nonlinear function. At the receiver, the driving signal is received and the message symbol is recovered dynamically by the STF with estimation of message symbol. Simulation results of Holmes map demonstrate that when message symbols are binary codes, STF can effectively recover the codes of the message from the noisy chaotic signals. Compared with the extended Kalman filter (EKF), STF has a lower bit error rate

  10. A new transiently chaotic flow with ellipsoid equilibria

    Science.gov (United States)

    Panahi, Shirin; Aram, Zainab; Jafari, Sajad; Pham, Viet-Thanh; Volos, Christos; Rajagopal, Karthikeyan

    2018-03-01

    In this article, a simple autonomous transiently chaotic flow with cubic nonlinearities is proposed. This system represents some unusual features such as having a surface of equilibria. We shall describe some dynamical properties and behaviours of this system in terms of eigenvalue structures, bifurcation diagrams, time series, and phase portraits. Various behaviours of this system such as periodic and transiently chaotic dynamics can be shown by setting special parameters in proper values. Our system belongs to a newly introduced category of transiently chaotic systems: systems with hidden attractors. Transiently chaotic behaviour of our proposed system has been implemented and tested by the OrCAD-PSpise software. We have found a proper qualitative similarity between circuit and simulation results.

  11. Cryptography with chaotic mixing

    International Nuclear Information System (INIS)

    Oliveira, Luiz P.L. de; Sobottka, Marcelo

    2008-01-01

    We propose a cryptosystem based on one-dimensional chaotic maps of the form H p (x)=r p -1 0G0r p (x) defined in the interval [0, 10 p ) for a positive integer parameter p, where G(x)=10x(mod10) and r p (x)= p √(x), which is a topological conjugacy between G and the shift map σ on the space Σ of the sequences with 10 symbols. There are three advantages in comparison with the recently proposed cryptosystem based on chaotic logistic maps F μ (x)=μx(1-x) with 3 p is always chaotic for all parameters p, (b) the knowledge of an ergodic measure allows assignments of the alphabetic symbols to equiprobable sites of H p 's domain and (c) for each p, the security of the cryptosystem is manageable against brute force attacks

  12. Experimental chaos in nonlinear vibration isolation system

    International Nuclear Information System (INIS)

    Lou Jingjun; Zhu Shijian; He Lin; He Qiwei

    2009-01-01

    The chaotic vibration isolation method was studied thoroughly from an experimental perspective. The nonlinear load-deflection characteristic of the conical coil spring used in the experiment was surveyed. Chaos and subharmonic responses including period-2 and period-6 motions were observed. The line spectrum reduction and the drop of the acceleration vibration level in chaotic state and that in non-chaotic state were compared, respectively. It was concluded from the experiment that the nonlinear vibration isolation system in chaotic state has strong ability in line spectrum reduction.

  13. Benchmark studies of the gyro-Landau-fluid code and gyro-kinetic codes on kinetic ballooning modes

    Energy Technology Data Exchange (ETDEWEB)

    Tang, T. F. [Dalian University of Technology, Dalian 116024 (China); Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Xu, X. Q. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Ma, C. H. [Fusion Simulation Center, School of Physics, Peking University, Beijing (China); Bass, E. M.; Candy, J. [General Atomics, P.O. Box 85608, San Diego, California 92186-5608 (United States); Holland, C. [University of California San Diego, La Jolla, California 92093-0429 (United States)

    2016-03-15

    A Gyro-Landau-Fluid (GLF) 3 + 1 model has been recently implemented in BOUT++ framework, which contains full Finite-Larmor-Radius effects, Landau damping, and toroidal resonance [Ma et al., Phys. Plasmas 22, 055903 (2015)]. A linear global beta scan has been conducted using the JET-like circular equilibria (cbm18 series), showing that the unstable modes are kinetic ballooning modes (KBMs). In this work, we use the GYRO code, which is a gyrokinetic continuum code widely used for simulation of the plasma microturbulence, to benchmark with GLF 3 + 1 code on KBMs. To verify our code on the KBM case, we first perform the beta scan based on “Cyclone base case parameter set.” We find that the growth rate is almost the same for two codes, and the KBM mode is further destabilized as beta increases. For JET-like global circular equilibria, as the modes localize in peak pressure gradient region, a linear local beta scan using the same set of equilibria has been performed at this position for comparison. With the drift kinetic electron module in the GYRO code by including small electron-electron collision to damp electron modes, GYRO generated mode structures and parity suggest that they are kinetic ballooning modes, and the growth rate is comparable to the GLF results. However, a radial scan of the pedestal for a particular set of cbm18 equilibria, using GYRO code, shows different trends for the low-n and high-n modes. The low-n modes show that the linear growth rate peaks at peak pressure gradient position as GLF results. However, for high-n modes, the growth rate of the most unstable mode shifts outward to the bottom of pedestal and the real frequency of what was originally the KBMs in ion diamagnetic drift direction steadily approaches and crosses over to the electron diamagnetic drift direction.

  14. Initial conditions for chaotic inflation

    International Nuclear Information System (INIS)

    Brandenberger, R.; Kung, J.; Feldman, H.

    1991-01-01

    In contrast to many other inflationary Universe models, chaotic inflation does not depend on fine tuning initial conditions. Within the context of linear perturbation theory, it is shown that chaotic inflation is stable towards both metric and matter perturbations. Neglecting gravitational perturbations, it is shown that chaotic inflation is an attractor in initial condition space. (orig.)

  15. Exact folded-band chaotic oscillator.

    Science.gov (United States)

    Corron, Ned J; Blakely, Jonathan N

    2012-06-01

    An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.

  16. Bearing Health Assessment Based on Chaotic Characteristics

    Directory of Open Access Journals (Sweden)

    Chen Lu

    2013-01-01

    Full Text Available Vibration signals extracted from rotating parts of machinery carry a lot of useful information about the condition of operating machine. Due to the strong non-linear, complex and non-stationary characteristics of vibration signals from working bearings, an accurate and reliable health assessment method for bearing is necessary. This paper proposes to utilize the selected chaotic characteristics of vibration signal for health assessment of a bearing by using self-organizing map (SOM. Both Grassberger-Procaccia algorithm and Takens' theory are employed to calculate the characteristic vector which includes three chaotic characteristics, such as correlation dimension, largest Lyapunov exponent and Kolmogorov entropy. After that, SOM is used to map the three corresponding characteristics into a confidence value (CV which represents the health state of the bearing. Finally, a case study based on vibration datasets of a group of testing bearings was conducted to demonstrate that the proposed method can reliably assess the health state of bearing.

  17. Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control

    International Nuclear Information System (INIS)

    Deng Bin; Wang Jiang; Fei Xiangyang

    2006-01-01

    Backstepping design is a recursive procedure that combines the choice of a Lyapunov function with the design of a controller. In this paper, the backstepping control is used to synchronize two coupled chaotic neurons in external electrical stimulation. The coupled model is based on the nonlinear cable model and only one state variable can be controlled in practice. The backstepping design needs only one controller to synchronize two chaotic systems and it can be applied to a variety of chaotic systems whether they contain external excitation or not, so the two coupled chaotic neurons in external electrical stimulation can be synchronized perfectly by backstepping control. Numerical simulations demonstrate the effectiveness of this design

  18. Chaotic, fractional, and complex dynamics new insights and perspectives

    CERN Document Server

    Macau, Elbert; Sanjuan, Miguel

    2018-01-01

    The book presents nonlinear, chaotic and fractional dynamics, complex systems and networks, together with cutting-edge research on related topics. The fifteen chapters – written by leading scientists working in the areas of nonlinear, chaotic and fractional dynamics, as well as complex systems and networks – offer an extensive overview of cutting-edge research on a range of topics, including fundamental and applied research. These include but are not limited to aspects of synchronization in complex dynamical systems, universality features in systems with specific fractional dynamics, and chaotic scattering. As such, the book provides an excellent and timely snapshot of the current state of research, blending the insights and experiences of many prominent researchers.

  19. Eternal chaotic inflation

    International Nuclear Information System (INIS)

    Linde, A.D.

    1986-05-01

    It is shown that the universe evolution in the chaotic inflation scenario has no end and may have no beginning. According to this scenario, the universe consists of exponentially large number of different mini-universes inside which all possible metastable vacuum states and all possible types of compactification are realized. (author)

  20. Efficient chaotic based satellite power supply subsystem

    International Nuclear Information System (INIS)

    Ramos Turci, Luiz Felipe; Macau, Elbert E.N.; Yoneyama, Takashi

    2009-01-01

    In this work, we investigate the use of the Dynamical System Theory to increase the efficiency of the satellite power supply subsystems. The core of a satellite power subsystem relies on its DC/DC converter. This is a very nonlinear system that presents a multitude of phenomena ranging from bifurcations, quasi-periodicity, chaos, coexistence of attractors, among others. The traditional power subsystem design techniques try to avoid these nonlinear phenomena so that it is possible to use linear system theory in small regions about the equilibrium points. Here, we show that more efficiency can be drawn from a power supply subsystem if the DC/DC converter operates in regions of high nonlinearity. In special, if it operates in a chaotic regime, is has an intrinsic sensitivity that can be exploited to efficiently drive the power subsystem over high ranges of power requests by using control of chaos techniques.

  1. Efficient chaotic based satellite power supply subsystem

    Energy Technology Data Exchange (ETDEWEB)

    Ramos Turci, Luiz Felipe [Technological Institute of Aeronautics (ITA), Sao Jose dos Campos, SP (Brazil)], E-mail: felipeturci@yahoo.com.br; Macau, Elbert E.N. [National Institute of Space Research (Inpe), Sao Jose dos Campos, SP (Brazil)], E-mail: elbert@lac.inpe.br; Yoneyama, Takashi [Technological Institute of Aeronautics (ITA), Sao Jose dos Campos, SP (Brazil)], E-mail: takashi@ita.br

    2009-10-15

    In this work, we investigate the use of the Dynamical System Theory to increase the efficiency of the satellite power supply subsystems. The core of a satellite power subsystem relies on its DC/DC converter. This is a very nonlinear system that presents a multitude of phenomena ranging from bifurcations, quasi-periodicity, chaos, coexistence of attractors, among others. The traditional power subsystem design techniques try to avoid these nonlinear phenomena so that it is possible to use linear system theory in small regions about the equilibrium points. Here, we show that more efficiency can be drawn from a power supply subsystem if the DC/DC converter operates in regions of high nonlinearity. In special, if it operates in a chaotic regime, is has an intrinsic sensitivity that can be exploited to efficiently drive the power subsystem over high ranges of power requests by using control of chaos techniques.

  2. Chaotic waves in Hall thruster plasma

    International Nuclear Information System (INIS)

    Peradzynski, Zbigniew; Barral, S.; Kurzyna, J.; Makowski, K.; Dudeck, M.

    2006-01-01

    The set of hyperbolic equations of the fluid model describing the acceleration of plasma in a Hall thruster is analyzed. The characteristic feature of the flow is the existence of a trapped characteristic; i.e. there exists a characteristic line, which never intersects the boundary of the flow region in the thruster. To study the propagation of short wave perturbations, the approach of geometrical optics (like WKB) can be applied. This can be done in a linear as well as in a nonlinear version. The nonlinear version describes the waves of small but finite amplitude. As a result of such an approach one obtains so called transport equation, which are governing the wave amplitude. Due to the existence of trapped characteristics this transport equation appears to have chaotic (turbulent) solutions in both, linear and nonlinear versions

  3. Active synchronization between two different chaotic dynamical system

    International Nuclear Information System (INIS)

    Maheri, M.; Arifin, N. Md; Ismail, F.

    2015-01-01

    In this paper we investigate on the synchronization problem between two different chaotic dynamical system based on the Lyapunov stability theorem by using nonlinear control functions. Active control schemes are used for synchronization Liu system as drive and Rossler system as response. Numerical simulation by using Maple software are used to show effectiveness of the proposed schemes

  4. Active synchronization between two different chaotic dynamical system

    Energy Technology Data Exchange (ETDEWEB)

    Maheri, M. [Institute for Mathematical Research, 43400 UPM, Serdang, Selengor (Malaysia); Arifin, N. Md; Ismail, F. [Department of Mathematics, 43400 UPM, Serdang, Selengor (Malaysia)

    2015-05-15

    In this paper we investigate on the synchronization problem between two different chaotic dynamical system based on the Lyapunov stability theorem by using nonlinear control functions. Active control schemes are used for synchronization Liu system as drive and Rossler system as response. Numerical simulation by using Maple software are used to show effectiveness of the proposed schemes.

  5. Chaotic synchronization of three coupled oscillators with ring connection

    International Nuclear Information System (INIS)

    Kyprianidis, I.M.; Stouboulos, I.N.

    2003-01-01

    We study the evolution of three identical, resistively coupled with ring connection, nonlinear and nonautonomous electric circuits from nonsynchronized oscillations to synchronized ones, when they exhibit chaotic behavior. Phase-locked states are also observed, as the coupling parameter is varied. The system's dynamics depends on the way of coupling (unidirectional or bidirectional)

  6. Chaotic synchronization of three coupled oscillators with ring connection

    CERN Document Server

    Kyprianidis, I M

    2003-01-01

    We study the evolution of three identical, resistively coupled with ring connection, nonlinear and nonautonomous electric circuits from nonsynchronized oscillations to synchronized ones, when they exhibit chaotic behavior. Phase-locked states are also observed, as the coupling parameter is varied. The system's dynamics depends on the way of coupling (unidirectional or bidirectional).

  7. Stability of operation versus temperature of a three-phase clock-driven chaotic circuit

    International Nuclear Information System (INIS)

    Zhou Ji-Chao; Son Hyunsik; Song Han Jung; Kim Namtae

    2013-01-01

    We evaluate the influence of temperature on the behavior of a three-phase clock-driven metal—oxide—semiconductor (MOS) chaotic circuit. The chaotic circuit consists of two nonlinear functions, a level shifter, and three sample and hold blocks. It is necessary to analyze a CMOS-based chaotic circuit with respect to variation in temperature for stability because the circuit is sensitive to the behavior of the circuit design parameters. The temperature dependence of the proposed chaotic circuit is investigated via the simulation program with integrated circuit emphasis (SPICE) using 0.6-μm CMOS process technology with a 5-V power supply and a 20-kHz clock frequency. The simulation results demonstrate the effects of temperature on the chaotic dynamics of the proposed chaotic circuit. The time series, frequency spectra, bifurcation phenomena, and Lyapunov exponent results are provided. (general)

  8. Studies in astronomical time series analysis. IV - Modeling chaotic and random processes with linear filters

    Science.gov (United States)

    Scargle, Jeffrey D.

    1990-01-01

    While chaos arises only in nonlinear systems, standard linear time series models are nevertheless useful for analyzing data from chaotic processes. This paper introduces such a model, the chaotic moving average. This time-domain model is based on the theorem that any chaotic process can be represented as the convolution of a linear filter with an uncorrelated process called the chaotic innovation. A technique, minimum phase-volume deconvolution, is introduced to estimate the filter and innovation. The algorithm measures the quality of a model using the volume covered by the phase-portrait of the innovation process. Experiments on synthetic data demonstrate that the algorithm accurately recovers the parameters of simple chaotic processes. Though tailored for chaos, the algorithm can detect both chaos and randomness, distinguish them from each other, and separate them if both are present. It can also recover nonminimum-delay pulse shapes in non-Gaussian processes, both random and chaotic.

  9. Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system

    Directory of Open Access Journals (Sweden)

    Vaidyanathan Sundarapandian

    2015-09-01

    Full Text Available First, this paper announces a seven-term novel 3-D conservative chaotic system with four quadratic nonlinearities. The conservative chaotic systems are characterized by the important property that they are volume conserving. The phase portraits of the novel conservative chaotic system are displayed and the mathematical properties are discussed. An important property of the proposed novel chaotic system is that it has no equilibrium point. Hence, it displays hidden chaotic attractors. The Lyapunov exponents of the novel conservative chaotic system are obtained as L1 = 0.0395,L2 = 0 and L3 = −0.0395. The Kaplan-Yorke dimension of the novel conservative chaotic system is DKY =3. Next, an adaptive controller is designed to globally stabilize the novel conservative chaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical conservative chaotic systems with unknown parameters. MATLAB simulations have been depicted to illustrate the phase portraits of the novel conservative chaotic system and also the adaptive control results.

  10. Dynamics of chaotic strings

    International Nuclear Information System (INIS)

    Schaefer, Mirko

    2011-01-01

    The main topic of this thesis is the investigation of dynamical properties of coupled Tchebycheff map networks. The results give insights into the chaotic string model and its network generalization from a dynamical point of view. As a first approach, discrete symmetry transformations of the model are studied. These transformations are formulated in a general way in order to be also applicable to similar dynamics on bipartite network structures. The dynamics is studied numerically via Lyapunov measures, spatial correlations, and ergodic properties. It is shown that the zeros of the interaction energy are distinguished only with respect to this specific observable, but not by a more general dynamical principle. The original chaotic string model is defined on a one-dimensional lattice (ring-network) as the underlying network topology. This thesis studies a modification of the model based on the introduction of tunable disorder. The effects of inhomogeneous coupling weights as well as small-world perturbations of the ring-network structure on the interaction energy are discussed. Synchronization properties of the chaotic string model and its network generalization are studied in later chapters of this thesis. The analysis is based on the master stability formalism, which relates the stability of the synchronized state to the spectral properties of the network. Apart from complete synchronization, where the dynamics at all nodes of the network coincide, also two-cluster synchronization on bipartite networks is studied. For both types of synchronization it is shown that depending on the type of coupling the synchronized dynamics can display chaotic as well as periodic or quasi-periodic behaviour. The semi-analytical calculations reveal that the respective synchronized states are often stable for a wide range of coupling values even for the ring-network, although the respective basins of attraction may inhabit only a small fraction of the phase space. To provide

  11. Chaotic behaviour induced by space charge

    International Nuclear Information System (INIS)

    Lagniel, J.M.

    1994-01-01

    In numerous non-linear dynamical systems studied in various disciplines (fluid dynamics, celestial mechanisms, chemistry, biology, economy, ecology...), chaotic motions are generated by the dynamics itself whereas no random force is present. This phenomenon, already studied in the particle accelerator field to understand the beam-beam effect, is also observed in numerical experiments on space-charge dominated beams. Stochasticity threshold and halo formation are discussed for a continuous focusing channel (1D beam) and for a FODO channel (2D beam) with the possibility to take into account the defocusing effects of RF gaps localized between the quadrupoles. (authors). 7 refs., 4 figs

  12. Targeting engineering synchronization in chaotic systems

    Science.gov (United States)

    Bhowmick, Sourav K.; Ghosh, Dibakar

    2016-07-01

    A method of targeting engineering synchronization states in two identical and mismatch chaotic systems is explained in detail. The method is proposed using linear feedback controller coupling for engineering synchronization such as mixed synchronization, linear and nonlinear generalized synchronization and targeting fixed point. The general form of coupling design to target any desire synchronization state under unidirectional coupling with the help of Lyapunov function stability theory is derived analytically. A scaling factor is introduced in the coupling definition to smooth control without any loss of synchrony. Numerical results are done on two mismatch Lorenz systems and two identical Sprott oscillators.

  13. Chaotic combustion in spark ignition engines

    International Nuclear Information System (INIS)

    Wendeker, Miroslaw; Czarnigowski, Jacek; Litak, Grzegorz; Szabelski, Kazimierz

    2003-01-01

    We analyse the combustion process in a spark ignition engine using the experimental data of an internal pressure during the combustion process and show that the system can be driven to chaotic behaviour. Our conclusion is based on the observation of unperiodicity in the time series, suitable stroboscopic maps and a complex structure of a reconstructed strange attractor. This analysis can explain that in some circumstances the level of noise in spark ignition engines increases considerably due to nonlinear dynamics of a combustion process

  14. Chaotic spectra: How to extract dynamic information

    International Nuclear Information System (INIS)

    Taylor, H.S.; Gomez Llorente, J.M.; Zakrzewski, J.; Kulander, K.C.

    1988-10-01

    Nonlinear dynamics is applied to chaotic unassignable atomic and molecular spectra with the aim of extracting detailed information about regular dynamic motions that exist over short intervals of time. It is shown how this motion can be extracted from high resolution spectra by doing low resolution studies or by Fourier transforming limited regions of the spectrum. These motions mimic those of periodic orbits (PO) and are inserts into the dominant chaotic motion. Considering these inserts and the PO as a dynamically decoupled region of space, resonant scattering theory and stabilization methods enable us to compute ladders of resonant states which interact with the chaotic quasi-continuum computed in principle from basis sets placed off the PO. The interaction of the resonances with the quasicontinuum explains the low resolution spectra seen in such experiments. It also allows one to associate low resolution features with a particular PO. The motion on the PO thereby supplies the molecular movements whose quantization causes the low resolution spectra. Characteristic properties of the periodic orbit based resonances are discussed. The method is illustrated on the photoabsorption spectrum of the hydrogen atom in a strong magnetic field and on the photodissociation spectrum of H 3 + . Other molecular systems which are currently under investigation using this formalism are also mentioned. 53 refs., 10 figs., 2 tabs

  15. Digital chaotic sequence generator based on coupled chaotic systems

    International Nuclear Information System (INIS)

    Shu-Bo, Liu; Jing, Sun; Jin-Shuo, Liu; Zheng-Quan, Xu

    2009-01-01

    Chaotic systems perform well as a new rich source of cryptography and pseudo-random coding. Unfortunately their digital dynamical properties would degrade due to the finite computing precision. Proposed in this paper is a modified digital chaotic sequence generator based on chaotic logistic systems with a coupling structure where one chaotic subsystem generates perturbation signals to disturb the control parameter of the other one. The numerical simulations show that the length of chaotic orbits, the output distribution of chaotic system, and the security of chaotic sequences have been greatly improved. Moreover the chaotic sequence period can be extended at least by one order of magnitude longer than that of the uncoupled logistic system and the difficulty in decrypting increases 2 128 *2 128 times indicating that the dynamical degradation of digital chaos is effectively improved. A field programmable gate array (FPGA) implementation of an algorithm is given and the corresponding experiment shows that the output speed of the generated chaotic sequences can reach 571.4 Mbps indicating that the designed generator can be applied to the real-time video image encryption. (general)

  16. Deterministic chaotic dynamics of Raba River flow (Polish Carpathian Mountains)

    Science.gov (United States)

    Kędra, Mariola

    2014-02-01

    Is the underlying dynamics of river flow random or deterministic? If it is deterministic, is it deterministic chaotic? This issue is still controversial. The application of several independent methods, techniques and tools for studying daily river flow data gives consistent, reliable and clear-cut results to the question. The outcomes point out that the investigated discharge dynamics is not random but deterministic. Moreover, the results completely confirm the nonlinear deterministic chaotic nature of the studied process. The research was conducted on daily discharge from two selected gauging stations of the mountain river in southern Poland, the Raba River.

  17. A note on synchronization between two different chaotic systems

    International Nuclear Information System (INIS)

    Park, Ju H.

    2009-01-01

    In this paper, a new control method based on the Lyapunov method and linear matrix inequality framework is proposed to design a stabilizing controller for synchronizing two different chaotic systems. The feedback controller is consisted of two parts: linear dynamic control law and nonlinear control one. By this control law, the exponential stability for synchronization between two different chaotic systems is guaranteed. As applications of proposed method, synchronization problem between Genesio-Tesi system and Chen system has been investigated, and then the similar approach is applied to the synchronization problem between Roessler system and Lorenz system.

  18. One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures

    DEFF Research Database (Denmark)

    Belykh, Vladimir N.; Mosekilde, Erik

    1996-01-01

    The paper presents a qualitative analysis of coupled map lattices (CMLs) for the case of arbitrary nonlinearity of the local map and with space-shift as well as diffusion coupling. The effect of synchronization where, independently of the initial conditions, all elements of a CML acquire uniform...... dynamics is investigated and stable chaotic time behaviors, steady structures, and traveling waves are described. Finally, the bifurcations occurring under the transition from spatiotemporal chaos to chaotic synchronization and the peculiarities of CMLs with specific symmetries are discussed....

  19. Stabilization at almost arbitrary points for chaotic systems

    International Nuclear Information System (INIS)

    Huang, C.-S.; Lian, K.-Y.; Su, C.-H.; Wu, J.-W.

    2008-01-01

    We consider how to design a feasible control input for chaotic systems via a suitable input channel to achieve the stabilization at arbitrary points. Regarding the nonlinear systems without naturally defined input vectors, we propose a local stabilization controller which works for almost arbitrary points. Subsequently, according to topologically transitive property for chaotic systems, the feedback control force is activated only when the trajectory passes through the neighboring region of the regulated point. Hence the global stabilization is achieved whereas the control effort of the hybrid controller is extremely low

  20. Controlling chaotic and hyperchaotic systems via energy regulation

    International Nuclear Information System (INIS)

    Laval, L.; M'Sirdi, N.K.

    2003-01-01

    This paper focuses on a new control approach to steer trajectories of chaotic or hyperchaotic systems towards stable periodic orbits or stationary points of interest. This approach mainly consists in a variable structure control (VSC) that we extend by explicitly considering the system energy as basis for both controller design and system stabilization. In this paper, we present some theoretical results for a class of nonlinear (possibly chaotic or hyperchaotic) systems. Then some capabilities of the proposed approach are illustrated through examples related to a four-dimensional hyperchaotic system

  1. Improved numerical solutions for chaotic-cancer-model

    Directory of Open Access Journals (Sweden)

    Muhammad Yasir

    2017-01-01

    Full Text Available In biological sciences, dynamical system of cancer model is well known due to its sensitivity and chaoticity. Present work provides detailed computational study of cancer model by counterbalancing its sensitive dependency on initial conditions and parameter values. Cancer chaotic model is discretized into a system of nonlinear equations that are solved using the well-known Successive-Over-Relaxation (SOR method with a proven convergence. This technique enables to solve large systems and provides more accurate approximation which is illustrated through tables, time history maps and phase portraits with detailed analysis.

  2. Improved numerical solutions for chaotic-cancer-model

    Science.gov (United States)

    Yasir, Muhammad; Ahmad, Salman; Ahmed, Faizan; Aqeel, Muhammad; Akbar, Muhammad Zubair

    2017-01-01

    In biological sciences, dynamical system of cancer model is well known due to its sensitivity and chaoticity. Present work provides detailed computational study of cancer model by counterbalancing its sensitive dependency on initial conditions and parameter values. Cancer chaotic model is discretized into a system of nonlinear equations that are solved using the well-known Successive-Over-Relaxation (SOR) method with a proven convergence. This technique enables to solve large systems and provides more accurate approximation which is illustrated through tables, time history maps and phase portraits with detailed analysis.

  3. Dynamic control of chaotic resonators

    KAUST Repository

    Di Falco, A.; Bruck, R.; Liu, C.; Muskens, O.; Fratalocchi, Andrea

    2016-01-01

    We report on the all-optical control of chaotic optical resonators based on silicon on insulator (SOI) platform. We show that simple non-chaotic cavities can be tuned to exhibit chaotic behavior via intense optical pump- ing, inducing a local change of refractive index. To this extent we have fabricated a number of devices and demonstrated experimentally and theoretically that chaos can be triggered on demand on an optical chip. © 2016 SPIE.

  4. Dynamic control of chaotic resonators

    KAUST Repository

    Di Falco, A.

    2016-02-16

    We report on the all-optical control of chaotic optical resonators based on silicon on insulator (SOI) platform. We show that simple non-chaotic cavities can be tuned to exhibit chaotic behavior via intense optical pump- ing, inducing a local change of refractive index. To this extent we have fabricated a number of devices and demonstrated experimentally and theoretically that chaos can be triggered on demand on an optical chip. © 2016 SPIE.

  5. Nonlinearly driven oscillations in the gyrotron traveling-wave amplifier

    International Nuclear Information System (INIS)

    Chiu, C. C.; Pao, K. F.; Yan, Y. C.; Chu, K. R.; Barnett, L. R.; Luhmann, N. C. Jr.

    2008-01-01

    By delivering unprecedented power and gain, the gyrotron traveling-wave amplifier (gyro-TWT) offers great promise for advanced millimeter wave radars. However, the underlying physics of this complex nonlinear system is yet to be fully elucidated. Here, we report a new phenomenon in the form of nonlinearly driven oscillations. A zero-drive stable gyro-TWT is shown to be susceptible to a considerably reduced dynamic range at the band edge, followed by a sudden transition into driven oscillations and then a hysteresis effect. An analysis of this unexpected behavior and its physical interpretation are presented.

  6. Controller Synthesis for Periodically Forced Chaotic Systems

    Science.gov (United States)

    Basso, Michele; Genesio, Roberto; Giovanardi, Lorenzo

    Delayed feedback controllers are an appealing tool for stabilization of periodic orbits in chaotic systems. Despite their conceptual simplicity, specific and reliable design procedures are difficult to obtain, partly also because of their inherent infinite-dimensional structure. This chapter considers the use of finite dimensional linear time invariant controllers for stabilization of periodic solutions in a general class of sinusoidally forced nonlinear systems. For such controllers — which can be interpreted as rational approximations of the delayed ones — we provide a computationally attractive synthesis technique based on Linear Matrix Inequalities (LMIs), by mixing results concerning absolute stability of nonlinear systems and robustness of uncertain linear systems. The resulting controllers prove to be effective for chaos suppression in electronic circuits and systems, as shown by two different application examples.

  7. Theory and Analysis of JolTech’s GyroPTO

    DEFF Research Database (Denmark)

    Kurniawan, Adi; Kofoed, Jens Peter; Kramer, Morten Mejlhede

    This report summarizes the work done by Aalborg University (AAU) for the project \\Gyro electric energy converter theory and analysis" (Olsen, 2015). The project's objective is to build a theoretical knowledge about gyro electric energy conversion systems, particularly for use in connection...

  8. Stochastic and Chaotic Relaxation Oscillations

    NARCIS (Netherlands)

    Grasman, J.; Roerdink, J.B.T.M.

    1988-01-01

    For relaxation oscillators stochastic and chaotic dynamics are investigated. The effect of random perturbations upon the period is computed. For an extended system with additional state variables chaotic behavior can be expected. As an example, the Van der Pol oscillator is changed into a

  9. Gyro-effect stabilizes unstable permanent maglev centrifugal pump.

    Science.gov (United States)

    Qian, Kun-Xi

    2007-03-01

    According to Earnshaw's Theorem (1839), the passive maglev cannot achieve stable equilibrium and thus an extra coil is needed to make the rotor electrically levitated in a heart pump. The author had developed a permanent maglev centrifugal pump utilizing only passive magnetic bearings, to keep the advantages but to avoid the disadvantages of the electric maglev pumps. The equilibrium stability was achieved by use of so-called "gyro-effect": a rotating body with certain high speed can maintain its rotation stably. This pump consisted of a rotor (driven magnets and an impeller), and a stator with motor coil and pump housing. Two passive magnetic bearings between rotor and stator were devised to counteract the attractive force between the motor coil iron core and the rotor driven magnets. Bench testing with saline demonstrated a levitated rotor under preconditions of higher than 3,250 rpm rotation and more than 1 l/min pumping flow. Rotor levitation was demonstrated by 4 Hall sensors on the stator, with evidence of reduced maximal eccentric distance from 0.15 mm to 0.07 mm. The maximal rotor vibration amplitude was 0.06 mm in a gap of 0.15 mm between rotor and stator. It concluded that Gyro-effect can help passive maglev bearings to achieve stabilization of permanent maglev pump; and that high flow rate indicates good hydraulic property of the pump, which helps also the stability of passive maglev pump.

  10. Pierce-Wiggler electron beam system for 250 GHz GYRO-BWO: Final report

    International Nuclear Information System (INIS)

    Pirkle, D.R.; Alford, C.W.; Anderson, M.H.; Garcia, R.F.; Legarra, J.R.; Nordquist, A.L.

    1989-01-01

    This final report summarizes the design and performance of the VUW-8028 Pierce-Wiggler electron beam systems, which can be used to power high frequency gyro-BWO's. The operator's manual for this gyro-BWO beamstick is included as appendix A. Researchers at Lawrence Livermore National Laboratory (LLNL) are developing a gyro-BWO with a center frequency of 250 GHz, 6% bandwidth, and 10 kV peak output power. The gyro-BWO will be used to drive a free electron laser amplifier at LLNL. The electron beam requirements of the gyro-BWO application are: Small beam size, .100 inch at 2500 gauss axial magnetic field; a large fraction of the electron energy in rotational velocity; ability to vary the electrons' axial velocity easily, for electronic tuning; and low velocity spread i.e. little variation in the axial velocities of the electrons in the interaction region. 1 ref., 13 figs

  11. Period multiplication and chaotic phenomena in atmospheric dielectric-barrier glow discharges

    International Nuclear Information System (INIS)

    Wang, Y. H.; Zhang, Y. T.; Wang, D. Z.; Kong, M. G.

    2007-01-01

    In this letter, evidence of temporal plasma nonlinearity in which atmospheric dielectric-barrier discharges undergo period multiplication and chaos using a one-dimensional fluid model is reported. Under the conditions conducive for chaotic states, several frequency windows are identified in which period multiplication and secondary bifurcations are observed. Such time-domain nonlinearity is important for controlling instabilities in atmospheric glow discharges

  12. Chaotic characteristics of corona discharges in atmospheric air

    International Nuclear Information System (INIS)

    Tan Xiangyu; Zhang Qiaogen; Wang Xiuhuan; Sun Fu; Zha Wei; Jia Zhijie

    2008-01-01

    A point-plane electrode system in atmospheric air is established to investigate the mechanism of the corona discharge. By using this system, the current pulses of the corona discharges under the 50 Hz ac voltage are measured using partial discharge (PD) measurement instrument and constitute the point-plane voltage-current (V-I) characteristic equation together with the voltage. Then, this paper constructs the nonlinear circuit model and differential equations of the system in an attempt to give the underlying dynamic mechanism based on the nonlinear V-I characteristics of the point-plane corona discharges. The results show that the chaotic phenomenon is found in the corona circuit by the experimental study and nonlinear dynamic analysis. The basic dynamic characteristics, including the Lyapunov exponent, the existence of the strange attractors, and the equilibrium points, are also found and analyzed in the development process of the corona circuit. Moreover, the time series of the corona current pulses obtained in the experiment is used to demonstrate the chaotic characteristics of the corona current based on the nonlinear dynamic circuit theory and the experimental basis. It is pointed out that the corona phenomenon is not a purely stochastic phenomenon but a short term deterministic chaotic activity

  13. Parameter Identification and Synchronization of Uncertain Chaotic Systems Based on Sliding Mode Observer

    Directory of Open Access Journals (Sweden)

    Li-lian Huang

    2013-01-01

    Full Text Available The synchronization of nonlinear uncertain chaotic systems is investigated. We propose a sliding mode state observer scheme which combines the sliding mode control with observer theory and apply it into the uncertain chaotic system with unknown parameters and bounded interference. Based on Lyapunov stability theory, the constraints of synchronization and proof are given. This method not only can realize the synchronization of chaotic systems, but also identify the unknown parameters and obtain the correct parameter estimation. Otherwise, the synchronization of chaotic systems with unknown parameters and bounded external disturbances is robust by the design of the sliding surface. Finally, numerical simulations on Liu chaotic system with unknown parameters and disturbances are carried out. Simulation results show that this synchronization and parameter identification has been totally achieved and the effectiveness is verified very well.

  14. Identifying Chaotic FitzHugh–Nagumo Neurons Using Compressive Sensing

    Directory of Open Access Journals (Sweden)

    Ri-Qi Su

    2014-07-01

    Full Text Available We develop a completely data-driven approach to reconstructing coupled neuronal networks that contain a small subset of chaotic neurons. Such chaotic elements can be the result of parameter shift in their individual dynamical systems and may lead to abnormal functions of the network. To accurately identify the chaotic neurons may thus be necessary and important, for example, applying appropriate controls to bring the network to a normal state. However, due to couplings among the nodes, the measured time series, even from non-chaotic neurons, would appear random, rendering inapplicable traditional nonlinear time-series analysis, such as the delay-coordinate embedding method, which yields information about the global dynamics of the entire network. Our method is based on compressive sensing. In particular, we demonstrate that identifying chaotic elements can be formulated as a general problem of reconstructing the nodal dynamical systems, network connections and all coupling functions, as well as their weights. The working and efficiency of the method are illustrated by using networks of non-identical FitzHugh–Nagumo neurons with randomly-distributed coupling weights.

  15. Nonlinear Hamiltonian systems

    DEFF Research Database (Denmark)

    Jørgensen, Michael Finn

    1995-01-01

    It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...... particular configurations of the Discrete Self-Trapping (DST) system are shown to be completely solvable. One of these systems includes the Toda lattice in a certain limit. An explicit integration is carried through for this Near-Toda lattice. The Near-Toda lattice is then generalized to include singular...

  16. Chaotic Darcy-Brinkman convection in a fluid saturated porous layer subjected to gravity modulation

    Directory of Open Access Journals (Sweden)

    Moli Zhao

    2018-06-01

    Full Text Available On the basis of Darcy-Brinkman model, the chaotic convection in a couple stress fluid saturated porous media under gravity modulation is investigated using the nonlinear stability analyses. The transition from steady convection to chaos is analysed with the effect of Darcy-Brinkman couple stress parameter and the gravity modulation. The results show that the chaotic behavior is connected with the critical value of Rayleigh number which is dependent upon the oscillation frequency and the Darcy-Brinkman couple stress parameter. If the oscillation frequency Ω is not zero, the Rayleigh number value R of the chaotic behavior increases with the increase of the Darcy-Brinkman couple stress parameter. The Darcy-Brinkman couple stress parameter and the gravity modulation decrease the rate of heat transfer. Keywords: Darcy-Brinkman model, Gravity modulation, Nonlinear stability, Chaotic convection

  17. Chaotic System Identification Based on a Fuzzy Wiener Model with Particle Swarm Optimization

    International Nuclear Information System (INIS)

    Yong, Li; Ying-Gan, Tang

    2010-01-01

    A fuzzy Wiener model is proposed to identify chaotic systems. The proposed fuzzy Wiener model consists of two parts, one is a linear dynamic subsystem and the other is a static nonlinear part, which is represented by the Takagi–Sugeno fuzzy model. Identification of chaotic systems is converted to find optimal parameters of the fuzzy Wiener model by minimizing the state error between the original chaotic system and the fuzzy Wiener model. Particle swarm optimization algorithm, a global optimizer, is used to search the optimal parameter of the fuzzy Wiener model. The proposed method can identify the parameters of the linear part and nonlinear part simultaneously. Numerical simulations for Henón and Lozi chaotic system identification show the effectiveness of the proposed method

  18. Chaos control in delayed chaotic systems via sliding mode based delayed feedback

    Energy Technology Data Exchange (ETDEWEB)

    Vasegh, Nastaran [Faculty of Electrical Engineering, K.N. Toosi University of Technology, Seyed Khandan Bridge, Shariati St. 16314, P.O. Box 16315-1355, Tehran (Iran, Islamic Republic of)], E-mail: vasegh@eetd.kntu.ac.ir; Sedigh, Ali Khaki [Faculty of Electrical Engineering, K.N. Toosi University of Technology, Seyed Khandan Bridge, Shariati St. 16314, P.O. Box 16315-1355, Tehran (Iran, Islamic Republic of)

    2009-04-15

    This paper investigates chaos control for scalar delayed chaotic systems using sliding mode control strategy. Sliding surface design is based on delayed feedback controller. It is shown that the proposed controller can achieve stability for an arbitrary unstable fixed point (UPF) or unstable periodic orbit (UPO) with arbitrary period. The chaotic system used in this study to illustrate the theoretical concepts is the well known Mackey-Glass model. Simulation results show the effectiveness of the designed nonlinear sliding mode controller.

  19. Chaos control in delayed chaotic systems via sliding mode based delayed feedback

    International Nuclear Information System (INIS)

    Vasegh, Nastaran; Sedigh, Ali Khaki

    2009-01-01

    This paper investigates chaos control for scalar delayed chaotic systems using sliding mode control strategy. Sliding surface design is based on delayed feedback controller. It is shown that the proposed controller can achieve stability for an arbitrary unstable fixed point (UPF) or unstable periodic orbit (UPO) with arbitrary period. The chaotic system used in this study to illustrate the theoretical concepts is the well known Mackey-Glass model. Simulation results show the effectiveness of the designed nonlinear sliding mode controller.

  20. Advances in the simulation of toroidal gyro Landau fluid model turbulence

    International Nuclear Information System (INIS)

    Waltz, R.E.; Kerbel, G.D.; Milovich, J.; Hammett, G.W.

    1994-12-01

    The gyro-Landau fluid (GLF) model equations for toroidal geometry have been recently applied to the study ion temperature gradient (ITG) mode turbulence using the 3D nonlinear ballooning mode representation (BMR). The present paper extends this work by treating some unresolved issues conceming ITG turbulence with adiabatic electrons. Although eddies are highly elongated in the radial direction long time radial correlation lengths are short and comparable to poloidal lengths. Although transport at vanishing shear is not particularly large, transport at reverse global shear, is significantly less. Electrostatic transport at moderate shear is not much effected by inclusion of local shear and average favorable curvature. Transport is suppressed when critical ExB rotational shear is comparable to the maximum linear growth rate with only a weak dependence on magnetic shear. Self consistent turbulent transport of toroidal momentum can result in a transport bifurcation at suffciently large r/(Rq). However the main thrust of the new formulation in the paper deals with advances in the development of finite beta GLF models with trapped electron and BMR numerical methods for treating the fast parallel field motion of the untrapped electrons

  1. Correlation control theory of chaotic laser systems

    International Nuclear Information System (INIS)

    Li Fuli.

    1986-04-01

    A novel control theory of chaotic systems is studied. The correlation functions are calculated and used as feedback signals of the chaotic lasers. Computer experiments have shown that in this way the chaotic systems can be controlled to have time-independent output when the external control parameters are in chaotic domain. (author)

  2. Mixed-mode chaotic circuit with Wien-bridge configuration: The results of experimental verification

    Energy Technology Data Exchange (ETDEWEB)

    Kilic, Recai [Erciyes University, Department of Electronic Engineering, 38039 Kayseri (Turkey)]. E-mail: kilic@erciyes.edu.tr

    2007-05-15

    In this paper, we deal with the experimentally implementation of inductorless Wien bridge-based mixed-mode chaotic circuit (MMCC) which is capable to exhibit both linear and nonlinear oscillations. The results of experimental implementation agree with the results of theoretical and computer simulation presented in literature. Since the proposed implementation of MMCC circuit uses different design blocks such as Wien bridge-based autonomous circuit part, CFOA (current feedback operational amplifier)-based floating inductance simulator, CFOA-based Chua's diode and switching mechanism, it offers very versatile chaotic circuit model for studying autonomous and nonautonomous chaotic dynamics.

  3. Mixed-mode chaotic circuit with Wien-bridge configuration: The results of experimental verification

    International Nuclear Information System (INIS)

    Kilic, Recai

    2007-01-01

    In this paper, we deal with the experimentally implementation of inductorless Wien bridge-based mixed-mode chaotic circuit (MMCC) which is capable to exhibit both linear and nonlinear oscillations. The results of experimental implementation agree with the results of theoretical and computer simulation presented in literature. Since the proposed implementation of MMCC circuit uses different design blocks such as Wien bridge-based autonomous circuit part, CFOA (current feedback operational amplifier)-based floating inductance simulator, CFOA-based Chua's diode and switching mechanism, it offers very versatile chaotic circuit model for studying autonomous and nonautonomous chaotic dynamics

  4. Fuzzy model-based adaptive synchronization of time-delayed chaotic systems

    International Nuclear Information System (INIS)

    Vasegh, Nastaran; Majd, Vahid Johari

    2009-01-01

    In this paper, fuzzy model-based synchronization of a class of first order chaotic systems described by delayed-differential equations is addressed. To design the fuzzy controller, the chaotic system is modeled by Takagi-Sugeno fuzzy system considering the properties of the nonlinear part of the system. Assuming that the parameters of the chaotic system are unknown, an adaptive law is derived to estimate these unknown parameters, and the stability of error dynamics is guaranteed by Lyapunov theory. Numerical examples are given to demonstrate the validity of the proposed adaptive synchronization approach.

  5. Application of fixed point theory to chaotic attractors of forced oscillators

    International Nuclear Information System (INIS)

    Stewart, H.B.

    1990-11-01

    A review of the structure of chaotic attractors of periodically forced second order nonlinear oscillators suggests that the theory of fixed points of transformations gives information about the fundamental topological structure of attractors. First a simple extension of the Levinson index formula is proved. Then numerical evidence is used to formulate plausible conjectures about absorbing regions containing chaotic attractors in forced oscillators. Applying the Levinson formula suggests a fundamental relation between the number of fixed points or periodic points in a section of the chaotic attractor on the one hand, and a topological invariant of an absorbing region on the other hand. (author)

  6. Memcapacitor model and its application in chaotic oscillator with memristor.

    Science.gov (United States)

    Wang, Guangyi; Zang, Shouchi; Wang, Xiaoyuan; Yuan, Fang; Iu, Herbert Ho-Ching

    2017-01-01

    Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.

  7. NATO Advanced Study Institute on Chaotic Dynamics : Theory and Practice

    CERN Document Server

    1992-01-01

    Many conferences, meetings, workshops, summer schools and symposia on nonlinear dynamical systems are being organized these days, dealing with a great variety of topics and themes -classical and quantum, theoretical and experimental. Some focus on integrability, or discuss the mathematical foundations of chaos. Others explore the beauty of fractals, or examine endless possibilities of applications to problems of physics, chemistry, biology and other sciences. A new scientific discipline has thus emerged, with its own distinct philosophical viewpoint and an impressive arsenal of new methods and techniques, which may be called Chaotic Dynamics. Perhaps its most outstanding achievement so far has been to shed new light on many long­ standing issues involving complicated, irregular or "chaotic" nonlinear phenomena. The concepts of randomness, complexity and unpredictability have been critically re-examined and the fundamental importance of scaling, self-similarity and sensitive dependence on parameters a...

  8. Chaotic time series. Part II. System Identification and Prediction

    Directory of Open Access Journals (Sweden)

    Bjørn Lillekjendlie

    1994-10-01

    Full Text Available This paper is the second in a series of two, and describes the current state of the art in modeling and prediction of chaotic time series. Sample data from deterministic non-linear systems may look stochastic when analysed with linear methods. However, the deterministic structure may be uncovered and non-linear models constructed that allow improved prediction. We give the background for such methods from a geometrical point of view, and briefly describe the following types of methods: global polynomials, local polynomials, multilayer perceptrons and semi-local methods including radial basis functions. Some illustrative examples from known chaotic systems are presented, emphasising the increase in prediction error with time. We compare some of the algorithms with respect to prediction accuracy and storage requirements, and list applications of these methods to real data from widely different areas.

  9. Chaotic behavior in nuclei

    International Nuclear Information System (INIS)

    Mitchel, G.; Shriner, J.

    2005-01-01

    Although the predictions of Random Matrix Theory (RMT) were available by the early 1960s, data of sufficiently high quality to adequately test the theory were only obtained a decade later by Rainwater. It was another decade later that Bohigas, Haq and Pandey combined the best available nuclear resonance data - the Columbia neutron resonances in heavy nuclei and the TUNL proton resonances in lighter nuclei - to form the Nuclear Data Ensemble. They obtained excellent agreement for the level statistics with the RMT predictions. The expected Porter-Thomas (PT) distribution was considered very early. However, since the widths (amplitudes squared) are measured, the predicted Gaussian distribution for the amplitudes was only qualitatively confirmed. A much more sensitive test was performed by measuring two widths and the relative phase between the two amplitudes. By comparison of the width and amplitude correlations, the Gaussian distribution was confirmed at the 1% level. Following the Bohigas conjecture - that quantum analogs of classically chaotic systems obey RMT - there was an explosion of activity utilizing level statistics in many different quantum systems. In nuclei the focus was verifying the range of applicability of RMT. Of particular interest was the effect of collectivity and of excitation energy on statistical properties. The effect of symmetry breaking on level statistics was examined and early predictions by Dyson were confirmed. The effect of symmetry breaking on the width distribution was also measured for the first time. Although heuristic arguments predicted no change from the PT distribution, experimentally there was a large deviation from the PT prediction. Later theoretical efforts were consistent with this result. The stringent conditions placed on the experiments - for eigenvalue tests the data need to be essentially perfect (few or no missing levels or mis assigned quantum numbers) - has limited the amount of suitable experimental data. The

  10. Chaotic advection in the ocean

    Energy Technology Data Exchange (ETDEWEB)

    Koshel' , Konstantin V; Prants, Sergei V [V.I. Il' ichev Pacific Oceanological Institute, Far-Eastern Division of the Russian Academy of Sciences, Vladivostok (Russian Federation)

    2006-11-30

    The problem of chaotic advection of passive scalars in the ocean and its topological, dynamical, and fractal properties are considered from the standpoint of the theory of dynamical systems. Analytic and numerical results on Lagrangian transport and mixing in kinematic and dynamic chaotic advection models are described for meandering jet currents, topographical eddies in a barotropic ocean, and a two-layer baroclinic ocean. Laboratory experiments on hydrodynamic flows in rotating tanks as an imitation of geophysical chaotic advection are described. Perspectives of a dynamical system approach in physical oceanography are discussed. (reviews of topical problems)

  11. Eigenfunctions in chaotic quantum systems

    Energy Technology Data Exchange (ETDEWEB)

    Baecker, Arnd

    2007-07-01

    The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)

  12. Eigenfunctions in chaotic quantum systems

    International Nuclear Information System (INIS)

    Baecker, Arnd

    2007-01-01

    The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)

  13. Experimental chaotic quantification in bistable vortex induced vibration systems

    Science.gov (United States)

    Huynh, B. H.; Tjahjowidodo, T.

    2017-02-01

    The study of energy harvesting by means of vortex induced vibration systems has been initiated a few years ago and it is considered to be potential as a low water current energy source. The energy harvester is realized by exposing an elastically supported blunt structure under water flow. However, it is realized that the system will only perform at a limited operating range (water flow) that is attributed to the resonance phenomenon that occurs only at a frequency that corresponds to the fluid flow. An introduction of nonlinear elements seems to be a prominent solution to overcome the problem. Among many nonlinear elements, a bistable spring is known to be able to improve the harvested power by a vortex induced vibrations (VIV) based energy converter at the low velocity water flows. However, it is also observed that chaotic vibrations will occur at different operating ranges that will erratically diminish the harvested power and cause a difficulty in controlling the system that is due to the unpredictability in motions of the VIV structure. In order to design a bistable VIV energy converter with improved harvested power and minimum negative effect of chaotic vibrations, the bifurcation map of the system for varying governing parameters is highly on demand. In this study, chaotic vibrations of a VIV energy converter enhanced by a bistable stiffness element are quantified in a wide range of the governing parameters, i.e. damping and bistable gap. Chaotic vibrations of the bistable VIV energy converter are simulated by utilization of a wake oscillator model and quantified based on the calculation of the Lyapunov exponent. Ultimately, a series of experiments of the system in a water tunnel, facilitated by a computer-based force-feedback testing platform, is carried out to validate the existence of chaotic responses. The main challenge in dealing with experimental data is in distinguishing chaotic response from noise-contaminated periodic responses as noise will smear

  14. Accurate frequency measurements on gyrotrons using a ''gyro-radiometer''

    International Nuclear Information System (INIS)

    Rebuffi, L.

    1986-08-01

    Using an heterodyne system, called ''Gyro-radiometer'', accurated frequency measurements have been carried out on VARIAN 60 GHz gyrotrons. Changing the principal tuning parameters of a gyrotron, we have detected frequency variations up to 100 MHz, ∼ 40 MHz frequency jumps and smaller jumps (∼ 10 MHz) when mismatches in the transmission line were present. FWHM bandwidth of 300 KHz, parasitic frequencies and frequency drift during 100 msec pulses have also been observed. An efficient method to find a stable-, high power-, long pulse-working point of a gyrotron loaded by a transmission line, has been derived. In general, for any power value it is possible to find stable working conditions tuning the principal parameters of the tube in correspondance of a maximum of the emitted frequency

  15. Bridge continuous deformation measurement technology based on fiber optic gyro

    Science.gov (United States)

    Gan, Weibing; Hu, Wenbin; Liu, Fang; Tang, Jianguang; Li, Sheng; Yang, Yan

    2016-03-01

    Bridge is an important part of modern transportation systems and deformation is a key index for bridge's safety evaluation. To achieve the long span bridge curve measurement rapidly and timely and accurately locate the bridge maximum deformation, the continuous deformation measurement system (CDMS) based on inertial platform is presented and validated in this paper. Firstly, based on various bridge deformation measurement methods, the method of deformation measurement based on the fiber optic gyro (FOG) is introduced. Secondly, the basic measurement principle based on FOG is presented and the continuous curve trajectory is derived by the formula. Then the measurement accuracy is analyzed in theory and the relevant factors are presented to ensure the measurement accuracy. Finally, the deformation measurement experiments are conducted on a bridge across the Yangtze River. Experimental results show that the presented deformation measurement method is feasible, practical, and reliable; the system can accurately and quickly locate the maximum deformation and has extensive and broad application prospects.

  16. Complex network synchronization of chaotic systems with delay coupling

    International Nuclear Information System (INIS)

    Theesar, S. Jeeva Sathya; Ratnavelu, K.

    2014-01-01

    The study of complex networks enables us to understand the collective behavior of the interconnected elements and provides vast real time applications from biology to laser dynamics. In this paper, synchronization of complex network of chaotic systems has been studied. Every identical node in the complex network is assumed to be in Lur’e system form. In particular, delayed coupling has been assumed along with identical sector bounded nonlinear systems which are interconnected over network topology

  17. Small-world networks of fuzzy chaotic oscillators

    CERN Document Server

    Bucolo, M; Fortuna, L

    2003-01-01

    Small-world topology has been used to build lattices of nonlinear fuzzy systems. Chaotic units, ruled by linguistic description and with specified Lyapunov exponent, have been realized and connected using linear diffusion coefficient. The dynamic features of the networks versus the number of systems connected have been investigated to underline phenomena like spatiotemporal chaos and complete regularization. The synchronization characteristics in case of sparse long-term connections and the performances comparison with regular and random network configurations are shown.

  18. Experimentally determined chaotic phase synchronization in a neuronal system

    OpenAIRE

    Makarenko, Vladimir; Llinás, Rodolfo

    1998-01-01

    Mathematical analysis of the subthreshold oscillatory properties of inferior olivary neurons in vitro indicates that the oscillation is nonlinear and supports low dimensional chaotic dynamics. This property leads to the generation of complex functional states that can be attained rapidly via phase coherence that conform to the category of “generalized synchronization.” Functionally, this translates into neuronal ensemble properties that can support maximum functional permissiveness and that r...

  19. Characterization of the Bell-Shaped Vibratory Angular Rate Gyro

    Directory of Open Access Journals (Sweden)

    Junfang Fan

    2013-08-01

    Full Text Available The bell-shaped vibratory angular rate gyro (abbreviated as BVG is a novel shell vibratory gyroscope, which is inspired by the Chinese traditional bell. It sensitizes angular velocity through the standing wave precession effect. The bell-shaped resonator is a core component of the BVG and looks like the millimeter-grade Chinese traditional bell, such as QianLong Bell and Yongle Bell. It is made of Ni43CrTi, which is a constant modulus alloy. The exciting element, control element and detection element are uniformly distributed and attached to the resonator, respectively. This work presents the design, analysis and experimentation on the BVG. It is most important to analyze the vibratory character of the bell-shaped resonator. The strain equation, internal force and the resonator's equilibrium differential equation are derived in the orthogonal curvilinear coordinate system. When the input angular velocity is existent on the sensitive axis, an analysis of the vibratory character is performed using the theory of thin shells. On this basis, the mode shape function and the simplified second order normal vibration mode dynamical equation are obtained. The coriolis coupling relationship about the primary mode and secondary mode is established. The methods of the signal processing and control loop are presented. Analyzing the impact resistance property of the bell-shaped resonator, which is compared with other shell resonators using the Finite Element Method, demonstrates that BVG has the advantage of a better impact resistance property. A reasonable means of installation and a prototypal gyro are designed. The gyroscopic effect of the BVG is characterized through experiments. Experimental results show that the BVG has not only the advantages of low cost, low power, long work life, high sensitivity, and so on, but, also, of a simple structure and a better impact resistance property for low and medium angular velocity measurements.

  20. Symposium Gyro Technology 1984; Proceedings of the Symposium, Universitaet Stuttgart, West Germany, September 11, 12, 1984

    Science.gov (United States)

    Sorg, H.

    Among the topics discussed are: drift and scale factor tests on the SEL fiber gyro; integrated optical rate sensor development; and the beam geometry of a ring laser gyro in relation to its performance. Consideration is also given to: a fast filtering technique for measuring random walk in a laser gyro; vibratory gyroscopic sensors; a redundant strapdown reference for advanced aircraft flight control systems; and a low-cost piezoelectric rate/acceleration sensor. Additional topics include: an inertial guidance system for a Low-Earth-Orbit (LEO) vehicle; and signal disturbance effects in a strapdown northfinder.

  1. Electron collisions in the trapped gyro-Landau fluid transport model

    International Nuclear Information System (INIS)

    Staebler, G. M.; Kinsey, J. E.

    2010-01-01

    Accurately modeling electron collisions in the trapped gyro-Landau fluid (TGLF) equations has been a major challenge. Insights gained from numerically solving the gyrokinetic equation have lead to a significant improvement of the low order TGLF model. The theoretical motivation and verification of this model with the velocity-space gyrokinetic code GYRO[J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] will be presented. The improvement in the fidelity of TGLF to GYRO is shown to also lead to better prediction of experimental temperature profiles by TGLF for a dedicated collision frequency scan.

  2. Nuclear friction and chaotic motion

    International Nuclear Information System (INIS)

    Srokowski, T.; Szczurek, A.; Drozdz, S.

    1990-01-01

    The concept of nuclear friction is considered from the point of view of regular versus chaotic motion in an atomic nucleus. Using a realistic nuclear Hamiltonian it is explicitly shown that the frictional description of the gross features of nuclear collisions is adequate if the system behaves chaotically. Because of the core in the Hamiltonian, the three-body nuclear system already reveals a structure of the phase space rich enough for this concept to be applicable

  3. Chaotic diagonal recurrent neural network

    International Nuclear Information System (INIS)

    Wang Xing-Yuan; Zhang Yi

    2012-01-01

    We propose a novel neural network based on a diagonal recurrent neural network and chaos, and its structure and learning algorithm are designed. The multilayer feedforward neural network, diagonal recurrent neural network, and chaotic diagonal recurrent neural network are used to approach the cubic symmetry map. The simulation results show that the approximation capability of the chaotic diagonal recurrent neural network is better than the other two neural networks. (interdisciplinary physics and related areas of science and technology)

  4. Identification of chaotic memristor systems based on piecewise adaptive Legendre filters

    International Nuclear Information System (INIS)

    Zhao, Yibo; Zhang, Xiuzai; Xu, Jin; Guo, Yecai

    2015-01-01

    Memristor is a nonlinear device, which plays an important role in the design and implementation of chaotic systems. In order to be able to understand in-depth the complex nonlinear dynamic behaviors in chaotic memristor systems, modeling or identification of its nonlinear model is very important premise. This paper presents a chaotic memristor system identification method based on piecewise adaptive Legendre filters. The threshold decomposition is carried out for the input vector, and also the input signal subintervals via decomposition satisfy the convergence condition of the adaptive Legendre filters. Then the adaptive Legendre filter structure and adaptive weight update algorithm are derived. Final computer simulation results show the effectiveness as well as fast convergence characteristics.

  5. Chaotic mechanics in systems with impacts and friction

    CERN Document Server

    Blazejczyk-Okolewska, Barbara; Kapitaniak, Tomasz; Wojewoda, Jerzy

    1999-01-01

    This book is devoted to the theory of chaotic oscillations in mechanical systems. Detailed descriptions of the basic types of nonlinearity - impacts and dry friction - are presented. The properties of such behavior are discussed, and the numerical and experimental results obtained by the authors are presented.The dynamic properties of systems described here can be useful in the proper design and use of mechanics where such behavior still creates problems.This book will be very useful for anyone with a fundamental knowledge of nonlinear mechanics who is beginning research in the field.

  6. The North American natural gas liquids markets are chaotic

    Energy Technology Data Exchange (ETDEWEB)

    Serletis, A.; Gogas, P. (Univ. of Calgary, Alberta (Canada). Dept. of Economics)

    1999-01-01

    In this paper the authors test for deterministic chaos (i.e., nonlinear deterministic processes which look random) in seven Mont Belview, Texas hydrocarbon markets, using monthly data from 1985:1 to 1996:12--the markets are those of ethane, propane, normal butane, iso-butane, naptha, crude oil, and natural gas. In doing so, they use the Lyapunov exponent estimator of Nychka, Ellner, Gallant, and McCaffrey. They conclude that there is evidence consistent with a chaotic nonlinear generation process in all five natural gas liquids markets.

  7. Evaluation of nonlinearity and validity of nonlinear modeling for complex time series.

    Science.gov (United States)

    Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo

    2007-10-01

    Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

  8. Dimension of chaotic attractors

    Energy Technology Data Exchange (ETDEWEB)

    Farmer, J.D.; Ott, E.; Yorke, J.A.

    1982-09-01

    Dimension is perhaps the most basic property of an attractor. In this paper we discuss a variety of different definitions of dimension, compute their values for a typical example, and review previous work on the dimension of chaotic attractors. The relevant definitions of dimension are of two general types, those that depend only on metric properties, and those that depend on probabilistic properties (that is, they depend on the frequency with which a typical trajectory visits different regions of the attractor). Both our example and the previous work that we review support the conclusion that all of the probabilistic dimensions take on the same value, which we call the dimension of the natural measure, and all of the metric dimensions take on a common value, which we call the fractal dimension. Furthermore, the dimension of the natural measure is typically equal to the Lyapunov dimension, which is defined in terms of Lyapunov numbers, and thus is usually far easier to calculate than any other definition. Because it is computable and more physically relevant, we feel that the dimension of the natural measure is more important than the fractal dimension.

  9. Chaotic behaviour of the Rossler model and its analysis by using bifurcations of limit cycles and chaotic attractors

    Science.gov (United States)

    Ibrahim, K. M.; Jamal, R. K.; Ali, F. H.

    2018-05-01

    The behaviour of certain dynamical nonlinear systems are described in term as chaos, i.e., systems’ variables change with the time, displaying very sensitivity to initial conditions of chaotic dynamics. In this paper, we study archetype systems of ordinary differential equations in two-dimensional phase spaces of the Rössler model. A system displays continuous time chaos and is explained by three coupled nonlinear differential equations. We study its characteristics and determine the control parameters that lead to different behavior of the system output, periodic, quasi-periodic and chaos. The time series, attractor, Fast Fourier Transformation and bifurcation diagram for different values have been described.

  10. GyroVR: Simulating Inertia in Virtual Reality using Head Worn Flywheels

    DEFF Research Database (Denmark)

    Gugenheimer, Jan; Wolf, Dennis; Eiríksson, Eyþór Rúnar

    2016-01-01

    We present GyroVR, head worn flywheels designed to render inertia in Virtual Reality (VR. Motions such as flying, diving or floating in outer space generate kinesthetic forces onto our body which impede movement and are currently not represented in VR. We simulate those kinesthetic forces...... by attaching flywheels to the users head, leveraging the gyroscopic effect of resistance when changing the spinning axis of rotation. GyroVR is an ungrounded, wireless and self contained device allowing the user to freely move inside the virtual environment. The generic shape allows to attach it to different...... positions on the users body. We evaluated the impact of GyroVR onto different mounting positions on the head (back and front) in terms of immersion, enjoyment and simulator sickness. Our results show, that attaching GyroVR onto the users head (front of the Head Mounted Display (HMD)) resulted in the highest...

  11. On the gyro resonance electron-whistler interaction in transition layers of near-earth plasma

    International Nuclear Information System (INIS)

    Erokhin, N.S.; Zol'nikova, N.N.; Mikhajlovskaya, L.A.

    1996-01-01

    Gyro resonance interaction of electrons with low amplitude triggered whistler in the transition layers of the ionospheric and magnetospheric plasma that correspond to the blurred jumps of the magnetic field and plasma concentration was studied

  12. Study of sensitivity enhancement and dead band elimination in laser gyros, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — The essential elements that characterize the performance of a laser gyro are (a) a bidirectional ring laser, (b) a lightweight, efficient instrument (c) a high...

  13. Studies in Chaotic adiabatic dynamics

    International Nuclear Information System (INIS)

    Jarzynski, C.

    1994-01-01

    Chaotic adiabatic dynamics refers to the study of systems exhibiting chaotic evolution under slowly time-dependent equations of motion. In this dissertation the author restricts his attention to Hamiltonian chaotic adiabatic systems. The results presented are organized around a central theme, namely, that the energies of such systems evolve diffusively. He begins with a general analysis, in which he motivates and derives a Fokker-Planck equation governing this process of energy diffusion. He applies this equation to study the open-quotes goodnessclose quotes of an adiabatic invariant associated with chaotic motion. This formalism is then applied to two specific examples. The first is that of a gas of noninteracting point particles inside a hard container that deforms slowly with time. Both the two- and three-dimensional cases are considered. The results are discussed in the context of the Wall Formula for one-body dissipation in nuclear physics, and it is shown that such a gas approaches, asymptotically with time, an exponential velocity distribution. The second example involves the Fermi mechanism for the acceleration of cosmic rays. Explicit evolution equations are obtained for the distribution of cosmic ray energies within this model, and the steady-state energy distribution that arises when this equation is modified to account for the injection and removal of cosmic rays is discussed. Finally, the author re-examines the multiple-time-scale approach as applied to the study of phase space evolution under a chaotic adiabatic Hamiltonian. This leads to a more rigorous derivation of the above-mentioned Fokker-Planck equation, and also to a new term which has relevance to the problem of chaotic adiabatic reaction forces (the forces acting on slow, heavy degrees of freedom due to their coupling to light, fast chaotic degrees)

  14. Adaptive Synchronization of Chaotic Systems considering Performance Parameters of Operational Amplifiers

    Directory of Open Access Journals (Sweden)

    Sergio Ruíz-Hernández

    2015-01-01

    Full Text Available This paper addresses an adaptive control approach for synchronizing two chaotic oscillators with saturated nonlinear function series as nonlinear functions. Mathematical models to characterize the behavior of the transmitter and receiver circuit were derived, including in the latter the adaptive control and taking into account, for both chaotic oscillators, the most influential performance parameters associated with operational amplifiers. Asymptotic stability of the full synchronization system is studied by using Lyapunov direct method. Theoretical derivations and related results are experimentally validated through implementations from commercially available devices. Finally, the full synchronization system can easily be reproducible at a low cost.

  15. Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

    KAUST Repository

    N U+02BC Doye, Ibrahima

    2018-02-13

    In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

  16. Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

    KAUST Repository

    N U+02BC Doye, Ibrahima; Salama, Khaled N.; Laleg-Kirati, Taous-Meriem

    2018-01-01

    In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

  17. Synchronization and anti-synchronization coexist in Chen-Lee chaotic systems

    International Nuclear Information System (INIS)

    Chen, J.-H.; Chen, H.-K.; Lin, Y.-K.

    2009-01-01

    This study demonstrates that synchronization and anti-synchronization can coexist in Chen-Lee chaotic systems by direct linear coupling. Based on Lyapunov's direct method, a linear controller was designed to assure that two different types of synchronization can simultaneously be achieved. Further, the hybrid projective synchronization of Chen-Lee chaotic systems was studied using a nonlinear control scheme. The nonlinear controller was designed according to the Lyapunov stability theory to guarantee the hybrid projective synchronization, including synchronization, anti-synchronization, and projective synchronization. Finally, numerical examples are presented in order to illustrate the proposed synchronization approach.

  18. Chaotic synchronization of nearest-neighbor diffusive coupling Hindmarsh-Rose neural networks in noisy environments

    International Nuclear Information System (INIS)

    Fang Xiaoling; Yu Hongjie; Jiang Zonglai

    2009-01-01

    The chaotic synchronization of Hindmarsh-Rose neural networks linked by a nonlinear coupling function is discussed. The HR neural networks with nearest-neighbor diffusive coupling form are treated as numerical examples. By the construction of a special nonlinear-coupled term, the chaotic system is coupled symmetrically. For three and four neurons network, a certain region of coupling strength corresponding to full synchronization is given, and the effect of network structure and noise position are analyzed. For five and more neurons network, the full synchronization is very difficult to realize. All the results have been proved by the calculation of the maximum conditional Lyapunov exponent.

  19. Electrical crosstalk-coupling measurement and analysis for digital closed loop fibre optic gyro

    International Nuclear Information System (INIS)

    Jing, Jin; Hai-Ting, Tian; Xiong, Pan; Ning-Fang, Song

    2010-01-01

    The phase modulation and the closed-loop controller can generate electrical crosstalk-coupling in digital closed-loop fibre optic gyro. Four electrical cross-coupling paths are verified by the open-loop testing approach. It is found the variation of ramp amplitude will lead to the alternation of gyro bias. The amplitude and the phase parameters of the electrical crosstalk signal are measured by lock-in amplifier, and the variation of gyro bias is confirmed to be caused by the alternation of phase according to the amplitude of the ramp. A digital closed-loop fibre optic gyro electrical crosstalk-coupling model is built by approximating the electrical cross-coupling paths as a proportion and integration segment. The results of simulation and experiment show that the modulation signal electrical crosstalk-coupling can cause the dead zone of the gyro when a small angular velocity is inputted, and it could also lead to a periodic vibration of the bias error of the gyro when a large angular velocity is inputted

  20. Fully Digital Chaotic Oscillators Applied to Pseudo Random Number Generation

    KAUST Repository

    Mansingka, Abhinav S.

    2012-05-01

    adapted for pseudo random number generation by truncating statistically defective bits. Finally, a novel post-processing technique using the Fibonacci series is proposed and implemented with a non-autonomous driven hyperchaotic system to provide pseudo random number generators with high nonlinear complexity and controllable period length that enables full utilization of all branches of the chaotic output as statistically secure pseudo random output.

  1. Chaotic scattering and quantum dynamics

    International Nuclear Information System (INIS)

    Doron, Eyal.

    1992-11-01

    The main concern of this thesis is the application of the semiclassical approximation to quantum chaotic scattering systems. We deal with two separate, although interconnected, subjects. The first subject dealt with is the semiclassical characterization of the fluctuations of the S matrix. A particular important parameter is the magnetic field B, and we show how the correlation length and line shape of S matrix elements under a change of B may be derived. An effect which is present in many physical wave systems is absorption of energy flux. We show how absorption affects both the reflectivity and the scattering phase and time delay of a scattering system. In the second part of the thesis, we show how the formalism and results obtained from chaotic scattering can be applied to the investigation of closed chaotic systems, and in particular to chaotic billiards. The semiclassical expansion for billiards is presented. In the last part of the thesis we deal with the statistics of S matrices of chaotic scattering systems. The main message of this work is that scattering matrix, and its classical counterpart the Poincare Scattering Map can be used to yield a powerful formulation of the quantum mechanical dynamics of bounded systems. (author)

  2. Online Estimation of ARW Coefficient of Fiber Optic Gyro

    Directory of Open Access Journals (Sweden)

    Yang Li

    2014-01-01

    Full Text Available As a standard method for noise analysis of fiber optic gyro (FOG, Allan variance has too large offline computational burden and data storages to be applied to online estimation. To overcome the barriers, the state space model is firstly established for FOG. Then the Sage-husa adaptive Kalman filter (SHAKF is introduced in this field. Through recursive calculation of measurement noise covariance matrix, SHAKF can avoid the storage of large amounts of history data. However, the precision and stability of this method are still the primary matters that needed to be addressed. Based on this point, a new online method for estimation of the coefficient of angular random walk is proposed. In the method, estimator of measurement noise is constructed by the recursive form of Allan variance at the shortest sampling time. Then the estimator is embedded into the SHAKF framework resulting in a new adaptive filter. The estimations of measurement noise variance and Kalman filter are independent of each other in this method. Therefore, it can address the problem of filtering divergence and precision degrading effectively. Test results of both digital simulation and experimental data of FOG verify the validity and feasibility of the proposed method.

  3. A survey of Wien bridge-based chaotic oscillators: Design and experimental issues

    Energy Technology Data Exchange (ETDEWEB)

    Kilic, Recai [Erciyes University, Department of Electrical and Electronic Engineering, 38039 Kayseri (Turkey)], E-mail: kilic@erciyes.edu.tr; Yildirim, Fatma [Erciyes University, Civil Aviation School, 38039 Kayseri (Turkey)

    2008-12-15

    This paper presents a comparative study on design and implementation of Wien type chaotic oscillators. By making a collection of almost all Wien bridge-based chaotic circuits, we have investigated these oscillators in terms of chaotic dynamics, circuit structures, active building blocks, nonlinear element structures and operating frequency by using PSpice simulations and laboratory experiments. In addition to this comparative investigation, we present our two basic experimental contributions to referred implementations. While the first of our experimental contributions consists of the experimentally implementation of CFOA-based Chua's circuit modified for very high chaotic oscillations, the scope of the second is to experimentally implement a Wien type high frequency chaos generator, which has the diode-inductor composite, in the inductorless form by using CFOA-based synthetic inductor.

  4. A survey of Wien bridge-based chaotic oscillators: Design and experimental issues

    International Nuclear Information System (INIS)

    Kilic, Recai; Yildirim, Fatma

    2008-01-01

    This paper presents a comparative study on design and implementation of Wien type chaotic oscillators. By making a collection of almost all Wien bridge-based chaotic circuits, we have investigated these oscillators in terms of chaotic dynamics, circuit structures, active building blocks, nonlinear element structures and operating frequency by using PSpice simulations and laboratory experiments. In addition to this comparative investigation, we present our two basic experimental contributions to referred implementations. While the first of our experimental contributions consists of the experimentally implementation of CFOA-based Chua's circuit modified for very high chaotic oscillations, the scope of the second is to experimentally implement a Wien type high frequency chaos generator, which has the diode-inductor composite, in the inductorless form by using CFOA-based synthetic inductor

  5. Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System

    Directory of Open Access Journals (Sweden)

    M. S. H. Chowdhury

    2012-01-01

    Full Text Available Finding accurate solution of chaotic system by using efficient existing numerical methods is very hard for its complex dynamical behaviors. In this paper, the multistage homotopy-perturbation method (MHPM is applied to the Chaotic Genesio system. The MHPM is a simple reliable modification based on an adaptation of the standard homotopy-perturbation method (HPM. The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the Chaotic Genesio system. Numerical comparisons between the MHPM and the classical fourth-order Runge-Kutta (RK4 solutions are made. The results reveal that the new technique is a promising tool for the nonlinear chaotic systems of ordinary differential equations.

  6. Spectral statistics of chaotic many-body systems

    International Nuclear Information System (INIS)

    Dubertrand, Rémy; Müller, Sebastian

    2016-01-01

    We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schrödinger (or Gross–Pitaevski) equation. Our formula applies to bosonic systems with discretised positions, such as the Bose–Hubbard model, in the semiclassical limit as well as in the limit where the number of particles is taken to infinity. We use the trace formula to investigate the spectral statistics of these systems, by studying interference between solutions of the nonlinear Schrödinger equation. We show that in the limits taken the statistics of fully chaotic many-particle systems becomes universal and agrees with predictions from the Wigner–Dyson ensembles of random matrix theory. The conditions for Wigner–Dyson statistics involve a gap in the spectrum of the Frobenius–Perron operator, leaving the possibility of different statistics for systems with weaker chaotic properties. (paper)

  7. On synchronization of three chaotic systems

    International Nuclear Information System (INIS)

    Yan Jianping; Li Changpin

    2005-01-01

    In this paper, a simple but efficient method is applied to the synchronization of three chaotic systems, i.e., the chaotic Lorenz, Chua, and Chen systems. Numerical simulations show this method works very well

  8. Intermittent chaotic chimeras for coupled rotators

    DEFF Research Database (Denmark)

    Olmi, Simona; Martens, Erik Andreas; Thutupalli, Shashi

    2015-01-01

    Two symmetrically coupled populations of N oscillators with inertia m display chaotic solutions with broken symmetry similar to experimental observations with mechanical pendulums. In particular, we report evidence of intermittent chaotic chimeras, where one population is synchronized and the other...

  9. On the Design of Chaotic Oscillators

    DEFF Research Database (Denmark)

    Lindberg, Erik; Tamasevicius, A; Cenys, A.

    1998-01-01

    A discussion of the chaotic oscillator concept from a design methodology pointof view. The attributes of some chaoticoscillators are discussed and a systematicdesign method based on eigenvalue investigation is proposed. The method isillustrated with a chaotic Wien-bridgeoscillator design....

  10. Generation of multi-wing chaotic attractor in fractional order system

    International Nuclear Information System (INIS)

    Zhang Chaoxia; Yu Simin

    2011-01-01

    Highlights: → We investigate a novel approach for generating multi-wing chaotic attractors. → We introduce a fundamental fractional differential nominal linear system. → A proper nonlinear state feedback controller is designed. → The controlled system can generate fractional-order multi-wing chaotic attractors. - Abstract: In this paper, a novel approach is proposed for generating multi-wing chaotic attractors from the fractional linear differential system via nonlinear state feedback controller equipped with a duality-symmetric multi-segment quadratic function. The main idea is to design a proper nonlinear state feedback controller by using four construction criterions from a fundamental fractional differential nominal linear system, so that the controlled fractional differential system can generate multi-wing chaotic attractors. It is the first time in the literature to report the multi-wing chaotic attractors from an uncoupled fractional differential system. Furthermore, some basic dynamical analysis and numerical simulations are also given, confirming the effectiveness of the proposed method.

  11. On Chaotic Nature of the Emerging European Forex Markets

    Directory of Open Access Journals (Sweden)

    Anoop S Kumar

    2014-06-01

    Full Text Available This study attempts to analyze the presence deterministic chaos in the forex markets of select European countries namely Bulgaria, Croatia, Czech Republic, Hungary Poland, Romania, Russia, Slovakia and Slovenia. Monthly NEER data ranging from jan-1994 to Dec-2013 is used for the purpose of analysis. A two step methodology is employed where in the first step, non-linear dependence structure in the underlying time series is verified using BDS test. The results show that all the markets under study exhibit non-linear dependence. In the next stage, it is enquired whether this non-linear behavior is due to the presence of chaotic dynamics in the markets. This is achieved by estimating Lyapunov exponents for the time series under analysis. An EGARCH (1, 1 filter is applied to see if the non-linearity could be explained by a GARCH process. From the Lyapunov exponent values, it is found that the GARCH process is unable to explain the forex markets behavior in a satisfying manner. It is concluded that the forex markets under study exhibit deterministic chaotic behavior.

  12. A new chaotic secure communication scheme

    International Nuclear Information System (INIS)

    Hua Changchun; Yang Bo; Ouyang Gaoxiang; Guan Xinping

    2005-01-01

    A new chaotic secure communication scheme is constructed. Unified chaotic system is used to encrypt the emitted signal. Different from the existing chaotic secure communication methods, the useful information is embodied in the parameter of chaotic systems in this Letter. The receiver is designed which can succeed in recovering the former signal. Finally computer simulations are done to verify the proposed methods, and the results show that the obtained theoretic results are feasible and efficient

  13. Chaotic signals in digital communications

    CERN Document Server

    Eisencraft, Marcio; Suyama, Ricardo

    2013-01-01

    Chaotic Signals in Digital Communications combines fundamental background knowledge with state-of-the-art methods for using chaotic signals and systems in digital communications. The book builds a bridge between theoretical works and practical implementation to help researchers attain consistent performance in realistic environments. It shows the possible shortcomings of the chaos-based communication systems proposed in the literature, particularly when they are subjected to non-ideal conditions. It also presents a toolbox of techniques for researchers working to actually implement such system

  14. System Design and Performance of the Two-Gyro Science Mode For the Hubble Space Telescope

    Science.gov (United States)

    Prior, Michael; Dunham, Larry

    2005-01-01

    For fifteen years, the science mission of the Hubble Space Telescope (HST) required using at least three of the six on-board rate gyros for attitude control. Failed gyros were eventually replaced through Space Shuttle Servicing Missions. The tragic loss of the Space Shuttle Columbia has resulted in the cancellation of all planned Shuttle based missions to HST. While a robotic servicing mission is currently being planned instead, controlling with alternate sensors to replace failed gyros can extend the HST science gathering until a servicing mission can be performed, and also extend science at HST s end of life. Additionally, sufficient performance may allow a permanent transition to operations with less than 3 gyros (by intentionally turning off working gyros saving them for later use) allowing for an even greater science mission extension. To meet this need, a Two Gyro Science (TGS) mode has been designed and implemented using magnetometers (Magnetic Sensing System - MSS), Fixed Head Star Trackers (FHSTs), and Fine Guidance Sensors (FGSs) to control vehicle rate about the missing gyro input axis. The development of the TGS capability is the largest re-design of HST operations undertaken, since it affects several major spacecraft subsystems, the most heavily being the Pointing Control System (PCS) and Flight Software (FSW). Additionally, and equally important, are the extensive modifications and enhancements of the Planning and Scheduling system which must now be capable of scheduling science observations while taking into account several new constraints imposed by the TGS operational modes (such as FHST availability and magnetic field geometry) that will impact science gathering efficiency and target availability. This paper discusses the systems engineering design, development, and performance of the TGS mode, now in its final stages of completion.

  15. Contraction theory based adaptive synchronization of chaotic systems

    International Nuclear Information System (INIS)

    Sharma, B.B.; Kar, I.N.

    2009-01-01

    Contraction theory based stability analysis exploits the incremental behavior of trajectories of a system with respect to each other. Application of contraction theory provides an alternative way for stability analysis of nonlinear systems. This paper considers the design of a control law for synchronization of certain class of chaotic systems based on backstepping technique. The controller is selected so as to make the error dynamics between the two systems contracting. Synchronization problem with and without uncertainty in system parameters is discussed and necessary stability proofs are worked out using contraction theory. Suitable adaptation laws for unknown parameters are proposed based on the contraction principle. The numerical simulations verify the synchronization of the chaotic systems. Also parameter estimates converge to their true values with the proposed adaptation laws.

  16. Spread-spectrum communication using binary spatiotemporal chaotic codes

    International Nuclear Information System (INIS)

    Wang Xingang; Zhan Meng; Gong Xiaofeng; Lai, C.H.; Lai, Y.-C.

    2005-01-01

    We propose a scheme to generate binary code for baseband spread-spectrum communication by using a chain of coupled chaotic maps. We compare the performances of this type of spatiotemporal chaotic code with those of a conventional code used frequently in digital communication, the Gold code, and demonstrate that our code is comparable or even superior to the Gold code in several key aspects: security, bit error rate, code generation speed, and the number of possible code sequences. As the field of communicating with chaos faces doubts in terms of performance comparison with conventional digital communication schemes, our work gives a clear message that communicating with chaos can be advantageous and it deserves further attention from the nonlinear science community

  17. Robust PRNG based on homogeneously distributed chaotic dynamics

    International Nuclear Information System (INIS)

    Garasym, Oleg; Taralova, Ina; Lozi, René

    2016-01-01

    This paper is devoted to the design of new chaotic Pseudo Random Number Generator (CPRNG). Exploring several topologies of network of 1-D coupled chaotic mapping, we focus first on two dimensional networks. Two topologically coupled maps are studied: TTL rc non-alternate, and TTL SC alternate. The primary idea of the novel maps has been based on an original coupling of the tent and logistic maps to achieve excellent random properties and homogeneous /uniform/ density in the phase plane, thus guaranteeing maximum security when used for chaos base cryptography. In this aim two new nonlinear CPRNG: MTTL 2 sc and NTTL 2 are proposed. The maps successfully passed numerous statistical, graphical and numerical tests, due to proposed ring coupling and injection mechanisms. (paper)

  18. Discriminating chaotic and stochastic dynamics through the permutation spectrum test

    Energy Technology Data Exchange (ETDEWEB)

    Kulp, C. W., E-mail: Kulp@lycoming.edu [Department of Astronomy and Physics, Lycoming College, Williamsport, Pennsylvania 17701 (United States); Zunino, L., E-mail: lucianoz@ciop.unlp.edu.ar [Centro de Investigaciones Ópticas (CONICET La Plata—CIC), C.C. 3, 1897 Gonnet (Argentina); Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900 La Plata (Argentina)

    2014-09-01

    In this paper, we propose a new heuristic symbolic tool for unveiling chaotic and stochastic dynamics: the permutation spectrum test. Several numerical examples allow us to confirm the usefulness of the introduced methodology. Indeed, we show that it is robust in situations in which other techniques fail (intermittent chaos, hyperchaotic dynamics, stochastic linear and nonlinear correlated dynamics, and deterministic non-chaotic noise-driven dynamics). We illustrate the applicability and reliability of this pragmatic method by examining real complex time series from diverse scientific fields. Taking into account that the proposed test has the advantages of being conceptually simple and computationally fast, we think that it can be of practical utility as an alternative test for determinism.

  19. Output synchronization of chaotic systems under nonvanishing perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Lopez-Mancilla, Didier [Departamento de Ciencias Exactas y Tecnologicas, Centro Universitario de los Lagos, Universidad de Guadalajara (CULagos-UdeG), Enrique Diaz de Leon s/n, 47460 Lagos de Moreno, Jal. (Mexico)], E-mail: didier@uabc.mx; Cruz-Hernandez, Cesar [Electronics and Telecommunications Department, Scientific Research and Advanced Studies of Ensenada (CICESE), Km. 107, Carretera Tijuana-Ensenada, 22860 Ensenada, B.C. (Mexico)], E-mail: ccruz@cicese.mx

    2008-08-15

    In this paper, an analysis for chaos synchronization under nonvanishing perturbations is presented. In particular, we use model-matching approach from nonlinear control theory for output synchronization of identical and nonidentical chaotic systems under nonvanishing perturbations in a master-slave configuration. We show that the proposed approach is indeed suitable to synchronize a class of perturbed slaves with a chaotic master system; that is the synchronization error trajectories remain bounded if the perturbations satisfy some conditions. In order to illustrate this robustness synchronization property, we present two cases of study: (i) for identical systems, a pair of coupled Roessler systems, the first like a master and the other like a perturbed slave, and (ii) for nonidentical systems, a Chua's circuit driving a Roessler/slave system with a perturbed control law, in both cases a quantitative analysis on the perturbation is included.

  20. Output synchronization of chaotic systems under nonvanishing perturbations

    International Nuclear Information System (INIS)

    Lopez-Mancilla, Didier; Cruz-Hernandez, Cesar

    2008-01-01

    In this paper, an analysis for chaos synchronization under nonvanishing perturbations is presented. In particular, we use model-matching approach from nonlinear control theory for output synchronization of identical and nonidentical chaotic systems under nonvanishing perturbations in a master-slave configuration. We show that the proposed approach is indeed suitable to synchronize a class of perturbed slaves with a chaotic master system; that is the synchronization error trajectories remain bounded if the perturbations satisfy some conditions. In order to illustrate this robustness synchronization property, we present two cases of study: (i) for identical systems, a pair of coupled Roessler systems, the first like a master and the other like a perturbed slave, and (ii) for nonidentical systems, a Chua's circuit driving a Roessler/slave system with a perturbed control law, in both cases a quantitative analysis on the perturbation is included

  1. Basic Studies on Chaotic Characteristics of Electric Power Market Price

    Science.gov (United States)

    Takeuchi, Yuya; Miyauchi, Hajime; Kita, Toshihiro

    Recently, deregulation and reform of electric power utilities have been progressing in many parts of the world. In Japan, partial deregulation has been started from generation sector since 1995 and partial deregulation of retail sector is executed through twice law revisions. Through the deregulation, because electric power is traded in the market and its price is always fluctuated, it is important for the electric power business to analyze and predict the price. Although the price data of the electric power market is time series data, it is not always proper to analyze by the linear model such as ARMA because the price sometimes changes suddenly. Therefore, in this paper, we apply the methods of chaotic time series analysis, one of non-linear analysis methods, and investigate the chaotic characteristics of the system price of JEPX.

  2. Nonlinear resonance phenomena of a doped fibre laser under cavity ...

    Indian Academy of Sciences (India)

    quence and other routes to chaos, generalized multistability and crisis. But, doped ... of chaos and synchronization of coupled chaotic lasers (for communication with a ... The two basic issues in focus here for the nonlinear dynamical studies.

  3. Spatial chaotic behavior of vortices in type-II superconductors with different pinning strength

    International Nuclear Information System (INIS)

    Lin, H.-T.; Pan, M.; Cheng, C.H.; Cui, Y.J.; Zhao, Y.

    2008-01-01

    Spatial chaotic character in systems where defects are arranged in periodic arrays has been investigated by computer simulation. Due to the high nonlinearity of the vortex-defect interaction, arrangement of the vortices in a periodic pinning array can be chaotic (glassy), depending on the vortex-defect interaction state and vortex-vortex interaction. Two types of disordered vortex states in the system are observed. The type-I disorder arises from the intrinsically chaotic nature of the nonlinear system, existing when the pinning disorder is low and the pinning strength is weak. The type-II disordered state is related to the pinning disorder, which is dominating when both the pinning disorder and the pinning strength are strong

  4. Spatial chaotic behavior of vortices in type-II superconductors with different pinning strength

    Energy Technology Data Exchange (ETDEWEB)

    Lin, H.-T. [Faculty of Information Management, Cheng Shui University, Taiwan (China); Pan, M. [Key Laboratory of Magnetic Levitation Technologies and Maglev Trains, Ministry of Education of China, Superconductivity R and D Center, Southwest Jiaotong University, Chengdu, Sichuan 610031 (China); Cheng, C.H. [Key Laboratory of Magnetic Levitation Technologies and Maglev Trains, Ministry of Education of China, Superconductivity R and D Center, Southwest Jiaotong University, Chengdu, Sichuan 610031 (China); School of Materials Science and Engineering, University of New South Wales, Sydney (Australia); Cui, Y.J. [Key Laboratory of Magnetic Levitation Technologies and Maglev Trains, Ministry of Education of China, Superconductivity R and D Center, Southwest Jiaotong University, Chengdu, Sichuan 610031 (China); Zhao, Y. [Key Laboratory of Magnetic Levitation Technologies and Maglev Trains, Ministry of Education of China, Superconductivity R and D Center, Southwest Jiaotong University, Chengdu, Sichuan 610031 (China); School of Materials Science and Engineering, University of New South Wales, Sydney (Australia)], E-mail: yzhao@swjtu.edu.cn

    2008-09-15

    Spatial chaotic character in systems where defects are arranged in periodic arrays has been investigated by computer simulation. Due to the high nonlinearity of the vortex-defect interaction, arrangement of the vortices in a periodic pinning array can be chaotic (glassy), depending on the vortex-defect interaction state and vortex-vortex interaction. Two types of disordered vortex states in the system are observed. The type-I disorder arises from the intrinsically chaotic nature of the nonlinear system, existing when the pinning disorder is low and the pinning strength is weak. The type-II disordered state is related to the pinning disorder, which is dominating when both the pinning disorder and the pinning strength are strong.

  5. Chaotic dynamics from interspike intervals

    DEFF Research Database (Denmark)

    Pavlov, A N; Sosnovtseva, Olga; Mosekilde, Erik

    2001-01-01

    Considering two different mathematical models describing chaotic spiking phenomena, namely, an integrate-and-fire and a threshold-crossing model, we discuss the problem of extracting dynamics from interspike intervals (ISIs) and show that the possibilities of computing the largest Lyapunov expone...

  6. Synchronization of spatiotemporal chaotic systems and application to secure communication of digital image

    International Nuclear Information System (INIS)

    Wang Xing-Yuan; Zhang Na; Ren Xiao-Li; Zhang Yong-Lei

    2011-01-01

    Coupled map lattices (CMLs) are taken as examples to study the synchronization of spatiotemporal chaotic systems. In this paper, we use the nonlinear coupled method to implement the synchronization of two coupled map lattices. Through the appropriate separation of the linear term from the nonlinear term of the spatiotemporal chaotic system, we set the nonlinear term as the coupling function and then we can achieve the synchronization of two coupled map lattices. After that, we implement the secure communication of digital image using this synchronization method. Then, the discrete characteristics of the nonlinear coupling spatiotemporal chaos are applied to the discrete pixel of the digital image. After the synchronization of both the communication parties, the receiver can decrypt the original image. Numerical simulations show the effectiveness and the feasibility of the proposed program. (general)

  7. Sector-condition-based results for adaptive control and synchronization of chaotic systems under input saturation

    International Nuclear Information System (INIS)

    Iqbal, Muhammad; Rehan, Muhammad; Hong, Keum-Shik; Khaliq, Abdul; Saeed-ur-Rehman

    2015-01-01

    This paper addresses the design of adaptive feedback controllers for two problems (namely, stabilization and synchronization) of chaotic systems with unknown parameters by considering input saturation constraints. A novel generalized sector condition is developed to deal with the saturation nonlinearities for synthesizing the nonlinear and the adaptive controllers for the stabilization and synchronization control objectives. By application of the proposed sector condition and rigorous regional stability analysis, control and adaptation laws are formulated to guarantee local stabilization of a nonlinear system under actuator saturation. Further, simple control and adaptation laws are developed to synchronize two chaotic systems under uncertain parameters and input saturation nonlinearity. Numerical simulation results for Rössler and FitzHugh–Nagumo models are provided to demonstrate the effectiveness of the proposed adaptive stabilization and synchronization control methodologies

  8. Applications of Chaotic Dynamics in Robotics

    Directory of Open Access Journals (Sweden)

    Xizhe Zang

    2016-03-01

    Full Text Available This article presents a summary of applications of chaos and fractals in robotics. Firstly, basic concepts of deterministic chaos and fractals are discussed. Then, fundamental tools of chaos theory used for identifying and quantifying chaotic dynamics will be shared. Principal applications of chaos and fractal structures in robotics research, such as chaotic mobile robots, chaotic behaviour exhibited by mobile robots interacting with the environment, chaotic optimization algorithms, chaotic dynamics in bipedal locomotion and fractal mechanisms in modular robots will be presented. A brief survey is reported and an analysis of the reviewed publications is also presented.

  9. Jump resonant frequency islands in nonlinear feedback control systems

    Science.gov (United States)

    Koenigsberg, W. D.; Dunn, J. C.

    1975-01-01

    A new type of jump resonance is predicted and observed in certain nonlinear feedback control systems. The new jump resonance characteristic is described as a 'frequency island' due to the fact that a portion of the input-output transfer characteristic is disjoint from the main body. The presence of such frequency islands was predicted by using a sinusoidal describing function characterization of the dynamics of an inertial gyro employing nonlinear ternary rebalance logic. While the general conditions under which such islands are possible has not been examined, a numerical approach is presented which can aid in establishing their presence. The existence of the frequency islands predicted for the ternary rebalanced gyro was confirmed by simulating the nonlinear system and measuring the transfer function.

  10. Attitude and gyro bias estimation by the rotation of an inertial measurement unit

    International Nuclear Information System (INIS)

    Wu, Zheming; Sun, Zhenguo; Zhang, Wenzeng; Chen, Qiang

    2015-01-01

    In navigation applications, the presence of an unknown bias in the measurement of rate gyros is a key performance-limiting factor. In order to estimate the gyro bias and improve the accuracy of attitude measurement, we proposed a new method which uses the rotation of an inertial measurement unit, which is independent from rigid body motion. By actively changing the orientation of the inertial measurement unit (IMU), the proposed method generates sufficient relations between the gyro bias and tilt angle (roll and pitch) error via ridge body dynamics, and the gyro bias, including the bias that causes the heading error, can be estimated and compensated. The rotation inertial measurement unit method makes the gravity vector measured from the IMU continuously change in a body-fixed frame. By theoretically analyzing the mathematic model, the convergence of the attitude and gyro bias to the true values is proven. The proposed method provides a good attitude estimation using only measurements from an IMU, when other sensors such as magnetometers and GPS are unreliable. The performance of the proposed method is illustrated under realistic robotic motions and the results demonstrate an improvement in the accuracy of the attitude estimation. (paper)

  11. Passive axial magnetic bearing with Halbach magnetized array in magnetically suspended control moment gyro application

    International Nuclear Information System (INIS)

    Sun Jinji; Ren Yuan; Fang Jiancheng

    2011-01-01

    The paper presents a special configuration of passive axial magnetic bearing with segmented Halbach magnetized array in magnetically suspended control moment gyro (MSCMG). Peculiarity of presented passive axial magnetic bearing is its ability to provide angular stiffness so that it can produce gyro moment when it is used in MSCMG. The MSCMG with this passive axial magnetic bearing can efficiently reduce the power loss when it supplies gyro moment compared with the five degrees of freedom (5-DOF) MSCMG. The characteristics of the suspension force and stiffness of the passive axial magnetic bearing are studied using finite element method (FEM). The performance of the presented passive axial magnetic bearing with Halbach magnetized array is verified by a prototyped MSCMG. - Research highlights: → Passive axial magnetic bearing is used to provide angular stiffness. → Passive axial magnetic bearing is based on repulsion. → Layers Halbach magnetized array realizes higher stiffness per bearing volume. → Passive axial magnetic bearing can provide gyro moment in CMG. → Power loss of MSCMG with PMB does not increase when it provides gyro moment.

  12. DC electrostatic gyro suspension system for the Gravity Probe B experiment

    Science.gov (United States)

    Wu, Chang-Huei

    1994-12-01

    The Gravity Probe B experiment is a satellite-based experiment primarily designed to test two aspects of Einstein's General Theory of Relativity by observing the spin axis drift of near-perfect gyroscopes in a 650-km circular polar orbit. The goal of this experiment is to measure the drift angles to an accuracy of 0.3 milli-arcsec after one year in orbit. As a result, electrostatically suspended free-spinning gyroscopes operating at a very low temperature became the final choice for their ultra-low Newtonian torque-induced drift rate. The Conventional AC current-driven suspension system faces two fundamental difficulties for ground gyro testing. Field emission causes rotor charging and arcing with an imperfect electrode or rotor surfaces because the electric field intensity needed to support a solid rotor in the 1-g field is more than 107 V/m. The system not only becomes unstable at a high rotor charge, which can be more than 500 volts, but may also lose control in case of arcing. Both the high voltage AC suspension signal and the high frequency (1 MHz) signal for rotor position sensing interfere with the superconducting SQUID magnetometer for spin axis readout through inductive coupling. These problems were resolved by using DC voltage to generate a suspension force and a low frequency position sensor. In addition to the Input/Output linearization algorithm developed to remove the system nonlinearity for global stability and dynamic performance, we also minimized the electric field intensity to reduce rotor charging. Experimental results verified the desired global stability and satisfactory dynamic performance. The problem of rotor charging is virtually eliminated. More importantly, the DC system is compatible with the SQUID readout system in the Science Mission configuration. Consequently, experiments in low magnetic field at a sub-micro-gauss level for SQUID design verification and trapped flux distribution study were finally realizable in ground environment

  13. Dynamic Parameter-Control Chaotic System.

    Science.gov (United States)

    Hua, Zhongyun; Zhou, Yicong

    2016-12-01

    This paper proposes a general framework of 1-D chaotic maps called the dynamic parameter-control chaotic system (DPCCS). It has a simple but effective structure that uses the outputs of a chaotic map (control map) to dynamically control the parameter of another chaotic map (seed map). Using any existing 1-D chaotic map as the control/seed map (or both), DPCCS is able to produce a huge number of new chaotic maps. Evaluations and comparisons show that chaotic maps generated by DPCCS are very sensitive to their initial states, and have wider chaotic ranges, better unpredictability and more complex chaotic behaviors than their seed maps. Using a chaotic map of DPCCS as an example, we provide a field-programmable gate array design of this chaotic map to show the simplicity of DPCCS in hardware implementation, and introduce a new pseudo-random number generator (PRNG) to investigate the applications of DPCCS. Analysis and testing results demonstrate the excellent randomness of the proposed PRNG.

  14. Chaotic attractors in tumor growth and decay: a differential equation model.

    Science.gov (United States)

    Harney, Michael; Yim, Wen-sau

    2015-01-01

    Tumorigenesis can be modeled as a system of chaotic nonlinear differential equations. A simulation of the system is realized by converting the differential equations to difference equations. The results of the simulation show that an increase in glucose in the presence of low oxygen levels decreases tumor growth.

  15. Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification

    International Nuclear Information System (INIS)

    Fotsin, H.B.; Daafouz, J.

    2005-01-01

    This Letter uses systematic tools from recent papers to design non-linear observers for synchronization of a chaotic colpitts oscillator both in the non adaptive and adaptive cases. It is shown that all parameters of a totally uncertain model of the oscillator can be estimated through adaptive synchronization. A strategy for practical implementation of a secure communication strategy is also discussed

  16. Visibility graphlet approach to chaotic time series

    Energy Technology Data Exchange (ETDEWEB)

    Mutua, Stephen [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China); Computer Science Department, Masinde Muliro University of Science and Technology, P.O. Box 190-50100, Kakamega (Kenya); Gu, Changgui, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn; Yang, Huijie, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China)

    2016-05-15

    Many novel methods have been proposed for mapping time series into complex networks. Although some dynamical behaviors can be effectively captured by existing approaches, the preservation and tracking of the temporal behaviors of a chaotic system remains an open problem. In this work, we extended the visibility graphlet approach to investigate both discrete and continuous chaotic time series. We applied visibility graphlets to capture the reconstructed local states, so that each is treated as a node and tracked downstream to create a temporal chain link. Our empirical findings show that the approach accurately captures the dynamical properties of chaotic systems. Networks constructed from periodic dynamic phases all converge to regular networks and to unique network structures for each model in the chaotic zones. Furthermore, our results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.

  17. Advances and applications in chaotic systems

    CERN Document Server

    Volos, Christos

    2016-01-01

    This book reports on the latest advances and applications of chaotic systems. It consists of 25 contributed chapters by experts who are specialized in the various topics addressed in this book. The chapters cover a broad range of topics of chaotic systems such as chaos, hyperchaos, jerk systems, hyperjerk systems, conservative and dissipative systems, circulant chaotic systems, multi-scroll chaotic systems, finance chaotic system, highly chaotic systems, chaos control, chaos synchronization, circuit realization and applications of chaos theory in secure communications, mobile robot, memristors, cellular neural networks, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in chaos theory. This book will serve as a reference book for graduate students and researchers with a basic knowledge of chaos theory and control systems. The resulting design procedures on the chaotic systems are emphasized using MATLAB software.

  18. Chaotic dynamics in optimal monetary policy

    Science.gov (United States)

    Gomes, O.; Mendes, V. M.; Mendes, D. A.; Sousa Ramos, J.

    2007-05-01

    There is by now a large consensus in modern monetary policy. This consensus has been built upon a dynamic general equilibrium model of optimal monetary policy as developed by, e.g., Goodfriend and King [ NBER Macroeconomics Annual 1997 edited by B. Bernanke and J. Rotemberg (Cambridge, Mass.: MIT Press, 1997), pp. 231 282], Clarida et al. [J. Econ. Lit. 37, 1661 (1999)], Svensson [J. Mon. Econ. 43, 607 (1999)] and Woodford [ Interest and Prices: Foundations of a Theory of Monetary Policy (Princeton, New Jersey, Princeton University Press, 2003)]. In this paper we extend the standard optimal monetary policy model by introducing nonlinearity into the Phillips curve. Under the specific form of nonlinearity proposed in our paper (which allows for convexity and concavity and secures closed form solutions), we show that the introduction of a nonlinear Phillips curve into the structure of the standard model in a discrete time and deterministic framework produces radical changes to the major conclusions regarding stability and the efficiency of monetary policy. We emphasize the following main results: (i) instead of a unique fixed point we end up with multiple equilibria; (ii) instead of saddle-path stability, for different sets of parameter values we may have saddle stability, totally unstable equilibria and chaotic attractors; (iii) for certain degrees of convexity and/or concavity of the Phillips curve, where endogenous fluctuations arise, one is able to encounter various results that seem intuitively correct. Firstly, when the Central Bank pays attention essentially to inflation targeting, the inflation rate has a lower mean and is less volatile; secondly, when the degree of price stickiness is high, the inflation rate displays a larger mean and higher volatility (but this is sensitive to the values given to the parameters of the model); and thirdly, the higher the target value of the output gap chosen by the Central Bank, the higher is the inflation rate and its

  19. A hybrid method for accurate star tracking using star sensor and gyros.

    Science.gov (United States)

    Lu, Jiazhen; Yang, Lie; Zhang, Hao

    2017-10-01

    Star tracking is the primary operating mode of star sensors. To improve tracking accuracy and efficiency, a hybrid method using a star sensor and gyroscopes is proposed in this study. In this method, the dynamic conditions of an aircraft are determined first by the estimated angular acceleration. Under low dynamic conditions, the star sensor is used to measure the star vector and the vector difference method is adopted to estimate the current angular velocity. Under high dynamic conditions, the angular velocity is obtained by the calibrated gyros. The star position is predicted based on the estimated angular velocity and calibrated gyros using the star vector measurements. The results of the semi-physical experiment show that this hybrid method is accurate and feasible. In contrast with the star vector difference and gyro-assisted methods, the star position prediction result of the hybrid method is verified to be more accurate in two different cases under the given random noise of the star centroid.

  20. Chaotic operation and chaos control of travelling wave ultrasonic motor.

    Science.gov (United States)

    Shi, Jingzhuo; Zhao, Fujie; Shen, Xiaoxi; Wang, Xiaojie

    2013-08-01

    The travelling wave ultrasonic motor, which is a nonlinear dynamic system, has complex chaotic phenomenon with some certain choices of system parameters and external inputs, and its chaotic characteristics have not been studied until now. In this paper, the preliminary study of the chaos phenomenon in ultrasonic motor driving system has been done. The experiment of speed closed-loop control is designed to obtain several groups of time sampling data sequence of the amplitude of driving voltage, and phase-space reconstruction is used to analyze the chaos characteristics of these time sequences. The largest Lyapunov index is calculated and the result is positive, which shows that the travelling wave ultrasonic motor has chaotic characteristics in a certain working condition Then, the nonlinear characteristics of travelling wave ultrasonic motor are analyzed which includes Lyapunov exponent map, the bifurcation diagram and the locus of voltage relative to speed based on the nonlinear chaos model of a travelling wave ultrasonic motor. After that, two kinds of adaptive delay feedback controllers are designed in this paper to control and suppress chaos in USM speed control system. Simulation results show that the method can control unstable periodic orbits, suppress chaos in USM control system. Proportion-delayed feedback controller was designed following and arithmetic of fuzzy logic was used to adaptively adjust the delay time online. Simulation results show that this method could fast and effectively change the chaos movement into periodic or fixed-point movement and make the system enter into stable state from chaos state. Finally the chaos behavior was controlled. Copyright © 2013 Elsevier B.V. All rights reserved.

  1. Psychotherapy Is Chaotic-(Not Only) in a Computational World.

    Science.gov (United States)

    Schiepek, Günter K; Viol, Kathrin; Aichhorn, Wolfgang; Hütt, Marc-Thorsten; Sungler, Katharina; Pincus, David; Schöller, Helmut J

    2017-01-01

    Objective: The aim of this article is to outline the role of chaotic dynamics in psychotherapy. Besides some empirical findings of chaos at different time scales, the focus is on theoretical modeling of change processes explaining and simulating chaotic dynamics. It will be illustrated how some common factors of psychotherapeutic change and psychological hypotheses on motivation, emotion regulation, and information processing of the client's functioning can be integrated into a comprehensive nonlinear model of human change processes. Methods: The model combines 5 variables (intensity of emotions, problem intensity, motivation to change, insight and new perspectives, therapeutic success) and 4 parameters into a set of 5 coupled nonlinear difference equations. The results of these simulations are presented as time series, as phase space embedding of these time series (i.e., attractors), and as bifurcation diagrams. Results: The model creates chaotic dynamics, phase transition-like phenomena, bi- or multi-stability, and sensibility of the dynamic patterns on parameter drift. These features are predicted by chaos theory and by Synergetics and correspond to empirical findings. The spectrum of these behaviors illustrates the complexity of psychotherapeutic processes. Conclusion: The model contributes to the development of an integrative conceptualization of psychotherapy. It is consistent with the state of scientific knowledge of common factors, as well as other psychological topics, such as: motivation, emotion regulation, and cognitive processing. The role of chaos theory is underpinned, not only in the world of computer simulations, but also in practice. In practice, chaos demands technologies capable of real-time monitoring and reporting on the nonlinear features of the ongoing process (e.g., its stability or instability). Based on this monitoring, a client-centered, continuous, and cooperative process of feedback and control becomes possible. By contrast, restricted

  2. Parameters identification and adaptive full state hybrid projective synchronization of chaotic (hyper-chaotic) systems

    International Nuclear Information System (INIS)

    Hu Manfeng; Xu Zhenyuan; Zhang Rong; Hu Aihua

    2007-01-01

    Based on the active control idea and the invariance principle of differential equations, a general scheme of adaptive full state hybrid projective synchronization (FSHPS) and parameters identification of a class of chaotic (hyper-chaotic) systems with linearly dependent uncertain parameters is proposed in this Letter. With this effective scheme parameters identification and FSHPS of chaotic and hyper-chaotic systems can be realized simultaneously. Numerical simulations on the chaotic Chen system and the hyper-chaotic Chen system are presented to verify the effectiveness of the proposed scheme

  3. Calibration of gyro G-sensitivity coefficients with FOG monitoring on precision centrifuge

    Science.gov (United States)

    Lu, Jiazhen; Yang, Yanqiang; Li, Baoguo; Liu, Ming

    2017-07-01

    The advantages of mechanical gyros, such as high precision, endurance and reliability, make them widely used as the core parts of inertial navigation systems (INS) utilized in the fields of aeronautics, astronautics and underground exploration. In a high-g environment, the accuracy of gyros is degraded. Therefore, the calibration and compensation of the gyro G-sensitivity coefficients is essential when the INS operates in a high-g environment. A precision centrifuge with a counter-rotating platform is the typical equipment for calibrating the gyro, as it can generate large centripetal acceleration and keep the angular rate close to zero; however, its performance is seriously restricted by the angular perturbation in the high-speed rotating process. To reduce the dependence on the precision of the centrifuge and counter-rotating platform, an effective calibration method for the gyro g-sensitivity coefficients under fiber-optic gyroscope (FOG) monitoring is proposed herein. The FOG can efficiently compensate spindle error and improve the anti-interference ability. Harmonic analysis is performed for data processing. Simulations show that the gyro G-sensitivity coefficients can be efficiently estimated to up to 99% of the true value and compensated using a lookup table or fitting method. Repeated tests indicate that the G-sensitivity coefficients can be correctly calibrated when the angular rate accuracy of the precision centrifuge is as low as 0.01%. Verification tests are performed to demonstrate that the attitude errors can be decreased from 0.36° to 0.08° in 200 s. The proposed measuring technology is generally applicable in engineering, as it can reduce the accuracy requirements for the centrifuge and the environment.

  4. Differential evolution optimization combined with chaotic sequences for image contrast enhancement

    Energy Technology Data Exchange (ETDEWEB)

    Santos Coelho, Leandro dos [Industrial and Systems Engineering Graduate Program, LAS/PPGEPS, Pontifical Catholic University of Parana, PUCPR Imaculada Conceicao, 1155, 80215-901 Curitiba, Parana (Brazil)], E-mail: leandro.coelho@pucpr.br; Sauer, Joao Guilherme [Industrial and Systems Engineering Graduate Program, LAS/PPGEPS, Pontifical Catholic University of Parana, PUCPR Imaculada Conceicao, 1155, 80215-901 Curitiba, Parana (Brazil)], E-mail: joao.sauer@gmail.com; Rudek, Marcelo [Industrial and Systems Engineering Graduate Program, LAS/PPGEPS, Pontifical Catholic University of Parana, PUCPR Imaculada Conceicao, 1155, 80215-901 Curitiba, Parana (Brazil)], E-mail: marcelo.rudek@pucpr.br

    2009-10-15

    Evolutionary Algorithms (EAs) are stochastic and robust meta-heuristics of evolutionary computation field useful to solve optimization problems in image processing applications. Recently, as special mechanism to avoid being trapped in local minimum, the ergodicity property of chaotic sequences has been used in various designs of EAs. Three differential evolution approaches based on chaotic sequences using logistic equation for image enhancement process are proposed in this paper. Differential evolution is a simple yet powerful evolutionary optimization algorithm that has been successfully used in solving continuous problems. The proposed chaotic differential evolution schemes have fast convergence rate but also maintain the diversity of the population so as to escape from local optima. In this paper, the image contrast enhancement is approached as a constrained nonlinear optimization problem. The objective of the proposed chaotic differential evolution schemes is to maximize the fitness criterion in order to enhance the contrast and detail in the image by adapting the parameters using a contrast enhancement technique. The proposed chaotic differential evolution schemes are compared with classical differential evolution to two testing images. Simulation results on three images show that the application of chaotic sequences instead of random sequences is a possible strategy to improve the performance of classical differential evolution optimization algorithm.

  5. A novel algorithm for image encryption based on mixture of chaotic maps

    International Nuclear Information System (INIS)

    Behnia, S.; Akhshani, A.; Mahmodi, H.; Akhavan, A.

    2008-01-01

    Chaos-based encryption appeared recently in the early 1990s as an original application of nonlinear dynamics in the chaotic regime. In this paper, an implementation of digital image encryption scheme based on the mixture of chaotic systems is reported. The chaotic cryptography technique used in this paper is a symmetric key cryptography. In this algorithm, a typical coupled map was mixed with a one-dimensional chaotic map and used for high degree security image encryption while its speed is acceptable. The proposed algorithm is described in detail, along with its security analysis and implementation. The experimental results based on mixture of chaotic maps approves the effectiveness of the proposed method and the implementation of the algorithm. This mixture application of chaotic maps shows advantages of large key space and high-level security. The ciphertext generated by this method is the same size as the plaintext and is suitable for practical use in the secure transmission of confidential information over the Internet

  6. Multi-machine power system stabilizers design using chaotic optimization algorithm

    Energy Technology Data Exchange (ETDEWEB)

    Shayeghi, H., E-mail: hshayeghi@gmail.co [Technical Engineering Department, University of Mohaghegh Ardabili, Ardabil (Iran, Islamic Republic of); Shayanfar, H.A. [Center of Excellence for Power System Automation and Operation, Electrical Engineering Department, Iran University of Science and Technology, Tehran (Iran, Islamic Republic of); Jalilzadeh, S.; Safari, A. [Technical Engineering Department, Zanjan University, Zanjan (Iran, Islamic Republic of)

    2010-07-15

    In this paper, a multiobjective design of the multi-machine power system stabilizers (PSSs) using chaotic optimization algorithm (COA) is proposed. Chaotic optimization algorithms, which have the features of easy implementation, short execution time and robust mechanisms of escaping from the local optimum, is a promising tool for the engineering applications. The PSSs parameters tuning problem is converted to an optimization problem which is solved by a chaotic optimization algorithm based on Lozi map. Since chaotic mapping enjoys certainty, ergodicity and the stochastic property, the proposed chaotic optimization problem introduces chaos mapping using Lozi map chaotic sequences which increases its convergence rate and resulting precision. Two different objective functions are proposed in this study for the PSSs design problem. The first objective function is the eigenvalues based comprising the damping factor, and the damping ratio of the lightly damped electro-mechanical modes, while the second is the time domain-based multi-objective function. The robustness of the proposed COA-based PSSs (COAPSS) is verified on a multi-machine power system under different operating conditions and disturbances. The results of the proposed COAPSS are demonstrated through eigenvalue analysis, nonlinear time-domain simulation and some performance indices. In addition, the potential and superiority of the proposed method over the classical approach and genetic algorithm is demonstrated.

  7. When Darwin meets Lorenz: Evolving new chaotic attractors through genetic programming

    International Nuclear Information System (INIS)

    Pan, Indranil; Das, Saptarshi

    2015-01-01

    Highlights: •New 3D continuous time chaotic systems with analytical expressions are obtained. •The multi-gene genetic programming (MGGP) paradigm is employed to achieve this. •Extends earlier works for evolving generalised family of Lorenz attractors. •Over one hundred of new chaotic attractors along with their parameters are reported. •The MGGP method have the potential for finding other similar chaotic attractors. -- Abstract: In this paper, we propose a novel methodology for automatically finding new chaotic attractors through a computational intelligence technique known as multi-gene genetic programming (MGGP). We apply this technique to the case of the Lorenz attractor and evolve several new chaotic attractors based on the basic Lorenz template. The MGGP algorithm automatically finds new nonlinear expressions for the different state variables starting from the original Lorenz system. The Lyapunov exponents of each of the attractors are calculated numerically based on the time series of the state variables using time delay embedding techniques. The MGGP algorithm tries to search the functional space of the attractors by aiming to maximise the largest Lyapunov exponent (LLE) of the evolved attractors. To demonstrate the potential of the proposed methodology, we report over one hundred new chaotic attractor structures along with their parameters, which are evolved from just the Lorenz system alone

  8. High accuracy attitude reference stabilization and pointing using the Teledyne SDG-5 gyro and the DRIRU II inertial reference unit

    Science.gov (United States)

    Green, K. N.; van Alstine, R. L.

    This paper presents the current performance levels of the SDG-5 gyro, a high performance two-axis dynamically tuned gyro, and the DRIRU II redundant inertial reference unit relating to stabilization and pointing applications. Also presented is a discussion of a product improvement program aimed at further noise reductions to meet the demanding requirements of future space defense applications.

  9. Predictions of the near edge transport shortfall in DIII-D L-mode plasmas using the trapped gyro-Landau-fluid model

    Energy Technology Data Exchange (ETDEWEB)

    Kinsey, J. E. [CompX, P.O. Box 2672, Del Mar, California 92014 (United States); Staebler, G. M.; Candy, J.; Petty, C. C.; Waltz, R. E. [General Atomics, P.O. Box 85608, San Diego, California 92186-5608 (United States); Rhodes, T. L. [Physics Department and PSTI, University of California, Los Angeles, California 90095 (United States)

    2015-01-15

    Previous studies of DIII-D L-mode plasmas have shown that a transport shortfall exists in that our current models of turbulent transport can significantly underestimate the energy transport in the near edge region. In this paper, the Trapped Gyro-Landau-Fluid (TGLF) drift wave transport model is used to simulate the near edge transport in a DIII-D L-mode experiment designed to explore the impact of varying the safety factor on the shortfall. We find that the shortfall systematically increases with increasing safety factor and is more pronounced for the electrons than for the ions. Within the shortfall dataset, a single high current case has been found where no transport shortfall is predicted. Reduced neutral beam injection power has been identified as the key parameter separating this discharge from other discharges exhibiting a shortfall. Further analysis shows that the energy transport in the L-mode near edge region is not stiff according to TGLF. Unlike the H-mode core region, the predicted temperature profiles are relatively more responsive to changes in auxiliary heating power. In testing the fidelity of TGLF for the near edge region, we find that a recalibration of the collision model is warranted. A recalibration improves agreement between TGLF and nonlinear gyrokinetic simulations performed using the GYRO code with electron-ion collisions. The recalibration only slightly impacts the predicted shortfall.

  10. Chaotic time series analysis in economics: Balance and perspectives

    International Nuclear Information System (INIS)

    Faggini, Marisa

    2014-01-01

    The aim of the paper is not to review the large body of work concerning nonlinear time series analysis in economics, about which much has been written, but rather to focus on the new techniques developed to detect chaotic behaviours in economic data. More specifically, our attention will be devoted to reviewing some of these techniques and their application to economic and financial data in order to understand why chaos theory, after a period of growing interest, appears now not to be such an interesting and promising research area

  11. Function projective lag synchronization of fractional-order chaotic systems

    International Nuclear Information System (INIS)

    Wang Sha; Yu Yong-Guang; Wang Hu; Rahmani Ahmed

    2014-01-01

    Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme. (general)

  12. Some chaotic features of intrinsically coupled Josephson junctions

    International Nuclear Information System (INIS)

    Kolahchi, M.R.; Shukrinov, Yu.M.; Hamdipour, M.; Botha, A.E.; Suzuki, M.

    2013-01-01

    Highlights: ► Intrinsically coupled Josephson junctions model a high-T c superconductor. ► Intrinsically coupled Josephson junctions can act as a chaotic nonlinear system. ► Chaos could be due to resonance overlap. ► Avoiding parameters that lead to chaos is important for the design of resonators. -- Abstract: We look for chaos in an intrinsically coupled system of Josephson junctions. This study has direct applications for the high-T c resonators which require coherence amongst the junctions

  13. Chaotic time series analysis in economics: Balance and perspectives

    Energy Technology Data Exchange (ETDEWEB)

    Faggini, Marisa, E-mail: mfaggini@unisa.it [Dipartimento di Scienze Economiche e Statistiche, Università di Salerno, Fisciano 84084 (Italy)

    2014-12-15

    The aim of the paper is not to review the large body of work concerning nonlinear time series analysis in economics, about which much has been written, but rather to focus on the new techniques developed to detect chaotic behaviours in economic data. More specifically, our attention will be devoted to reviewing some of these techniques and their application to economic and financial data in order to understand why chaos theory, after a period of growing interest, appears now not to be such an interesting and promising research area.

  14. Role of multistability in the transition to chaotic phase synchronization

    DEFF Research Database (Denmark)

    Postnov, D.E.; Vadivasova, T.E.; Sosnovtseva, Olga

    1999-01-01

    In this paper we describe the transition to phase synchronization for systems of coupled nonlinear oscillators that individually follow the Feigenbaum route to chaos. A nested structure of phase synchronized regions of different attractor families is observed. With this structure, the transition...... to nonsynchronous behavior is determined by the loss of stability for the most stable synchronous mode. It is shown that the appearance of hyperchaos and the transition from lag synchronization to phase synchronization are related to the merging of chaotic attractors from different families. Numerical examples...

  15. Extending the performance of single-degree-of-freedom rate integrating gyros in strapdown applications

    Science.gov (United States)

    Baker, G. N.

    This paper examines the constraints upon a typical manufacturer of gyros and strapdown systems. It describes that while being responsive to exchange and keeping abreast of 'state of the art' technology, there are many reasons why the manufacturer must satisfy the market using existing technology and production equipment. The Single-Degree-of-Freedom Rate Integrating Gyro is a well established product, yet is capable of achieving far higher performances than originally envisaged due to modelling and characterization within digital strapdown systems. The parameters involved are discussed, and a description given of the calibration process undertaken on a strapdown system being manufactured in a production environment in batch quantities.

  16. Illusion optics in chaotic light

    International Nuclear Information System (INIS)

    Zhang Suheng; Gan Shu; Xiong Jun; Zhang Xiangdong; Wang Kaige

    2010-01-01

    The time-reversal process provides the possibility to counteract the time evolution of a physical system. Recent research has shown that such a process can occur in the first-order field correlation of chaotic light and result in the spatial interference and phase-reversal diffraction in an unbalanced interferometer. Here we report experimental investigations on the invisibility cloak and illusion phenomena in chaotic light. In an unbalanced interferometer illuminated by thermal light, we have observed the cloak effect and the optical transformation of one object into another object. The experimental results can be understood by the phase-reversal diffraction, and they demonstrate the theoretical proposal of similar effects in complementary media.

  17. Chaotic attractors with separated scrolls

    International Nuclear Information System (INIS)

    Bouallegue, Kais

    2015-01-01

    This paper proposes a new behavior of chaotic attractors with separated scrolls while combining Julia's process with Chua's attractor and Lorenz's attractor. The main motivation of this work is the ability to generate a set of separated scrolls with different behaviors, which in turn allows us to choose one or many scrolls combined with modulation (amplitude and frequency) for secure communication or synchronization. This set seems a new class of hyperchaos because each element of this set looks like a simple chaotic attractor with one positive Lyapunov exponent, so the cardinal of this set is greater than one. This new approach could be used to generate more general higher-dimensional hyperchaotic attractor for more potential application. Numerical simulations are given to show the effectiveness of the proposed theoretical results

  18. Anomalous diffusion in chaotic scattering

    International Nuclear Information System (INIS)

    Srokowski, T.; Ploszajczak, M.

    1994-01-01

    The anomalous diffusion is found for peripheral collision of atomic nuclei described in the framework of the molecular dynamics. Similarly as for chaotic billiards, the long free paths are the source of the long-time correlations and the anomalous diffusion. Consequences of this finding for the energy dissipation in deep-inelastic collisions and the dynamics of fission in hot nuclei are discussed (authors). 30 refs., 2 figs

  19. Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing

    Science.gov (United States)

    Kumar, Suhas; Strachan, John Paul; Williams, R. Stanley

    2017-08-01

    At present, machine learning systems use simplified neuron models that lack the rich nonlinear phenomena observed in biological systems, which display spatio-temporal cooperative dynamics. There is evidence that neurons operate in a regime called the edge of chaos that may be central to complexity, learning efficiency, adaptability and analogue (non-Boolean) computation in brains. Neural networks have exhibited enhanced computational complexity when operated at the edge of chaos, and networks of chaotic elements have been proposed for solving combinatorial or global optimization problems. Thus, a source of controllable chaotic behaviour that can be incorporated into a neural-inspired circuit may be an essential component of future computational systems. Such chaotic elements have been simulated using elaborate transistor circuits that simulate known equations of chaos, but an experimental realization of chaotic dynamics from a single scalable electronic device has been lacking. Here we describe niobium dioxide (NbO2) Mott memristors each less than 100 nanometres across that exhibit both a nonlinear-transport-driven current-controlled negative differential resistance and a Mott-transition-driven temperature-controlled negative differential resistance. Mott materials have a temperature-dependent metal-insulator transition that acts as an electronic switch, which introduces a history-dependent resistance into the device. We incorporate these memristors into a relaxation oscillator and observe a tunable range of periodic and chaotic self-oscillations. We show that the nonlinear current transport coupled with thermal fluctuations at the nanoscale generates chaotic oscillations. Such memristors could be useful in certain types of neural-inspired computation by introducing a pseudo-random signal that prevents global synchronization and could also assist in finding a global minimum during a constrained search. We specifically demonstrate that incorporating such

  20. CHAOTIC CAPTURE OF NEPTUNE TROJANS

    International Nuclear Information System (INIS)

    Nesvorny, David; Vokrouhlicky, David

    2009-01-01

    Neptune Trojans (NTs) are swarms of outer solar system objects that lead/trail planet Neptune during its revolutions around the Sun. Observations indicate that NTs form a thick cloud of objects with a population perhaps ∼10 times more numerous than that of Jupiter Trojans and orbital inclinations reaching ∼25 deg. The high inclinations of NTs are indicative of capture instead of in situ formation. Here we study a model in which NTs were captured by Neptune during planetary migration when secondary resonances associated with the mean-motion commensurabilities between Uranus and Neptune swept over Neptune's Lagrangian points. This process, known as chaotic capture, is similar to that previously proposed to explain the origin of Jupiter's Trojans. We show that chaotic capture of planetesimals from an ∼35 Earth-mass planetesimal disk can produce a population of NTs that is at least comparable in number to that inferred from current observations. The large orbital inclinations of NTs are a natural outcome of chaotic capture. To obtain the ∼4:1 ratio between high- and low-inclination populations suggested by observations, planetary migration into a dynamically excited planetesimal disk may be required. The required stirring could have been induced by Pluto-sized and larger objects that have formed in the disk.

  1. Characterizing chaotic melodies in automatic music composition

    Science.gov (United States)

    Coca, Andrés E.; Tost, Gerard O.; Zhao, Liang

    2010-09-01

    In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.

  2. Experimental observations of EMI effects in autonomous Chua's chaotic circuit

    Energy Technology Data Exchange (ETDEWEB)

    Kilic, Recai [Erciyes University, Department of Electrical and Electronics Engineering, 38039 Kayseri (Turkey)]. E-mail: kilic@erciyes.edu.tr; Saracoglu, O. Galip [Erciyes University, Department of Electrical and Electronics Engineering, 38039 Kayseri (Turkey); Yildirim, Fatma [Erciyes University, Civil Aviation School, 38039 Kayseri (Turkey)

    2007-05-15

    This paper deals with the experimentally investigation of EMI effects in autonomous Chua's chaotic circuit. We realized this experimental investigation by constructing an experimental setup subject to a Chua's circuit and applying a 5-30 MHz/100-200 mV EMI signal to the input pins of voltage Op-Amps used for realizing nonlinear resistor in Chua's circuit. In addition, we also experimentally investigated whether EMI signals affect the chaos synchronization between two Chua's chaotic circuits or not.

  3. An aperiodic phenomenon of the unscented Kalman filter in filtering noisy chaotic signals

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    A non-periodic oscillatory behavior of the unscented Kalman filter (UKF) when used to filter noisy contaminated chaotic signals is reported. We show both theoretically and experimentally that the gain of the UKF may not converge or diverge but oscillate aperiodically. More precisely, when a nonlinear system is periodic, the Kalman gain and error covariance of the UKF converge to zero. However, when the system being considered is chaotic, the Kalman gain either converges to a fixed point with a magnitude larger than zero or oscillates aperiodically.

  4. Feedback control and adaptive synchronization of chaotic forced Bonhoeffer-van der Pol oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Kontchou, E W Chimi; Fotsin, H B [Laboratoire d' Electronique, Departement de Physique, Faculte des Sciences, Universite de Dschang, B P 67 Dschang (Cameroon); Woafo, P [Laboratory of Modelling and Simulation in Engineering and Biological Physics, Faculty of Science, University of Yaounde I, Box 812, Yaounde (Cameroon)], E-mail: hbfotsin@yahoo.fr

    2008-04-15

    This paper deals with chaos control and synchronization in forced Bonhoeffer-van der Pol (FBVP) oscillators. The state equations of the model are first established and the stability is analysed. A feedback control strategy for stabilizing the chaotic dynamics on a periodic orbit of the phase space is investigated. Adaptive synchronization of two FBVP oscillators, based on parameter estimation and a nonlinear observer approach, is also investigated. It appears that a particular unknown parameter of the model can be estimated, which gives the possibility of recovering information through chaotic masking. An application in secure communications is presented.

  5. Feedback control and adaptive synchronization of chaotic forced Bonhoeffer-van der Pol oscillators

    International Nuclear Information System (INIS)

    Kontchou, E W Chimi; Fotsin, H B; Woafo, P

    2008-01-01

    This paper deals with chaos control and synchronization in forced Bonhoeffer-van der Pol (FBVP) oscillators. The state equations of the model are first established and the stability is analysed. A feedback control strategy for stabilizing the chaotic dynamics on a periodic orbit of the phase space is investigated. Adaptive synchronization of two FBVP oscillators, based on parameter estimation and a nonlinear observer approach, is also investigated. It appears that a particular unknown parameter of the model can be estimated, which gives the possibility of recovering information through chaotic masking. An application in secure communications is presented

  6. Chaotic queue-based genetic algorithm for design of a self-tuning fuzzy logic controller

    Science.gov (United States)

    Saini, Sanju; Saini, J. S.

    2012-11-01

    This paper employs a chaotic queue-based method using logistic equation in a non-canonical genetic algorithm for optimizing the performance of a self-tuning Fuzzy Logic Controller, used for controlling a nonlinear double-coupled system. A comparison has been made with a standard canonical genetic algorithm implemented on the same plant. It has been shown that chaotic queue-method brings an improvement in the performance of the FLC for wide range of set point changes by a more profound initial population spread in the search space.

  7. Robust synchronization of chaotic systems via feedback

    Energy Technology Data Exchange (ETDEWEB)

    Femat, Ricardo [IPICYT, San Luis Potosi (Mexico). Dept. de Matematicas Aplicadas; Solis-Perales, Gualberto [Universidad de Guadalajara, Centro Univ. de Ciencias Exactas e Ingenierias (Mexico). Div. de Electronica y Computacion

    2008-07-01

    This volume includes the results derived during last ten years about both suppression and synchronization of chaotic -continuous time- systems. Along this time, the concept was to study how the intrinsic properties of dynamical systems can be exploited to suppress and to synchronize the chaotic behaviour and what synchronization phenomena can be found under feedback interconnection. A compilation of these findings is described in this book. This book shows a perspective on synchronization of chaotic systems. (orig.)

  8. COMPARISON OF CHAOTIC AND FRACTAL PROPERTIES OF POLAR FACULAE WITH SUNSPOT ACTIVITY

    Energy Technology Data Exchange (ETDEWEB)

    Deng, L. H.; Xiang, Y. Y.; Dun, G. T. [Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216 (China); Li, B., E-mail: wooden@escience.cn [Shandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, School of Space Science and Physics, Shandong University at Weihai, Weihai 264209 (China)

    2016-01-15

    The solar magnetic activity is governed by a complex dynamo mechanism and exhibits a nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar time series are of great importance to understanding the solar dynamo actions, especially with regard to the nonlinear dynamo theories. In the present work, several nonlinear analysis approaches are proposed to investigate the nonlinear dynamical behavior of the polar faculae and sunspot activity for the time interval from 1951 August to 1998 December. The following prominent results are found: (1) both the high- and the low-latitude solar activity are governed by a three-dimensional chaotic attractor, and the chaotic behavior of polar faculae is the most complex, followed by that of the sunspot areas, and then the sunspot numbers; (2) both the high- and low-latitude solar activity exhibit a high degree of persistent behavior, and their fractal nature is due to such long-range correlation; (3) the solar magnetic activity cycle is predictable in nature, but the high-accuracy prediction should only be done for short- to mid-term due to its intrinsically dynamical complexity. With the help of the Babcock–Leighton dynamo model, we suggest that the nonlinear coupling of the polar magnetic fields with strong active-region fields exhibits a complex manner, causing the statistical similarities and differences between the polar faculae and the sunspot-related indicators.

  9. Identification of inhomogenous optical absorptive response by chaotic photonic signals in Au nanoparticles

    International Nuclear Information System (INIS)

    Muñoz-César, J C; Torres-Torres, C; Urriolagoitia-Sosa, G; Moreno-Valenzuela, J; Torres-Torres, D; Trejo-Valdez, M

    2013-01-01

    A chaotic circuit allows us to identify with a high sensitivity the optical absorption associated with a highly transparent sample with Au nanoparticles embedded in a TiO 2 thin film prepared by a sol–gel method. The measurements are based on a comparison of the correlation between a controlled optical irradiance that propagates through different zones of the sample. Nanosecond nonlinear optical measurements were obtained by monitoring the transmittance and the amplitude modification for the vectorial components of the electric fields in a two-wave mixing interaction. In addition, we theoretically study chaotic physical behavior exhibited by optical signals under nonlinear optical absorption. Our numerical results point out that small intensity fluctuations related to excitations of the absorptive nonlinearity can be described using a simple fractal model. Potential applications for developing sensors and instrumentation of the optical response of advanced materials are contemplated. (paper)

  10. A note on chaotic synchronization of time-delay secure communication systems

    International Nuclear Information System (INIS)

    Li Demin; Wang Zidong; Zhou Jie; Fang Jianan; Ni Jinjin

    2008-01-01

    In a real world, the signals are often transmitted through a hostile environment, and therefore the secure communication system has attracted considerable research interests. In this paper, the observer-based chaotic synchronization problem is studied for a class of time-delay secure communication systems. The system under consideration is subject to delayed state and nonlinear disturbances. The time-delay is allowed to be time-varying, and the nonlinearities are assumed to satisfy global Lipschitz conditions. The problem addressed is the design of a synchronization scheme such that, for the admissible time-delay as well as nonlinear disturbances, the response system can globally synchronize the driving system. An effective algebraic matrix inequality approach is developed to solve the chaotic synchronization problem. A numerical example is presented to show the effectiveness and efficiency of the proposed secure communication scheme

  11. TOWARDS THRESHOLD FREQUENCY IN CHAOTIC COLPITTS OSCILLATOR

    DEFF Research Database (Denmark)

    Lindberg, Erik; Tamasevicius, Arunas; Mykolaitis, Gytis

    2007-01-01

    A novel version of chaotic Colpitts oscillator is described. Instead of a linear loss resistor, it includes an extra inductor and diode in the collector circuit of the transistor. The modified circuit in comparison with the common Colpitts oscillator may generate chaotic oscillations at the funda......A novel version of chaotic Colpitts oscillator is described. Instead of a linear loss resistor, it includes an extra inductor and diode in the collector circuit of the transistor. The modified circuit in comparison with the common Colpitts oscillator may generate chaotic oscillations...

  12. Unstable periodic orbits and chaotic economic growth

    International Nuclear Information System (INIS)

    Ishiyama, K.; Saiki, Y.

    2005-01-01

    We numerically find many unstable periodic solutions embedded in a chaotic attractor in a macroeconomic growth cycle model of two countries with different fiscal policies, and we focus on a special type of the unstable periodic solutions. It is confirmed that chaotic behavior represented by the model is qualitatively and quantitatively related to the unstable periodic solutions. We point out that the structure of a chaotic solution is dissolved into a class of finite unstable periodic solutions picked out among a large number of periodic solutions. In this context it is essential for the unstable periodic solutions to be embedded in the chaotic attractor

  13. On estimates of the balanced gyro drift and the accuracy of the magnus formula

    NARCIS (Netherlands)

    Amel'kin, N. I.

    2009-01-01

    We construct efficient estimates of the balanced gyro drift due to nutation oscillations. We show that, for oscillation amplitudes not exceeding one degree and for amajority of gyromotions, the relative error in the drift rate calculations on the basis of the obtained estimates does not exceed

  14. Hydraulic evaluation of Joltech’s GyroPTO for wave energy applications

    DEFF Research Database (Denmark)

    Kramer, Morten Mejlhede; Pecher, Arthur Francois Serge; Guaraldi, Irene

    The work presented in this report was completed under the support from the Danish Energy Technological Development and Demonstration Program (EUDP), project no. 64014-0129 “Gyro electric energy converter unit for wave energy”. Testing took place in the wave basin at the Department of Civil Engine...

  15. The research of a gyro-stabilized platform and POS application technology in airborne remote sensing

    Science.gov (United States)

    Xu, Jiang; Du, Qi

    2009-07-01

    The distortion of the collected images usually takes place since the attitude changes along with the flying aerocraft on airborne remote sensing. In order to get original images without distortion, it is necessary to use professional gyro-stabilized platform. In addition to this, another solution of correcting the original image distortion is to utilize later geometric rectification using position & orientation system ( POS ) data. The third way is to utilize medium-accuracy stabilized platform to control the distortion at a tolerant range, and then make use of the data obtained by high-solution posture measure system to correct the low-quality remote sensing images. The third way which takes advantage of both techniques is better than using only one of the two other ways. This paper introduces several kinds of structural forms of gyro-stabilized platforms, and POS acquiring instruments respectively. Then, the essay will make some analysis of their advantages and disadvantages, key technologies and the application experiment of the third method. After the analysis, the thesis discusses the design of the gyro-stabilized platform. The thesis provides crucial information not only for the application technology of gyro-stabilized platform and POS but also for future development.

  16. Gyro-viscosity and linear dispersion relations in pair-ion magnetized plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Kono, M. [Faculty of Policy Studies, Chuo University, Tokyo 192-0393 (Japan); Vranjes, J. [Instituto de Astrofisica de Canarias, Tenerife E38205 (Spain); Departamento de Astrofisica, Universidad de La Laguna, Tenerife E38205 (Spain)

    2015-11-15

    A fluid theory has been developed by taking account of gyro-viscosity to study wave propagation characteristics in a homogeneous pair-ion magnetized plasma with a cylindrical symmetry. The exact dispersion relations derived by the Hankel-Fourier transformation are shown comparable with those observed in the experiment by Oohara and co-workers. The gyro-viscosity is responsible for the change in propagation characteristics of the ion cyclotron wave from forward to backward by suppressing the effect of the thermal pressure which normally causes the forward nature of dispersion. Although the experiment has been already explained by a kinetic theory by the present authors, the kinetic derivations are so involved because of exact particle orbits in phase space, finite Lamor radius effects, and higher order ion cyclotron resonances. The present fluid theory provides a simple and transparent structure to the dispersion relations since the gyro-viscosity is renormalized into the ion cyclotron frequency which itself indicates the backward nature of dispersion. The usual disadvantage of a fluid theory, which treats only fundamental modes of eigen-waves excited in a system and is not able to describe higher harmonics that a kinetic theory does, is compensated by simple derivations and clear picture based on the renormalization of the gyro-viscosity.

  17. THE EFFECT OF INTERMITTENT GYRO-SCALE SLAB TURBULENCE ON PARALLEL AND PERPENDICULAR COSMIC-RAY TRANSPORT

    International Nuclear Information System (INIS)

    Le Roux, J. A.

    2011-01-01

    Earlier work based on nonlinear guiding center (NLGC) theory suggested that perpendicular cosmic-ray transport is diffusive when cosmic rays encounter random three-dimensional magnetohydrodynamic turbulence dominated by uniform two-dimensional (2D) turbulence with a minor uniform slab turbulence component. In this approach large-scale perpendicular cosmic-ray transport is due to cosmic rays microscopically diffusing along the meandering magnetic field dominated by 2D turbulence because of gyroresonant interactions with slab turbulence. However, turbulence in the solar wind is intermittent and it has been suggested that intermittent turbulence might be responsible for the observation of 'dropout' events in solar energetic particle fluxes on small scales. In a previous paper le Roux et al. suggested, using NLGC theory as a basis, that if gyro-scale slab turbulence is intermittent, large-scale perpendicular cosmic-ray transport in weak uniform 2D turbulence will be superdiffusive or subdiffusive depending on the statistical characteristics of the intermittent slab turbulence. In this paper we expand and refine our previous work further by investigating how both parallel and perpendicular transport are affected by intermittent slab turbulence for weak as well as strong uniform 2D turbulence. The main new finding is that both parallel and perpendicular transport are the net effect of an interplay between diffusive and nondiffusive (superdiffusive or subdiffusive) transport effects as a consequence of this intermittency.

  18. THE EFFECT OF INTERMITTENT GYRO-SCALE SLAB TURBULENCE ON PARALLEL AND PERPENDICULAR COSMIC-RAY TRANSPORT

    Energy Technology Data Exchange (ETDEWEB)

    Le Roux, J. A. [Department of Physics, University of Alabama in Huntsville, Huntsville, AL 35899 (United States)

    2011-12-10

    Earlier work based on nonlinear guiding center (NLGC) theory suggested that perpendicular cosmic-ray transport is diffusive when cosmic rays encounter random three-dimensional magnetohydrodynamic turbulence dominated by uniform two-dimensional (2D) turbulence with a minor uniform slab turbulence component. In this approach large-scale perpendicular cosmic-ray transport is due to cosmic rays microscopically diffusing along the meandering magnetic field dominated by 2D turbulence because of gyroresonant interactions with slab turbulence. However, turbulence in the solar wind is intermittent and it has been suggested that intermittent turbulence might be responsible for the observation of 'dropout' events in solar energetic particle fluxes on small scales. In a previous paper le Roux et al. suggested, using NLGC theory as a basis, that if gyro-scale slab turbulence is intermittent, large-scale perpendicular cosmic-ray transport in weak uniform 2D turbulence will be superdiffusive or subdiffusive depending on the statistical characteristics of the intermittent slab turbulence. In this paper we expand and refine our previous work further by investigating how both parallel and perpendicular transport are affected by intermittent slab turbulence for weak as well as strong uniform 2D turbulence. The main new finding is that both parallel and perpendicular transport are the net effect of an interplay between diffusive and nondiffusive (superdiffusive or subdiffusive) transport effects as a consequence of this intermittency.

  19. Artificial optical emissions at HAARP for pump frequencies near the third and second electron gyro-harmonic

    Directory of Open Access Journals (Sweden)

    M. J. Kosch

    2005-07-01

    Full Text Available High-power high-frequency radio waves beamed into the ionosphere cause plasma turbulence, which can accelerate electrons. These electrons collide with the F-layer neutral oxygen causing artificial optical emissions identical to natural aurora. Pumping at electron gyro-harmonic frequencies has special significance as many phenomena change their character. In particular, artificial optical emissions become strongly reduced for the third and higher gyro-harmonics. The High frequency Active Auroral Research Program (HAARP facility is unique in that it can select a frequency near the second gyro-harmonic. On 25 February 2004, HAARP was operated near the third and passed through the second gyro-harmonic for the first time in a weakening ionosphere. Two novel observations are: firstly, a strong enhancement of the artificial optical emission intensity near the second gyro-harmonic, which is opposite to higher gyro-harmonics; secondly, the optical enhancement maximum occurs for frequencies just above the second gyro-harmonic. We provide the first experimental evidence for these effects, which have been predicted theoretically. In addition, irregular optical structures were created when the pump frequency was above the ionospheric critical frequency.

    Keywords. Active experiments – Auroral ionosphere – Wave-particle interactions

  20. Artificial optical emissions at HAARP for pump frequencies near the third and second electron gyro-harmonic

    Directory of Open Access Journals (Sweden)

    M. J. Kosch

    2005-07-01

    Full Text Available High-power high-frequency radio waves beamed into the ionosphere cause plasma turbulence, which can accelerate electrons. These electrons collide with the F-layer neutral oxygen causing artificial optical emissions identical to natural aurora. Pumping at electron gyro-harmonic frequencies has special significance as many phenomena change their character. In particular, artificial optical emissions become strongly reduced for the third and higher gyro-harmonics. The High frequency Active Auroral Research Program (HAARP facility is unique in that it can select a frequency near the second gyro-harmonic. On 25 February 2004, HAARP was operated near the third and passed through the second gyro-harmonic for the first time in a weakening ionosphere. Two novel observations are: firstly, a strong enhancement of the artificial optical emission intensity near the second gyro-harmonic, which is opposite to higher gyro-harmonics; secondly, the optical enhancement maximum occurs for frequencies just above the second gyro-harmonic. We provide the first experimental evidence for these effects, which have been predicted theoretically. In addition, irregular optical structures were created when the pump frequency was above the ionospheric critical frequency.Keywords. Active experiments – Auroral ionosphere – Wave-particle interactions

  1. Characterization of chaotic dynamics in the human menstrual cycle

    Science.gov (United States)

    Derry, Gregory; Derry, Paula

    2010-03-01

    The human menstrual cycle exhibits much unexplained variability, which is typically dismissed as random variation. Given the many delayed nonlinear feedbacks in the reproductive endocrine system, however, the menstrual cycle might well be a nonlinear dynamical system in a chaotic trajectory, and that this instead accounts for the observed variability. Here, we test this hypothesis by performing a time series analysis on data for 7438 menstrual cycles from 38 women in the 20-40 year age range, using the database maintained by the Tremin Research Program on Women's Health. Using phase space reconstruction techniques with a maximum embedding dimension of 6, we find appropriate scaling behavior in the correlation sums for this data, indicating low dimensional deterministic dynamics. A correlation dimension of 2.6 is measured in this scaling regime, and this result is confirmed by recalculation using the Takens estimator. These results may be interpreted as offering an approximation to the fractal dimension of a strange attractor governing the chaotic dynamics of the menstrual cycle.

  2. Chaotic Traversal (CHAT): Very Large Graphs Traversal Using Chaotic Dynamics

    Science.gov (United States)

    Changaival, Boonyarit; Rosalie, Martin; Danoy, Grégoire; Lavangnananda, Kittichai; Bouvry, Pascal

    2017-12-01

    Graph Traversal algorithms can find their applications in various fields such as routing problems, natural language processing or even database querying. The exploration can be considered as a first stepping stone into knowledge extraction from the graph which is now a popular topic. Classical solutions such as Breadth First Search (BFS) and Depth First Search (DFS) require huge amounts of memory for exploring very large graphs. In this research, we present a novel memoryless graph traversal algorithm, Chaotic Traversal (CHAT) which integrates chaotic dynamics to traverse large unknown graphs via the Lozi map and the Rössler system. To compare various dynamics effects on our algorithm, we present an original way to perform the exploration of a parameter space using a bifurcation diagram with respect to the topological structure of attractors. The resulting algorithm is an efficient and nonresource demanding algorithm, and is therefore very suitable for partial traversal of very large and/or unknown environment graphs. CHAT performance using Lozi map is proven superior than the, commonly known, Random Walk, in terms of number of nodes visited (coverage percentage) and computation time where the environment is unknown and memory usage is restricted.

  3. Chaotic dynamics of large-scale double-diffusive convection in a porous medium

    Science.gov (United States)

    Kondo, Shutaro; Gotoda, Hiroshi; Miyano, Takaya; Tokuda, Isao T.

    2018-02-01

    We have studied chaotic dynamics of large-scale double-diffusive convection of a viscoelastic fluid in a porous medium from the viewpoint of dynamical systems theory. A fifth-order nonlinear dynamical system modeling the double-diffusive convection is theoretically obtained by incorporating the Darcy-Brinkman equation into transport equations through a physical dimensionless parameter representing porosity. We clearly show that the chaotic convective motion becomes much more complicated with increasing porosity. The degree of dynamic instability during chaotic convective motion is quantified by two important measures: the network entropy of the degree distribution in the horizontal visibility graph and the Kaplan-Yorke dimension in terms of Lyapunov exponents. We also present an interesting on-off intermittent phenomenon in the probability distribution of time intervals exhibiting nearly complete synchronization.

  4. Improving the security of chaotic encryption by using a simple modulating method

    International Nuclear Information System (INIS)

    Bu Shouliang; Wang Binghong

    2004-01-01

    In recent years, synchronization of chaotic systems has aroused much interest due to its potential application to secure communications. However, it is found by Perez and Cerdeira that an intruder, without the knowledge of the parameters of the system or even of the nonlinear system itself, may extract the messages from the carrier signal by producing a return map where the dynamics is attracted to an almost 1D set. To eliminate the weakness, in this letter, a simple but efficient method for synchronizing chaotic systems by modulating the transmitted signal with an appropriately choosing scalar signal is proposed. It turns out that this modulating strategy not only preserves all appropriate information required for synchronizing chaotic systems but also destroys the possibility of the phase space reconstruction of the sender dynamics such as a return map

  5. Extended chaotic domain in the long optical fibers based on SBS process

    International Nuclear Information System (INIS)

    Gao, Junbo; Ding, Yingchun; Chen, Zhaoyang; Lin, Chengyou

    2014-01-01

    Chaotic stimulated Brillouin scattering (SBS) in optical fibers with weak external optical feedback has been investigated experimentally and theoretically. However, only the bifurcation route to chaos through period-one and quasi-periodic emission was discovered in the former work because the chaotic domain is very short in the general nonlinear system. In order to control the chaos process and observe finer periodic-orbit structures, a novel experiment was designed to extend the chaotic domain by using long optical fibers in the SBS system. In this experiment, the period-one, period-doubling, period-four and period-eight cycle routes to the chaos laser process as well as the more details of chaos, have been observed.

  6. Extended substitution-diffusion based image cipher using chaotic standard map

    Science.gov (United States)

    Kumar, Anil; Ghose, M. K.

    2011-01-01

    This paper proposes an extended substitution-diffusion based image cipher using chaotic standard map [1] and linear feedback shift register to overcome the weakness of previous technique by adding nonlinearity. The first stage consists of row and column rotation and permutation which is controlled by the pseudo-random sequences which is generated by standard chaotic map and linear feedback shift register, second stage further diffusion and confusion is obtained in the horizontal and vertical pixels by mixing the properties of the horizontally and vertically adjacent pixels, respectively, with the help of chaotic standard map. The number of rounds in both stage are controlled by combination of pseudo-random sequence and original image. The performance is evaluated from various types of analysis such as entropy analysis, difference analysis, statistical analysis, key sensitivity analysis, key space analysis and speed analysis. The experimental results illustrate that performance of this is highly secured and fast.

  7. A numeric-analytic method for approximating the chaotic Chen system

    International Nuclear Information System (INIS)

    Mossa Al-sawalha, M.; Noorani, M.S.M.

    2009-01-01

    The epitome of this paper centers on the application of the differential transformation method (DTM) the renowned Chen system which is described as a three-dimensional system of ODEs with quadratic nonlinearities. Numerical comparisons are made between the DTM and the classical fourth-order Runge-Kutta method (RK4). Our work showcases the precision of the DTM as the Chen system transforms from a non-chaotic system to a chaotic one. Since the Lyapunov exponent for this system is much higher compared to other chaotic systems, we shall highlight the difficulties of the simulations with respect to its accuracy. We wrap up our investigations to reveal that this direct symbolic-numeric scheme is effective and accurate.

  8. Regular and chaotic dynamics in time-dependent relativistic mean-field theory

    International Nuclear Information System (INIS)

    Vretenar, D.; Ring, P.; Lalazissis, G.A.; Poeschl, W.

    1997-01-01

    Isoscalar and isovector monopole oscillations that correspond to giant resonances in spherical nuclei are described in the framework of time-dependent relativistic mean-field theory. Time-dependent and self-consistent calculations that reproduce experimental data on monopole resonances in 208 Pb show that the motion of the collective coordinate is regular for isoscalar oscillations, and that it becomes chaotic when initial conditions correspond to the isovector mode. Regular collective dynamics coexists with chaotic oscillations on the microscopic level. Time histories, Fourier spectra, state-space plots, Poincare sections, autocorrelation functions, and Lyapunov exponents are used to characterize the nonlinear system and to identify chaotic oscillations. Analogous considerations apply to higher multipolarities. copyright 1997 The American Physical Society

  9. Semiconductor lasers driven by self-sustained chaotic electronic oscillators and applications to optical chaos cryptography.

    Science.gov (United States)

    Kingni, Sifeu Takougang; Mbé, Jimmi Hervé Talla; Woafo, Paul

    2012-09-01

    In this work, we numerically study the dynamics of vertical cavity surface emitting laser (VCSEL) firstly when it is driven by Chua's oscillator, secondly in case where it is driven by a broad frequency spectral bandwidth chaotic oscillator developed by Nana et al. [Commun. Nonlinear Sci. Numer. Simul. 14, 2266 (2009)]. We demonstrated that the VCSEL generated robust chaotic dynamics compared to the ones found in VCSEL subject to a sinusoidally modulated current and therefore it is more suitable for chaos encryption techniques. The synchronization characteristics and the communication performances of unidirectional coupled VCSEL driven by the broad frequency spectral bandwidth chaotic oscillators are investigated numerically. The results show that high-quality synchronization and transmission of messages can be realized for suitable system parameters. Chaos shift keying method is successfully applied to encrypt a message at a high bitrate.

  10. A New Chaotic System with Multiple Attractors: Dynamic Analysis, Circuit Realization and S-Box Design

    Directory of Open Access Journals (Sweden)

    Qiang Lai

    2017-12-01

    Full Text Available This paper reports about a novel three-dimensional chaotic system with three nonlinearities. The system has one stable equilibrium, two stable equilibria and one saddle node, two saddle foci and one saddle node for different parameters. One salient feature of this novel system is its multiple attractors caused by different initial values. With the change of parameters, the system experiences mono-stability, bi-stability, mono-periodicity, bi-periodicity, one strange attractor, and two coexisting strange attractors. The complex dynamic behaviors of the system are revealed by analyzing the corresponding equilibria and using the numerical simulation method. In addition, an electronic circuit is given for implementing the chaotic attractors of the system. Using the new chaotic system, an S-Box is developed for cryptographic operations. Moreover, we test the performance of this produced S-Box and compare it to the existing S-Box studies.

  11. Regular and chaotic behaviors of plasma oscillations modeled by a modified Duffing equation

    International Nuclear Information System (INIS)

    Enjieu Kadji, H.G.; Chabi Orou, J.B.; Woafo, P.; Abdus Salam International Centre for Theoretical Physics, Trieste

    2005-07-01

    The regular and chaotic behavior of plasma oscillations governed by a modified Duffing equation is studied. The plasma oscillations are described by a nonlinear differential equation of the form x + w 0 2 x + βx 2 + αx 3 = 0 which is similar to a Duffing equation. By focusing on the quadratic term, which is mainly the term modifying the Duffing equation, the harmonic balance method and the fourth order Runge-Kutta algorithm are used to derive regular and chaotic motions respectively. A strong chaotic behavior exhibited by the system in that event when the system is subjected to an external periodic forcing oscillation is reported as β varies. (author)

  12. Modelling and prediction for chaotic fir laser attractor using rational function neural network.

    Science.gov (United States)

    Cho, S

    2001-02-01

    Many real-world systems such as irregular ECG signal, volatility of currency exchange rate and heated fluid reaction exhibit highly complex nonlinear characteristic known as chaos. These chaotic systems cannot be retreated satisfactorily using linear system theory due to its high dimensionality and irregularity. This research focuses on prediction and modelling of chaotic FIR (Far InfraRed) laser system for which the underlying equations are not given. This paper proposed a method for prediction and modelling a chaotic FIR laser time series using rational function neural network. Three network architectures, TDNN (Time Delayed Neural Network), RBF (radial basis function) network and the RF (rational function) network, are also presented. Comparisons between these networks performance show the improvements introduced by the RF network in terms of a decrement in network complexity and better ability of predictability.

  13. Chaotic bursting in semiconductor lasers

    Science.gov (United States)

    Ruschel, Stefan; Yanchuk, Serhiy

    2017-11-01

    We investigate the dynamic mechanisms for low frequency fluctuations in semiconductor lasers subjected to delayed optical feedback, using the Lang-Kobayashi model. This system of delay differential equations displays pronounced envelope dynamics, ranging from erratic, so called low frequency fluctuations to regular pulse packages, if the time scales of fast oscillations and envelope dynamics are well separated. We investigate the parameter regions where low frequency fluctuations occur and compute their Lyapunov spectra. Using the geometric singular perturbation theory, we study this intermittent chaotic behavior and characterize these solutions as bursting slow-fast oscillations.

  14. Chaotic fluctuations in mathematical economics

    Energy Technology Data Exchange (ETDEWEB)

    Yoshida, Hiroyuki, E-mail: yoshida.hiroyuki@nihon-u.ac.jp [College of Economics, Nihon University, Chiyoda-ku, Tokyo 101-8360 (Japan)

    2011-03-01

    In this paper we examine a Cournot duopoly model, which expresses the strategic interaction between two firms. We formulate the dynamic adjustment process and investigate the dynamic properties of the stationary point. By introducing a memory mechanism characterized by distributed lag functions, we presuppose that each firm makes production decisions in a cautious manner. This implies that we have to deal with the system of integro-differential equations. By means of numerical simulations we show the occurrence of chaotic fluctuations in the case of fixed delays.

  15. Theory and practice of chaotic cryptography

    International Nuclear Information System (INIS)

    Amigo, J.M.; Kocarev, L.; Szczepanski, J.

    2007-01-01

    In this Letter we address some basic questions about chaotic cryptography, not least the very definition of chaos in discrete systems. We propose a conceptual framework and illustrate it with different examples from private and public key cryptography. We elaborate also on possible limits of chaotic cryptography

  16. Synchronization of Time-Continuous Chaotic Oscillators

    DEFF Research Database (Denmark)

    Yanchuk, S.; Maistrenko, Yuri; Mosekilde, Erik

    2003-01-01

    Considering a system of two coupled identical chaotic oscillators, the paper first establishes the conditions of transverse stability for the fully synchronized chaotic state. Periodic orbit threshold theory is applied to determine the bifurcations through which low-periodic orbits embedded...

  17. Synthesizing chaotic maps with prescribed invariant densities

    International Nuclear Information System (INIS)

    Rogers, Alan; Shorten, Robert; Heffernan, Daniel M.

    2004-01-01

    The Inverse Frobenius-Perron Problem (IFPP) concerns the creation of discrete chaotic mappings with arbitrary invariant densities. In this Letter, we present a new and elegant solution to the IFPP, based on positive matrix theory. Our method allows chaotic maps with arbitrary piecewise-constant invariant densities, and with arbitrary mixing properties, to be synthesized

  18. A Hybrid Chaotic Quantum Evolutionary Algorithm

    DEFF Research Database (Denmark)

    Cai, Y.; Zhang, M.; Cai, H.

    2010-01-01

    A hybrid chaotic quantum evolutionary algorithm is proposed to reduce amount of computation, speed up convergence and restrain premature phenomena of quantum evolutionary algorithm. The proposed algorithm adopts the chaotic initialization method to generate initial population which will form a pe...... tests. The presented algorithm is applied to urban traffic signal timing optimization and the effect is satisfied....

  19. Approximating chaotic saddles for delay differential equations.

    Science.gov (United States)

    Taylor, S Richard; Campbell, Sue Ann

    2007-04-01

    Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a "logistic" delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.

  20. Approximating chaotic saddles for delay differential equations

    Science.gov (United States)

    Taylor, S. Richard; Campbell, Sue Ann

    2007-04-01

    Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a “logistic” delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.

  1. Investigation of a chaotic thermostat

    Science.gov (United States)

    Morales, G. J.

    2018-03-01

    A numerical study is presented of a free particle interacting with a deterministic thermostat in which the usual friction force is supplemented with a fluctuating force that depends on the self-consistent damping coefficient associated with coupling to the heat bath. It is found that this addition results in a chaotic environment in which a particle self-heats from rest and moves in positive and negative directions, exhibiting a characteristic diffusive behavior. The frequency power spectrum of the dynamical quantities displays the exponential frequency dependence ubiquitous to chaotic dynamics. The velocity distribution function approximates a Maxwellian distribution, but it does show departures from perfect thermal equilibrium, while the distribution function for the damping coefficient shows a closer fit. The behavior for the classic Nosé-Hoover (NH) thermostat is compared to that of the enlarged Martyna-Klein-Tuckerman (MKT) model. Over a narrow amplitude range, the application of a constant external force results quantitatively in the Einstein relation for the NH thermostat, and for the MKT model it differs by a factor of 2.

  2. Hybrid chaotic ant swarm optimization

    International Nuclear Information System (INIS)

    Li Yuying; Wen Qiaoyan; Li Lixiang; Peng Haipeng

    2009-01-01

    Chaotic ant swarm optimization (CASO) is a powerful chaos search algorithm that is used to find the global optimum solution in search space. However, the CASO algorithm has some disadvantages, such as lower solution precision and longer computational time, when solving complex optimization problems. To resolve these problems, an improved CASO, called hybrid chaotic swarm optimization (HCASO), is proposed in this paper. The new algorithm introduces preselection operator and discrete recombination operator into the CASO; meanwhile it replaces the best position found by own and its neighbors' ants with the best position found by preselection operator and discrete recombination operator in evolution equation. Through testing five benchmark functions with large dimensionality, the experimental results show the new method enhances the solution accuracy and stability greatly, as well as reduces the computational time and computer memory significantly when compared to the CASO. In addition, we observe the results can become better with swarm size increasing from the sensitivity study to swarm size. And we gain some relations between problem dimensions and swam size according to scalability study.

  3. Chaotic Transport in Circumterrestrial Orbits

    Science.gov (United States)

    Rosengren, Aaron Jay

    2018-04-01

    The slow deformation of circumterrestrial orbits in the medium region, subject to lunisolar secular resonances, is well approximated by a Hamiltonian system with 2.5 degrees of freedom. This dynamical model is referred to in the astrophysical and celestial dynamics communities as the quadrupolar, secular, hierarchical three-body problem, and, in the non-autonomous case, gives rise to the classical Kozai-Lidov mechanism. In the time-dependent model, brought about in our case by the Moon's perturbed motion, the action variables of the system may experience chaotic variations and large drifts due to the possible overlap of nearby resonances. Using variational chaos indicators, we compute high-resolution portraits of the action space, revealing the existence of tori and structures filling chaotic regions. Our refined and elaborate calculations allow us to isolate precise initial conditions near specific areas of interest and to study their asymptotic behavior in time. We highlight in particular how the drift in phase space is mediated by the complement of the numerically detected KAM tori. Despite their reputed normality, Earth satellite orbits can possess an extraordinarily rich spectrum of dynamical behaviors, and, like the small body remnants of Solar system formation, they have all the complications that make them very interesting candidates for testing the modern tools of chaos theory.

  4. Power Forecasting of Combined Heating and Cooling Systems Based on Chaotic Time Series

    Directory of Open Access Journals (Sweden)

    Liu Hai

    2015-01-01

    Full Text Available Theoretic analysis shows that the output power of the distributed generation system is nonlinear and chaotic. And it is coupled with the microenvironment meteorological data. Chaos is an inherent property of nonlinear dynamic system. A predicator of the output power of the distributed generation system is to establish a nonlinear model of the dynamic system based on real time series in the reconstructed phase space. Firstly, chaos should be detected and quantified for the intensive studies of nonlinear systems. If the largest Lyapunov exponent is positive, the dynamical system must be chaotic. Then, the embedding dimension and the delay time are chosen based on the improved C-C method. The attractor of chaotic power time series can be reconstructed based on the embedding dimension and delay time in the phase space. By now, the neural network can be trained based on the training samples, which are observed from the distributed generation system. The neural network model will approximate the curve of output power adequately. Experimental results show that the maximum power point of the distributed generation system will be predicted based on the meteorological data. The system can be controlled effectively based on the prediction.

  5. Bifurcations and chaos of the nonlinear viscoelastic plates subjected to subsonic flow and external loads

    International Nuclear Information System (INIS)

    An, Fengxian; Chen, Fangqi

    2016-01-01

    Highlights: • The subharmonic bifurcations and chaotic motions are studied by means of Melnikov method. • The critical conditions for the occurrence of chaotic motions and subharmonic bifurcations are obtained. • The chaotic features on the system parameters are discussed. • The theoretical predictions are confirmed by numerical simulations. - Abstract: The subharmonic bifurcations and chaotic motions of the nonlinear viscoelastic plates subjected to subsonic flow and external loads are studied by means of Melnikov method. The critical conditions for the occurrence of chaotic motions are obtained. The chaotic features on the system parameters are discussed in detail. The conditions for subharmonic bifurcations are also obtained. For the system with no structural damping, chaotic motions can occur through infinite subharmonic bifurcations of odd orders. Furthermore, we confirm our theoretical predictions by numerical simulations. The theoretical results obtained here can help us to eliminate or suppress large nonlinear vibrations and chaotic motions of the nonlinear viscoelastic plates. Based on Melnikov method, complex dynamical behaviors of the nonlinear viscoelastic plates can be controlled by modifying the system parameters.

  6. Stabilizing unstable fixed points of chaotic maps via minimum entropy control

    Energy Technology Data Exchange (ETDEWEB)

    Salarieh, Hassan [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Tehran (Iran, Islamic Republic of)

    2008-08-15

    In this paper the problem of chaos control in nonlinear maps using minimization of entropy function is investigated. Invariant probability measure of a chaotic dynamics can be used to produce an entropy function in the sense of Shannon. In this paper it is shown that how the entropy control technique is utilized for chaos elimination. Using only the measured states of a chaotic map the probability measure of the system is numerically estimated and this estimated measure is used to obtain an estimation for the entropy of the chaotic map. The control variable of the chaotic system is determined in such a way that the entropy function descends until the chaotic trajectory of the map is replaced with a regular one. The proposed idea is applied for stabilizing the fixed points of the logistic and the Henon maps as some cases of study. Simulation results show the effectiveness of the method in chaos rejection when only the statistical information is available from the under-study systems.

  7. A novel grid multiwing chaotic system with only non-hyperbolic equilibria

    Science.gov (United States)

    Zhang, Sen; Zeng, Yicheng; Li, Zhijun; Wang, Mengjiao; Xiong, Le

    2018-05-01

    The structure of the chaotic attractor of a system is mainly determined by the nonlinear functions in system equations. By using a new saw-tooth wave function and a new stair function, a novel complex grid multiwing chaotic system which belongs to non-Shil'nikov chaotic system with non-hyperbolic equilibrium points is proposed in this paper. It is particularly interesting that the complex grid multiwing attractors are generated by increasing the number of non-hyperbolic equilibrium points, which are different from the traditional methods of realising multiwing attractors by adding the index-2 saddle-focus equilibrium points in double-wing chaotic systems. The basic dynamical properties of the new system, such as dissipativity, phase portraits, the stability of the equilibria, the time-domain waveform, power spectrum, bifurcation diagram, Lyapunov exponents, and so on, are investigated by theoretical analysis and numerical simulations. Furthermore, the corresponding electronic circuit is designed and simulated on the Multisim platform. The Multisim simulation results and the hardware experimental results are in good agreement with the numerical simulations of the same system on Matlab platform, which verify the feasibility of this new grid multiwing chaotic system.

  8. Chaos synchronization of nonlinear Bloch equations

    International Nuclear Information System (INIS)

    Park, Ju H.

    2006-01-01

    In this paper, the problem of chaos synchronization of Bloch equations is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical example is given to illuminate the design procedure and advantage of the result derived

  9. Tuning chaos in network sharing common nonlinearity

    Science.gov (United States)

    Paul Asir, M.; Jeevarekha, A.; Philominathan, P.

    2016-06-01

    In this paper, a novel type of network called network sharing common nonlinearity comprising both autonomous and non-autonomous oscillators have been investigated. We propose that these networks are robust for operating at desired modes i.e., chaotic or periodic by altering the v-i characteristics of common nonlinear element alone. The dynamics of these networks were examined through numerical, analytical, experimental and Multisim simulations.

  10. Nonlinear and Complex Dynamics in Real Systems

    OpenAIRE

    William Barnett; Apostolos Serletis; Demitre Serletis

    2005-01-01

    This paper was produced for the El-Naschie Symposium on Nonlinear Dynamics in Shanghai in December 2005. In this paper we provide a review of the literature with respect to fluctuations in real systems and chaos. In doing so, we contrast the order and organization hypothesis of real systems with nonlinear chaotic dynamics and discuss some techniques used in distinguishing between stochastic and deterministic behavior. Moreover, we look at the issue of where and when the ideas of chaos could p...

  11. Projective-anticipating, projective and projective-lag synchronization of chaotic systems with time-varying delays

    International Nuclear Information System (INIS)

    Feng Cunfang; Guan Wei; Wang Yinghai

    2013-01-01

    We investigate different types of projective (projective-anticipating, projective and projective-lag) synchronization in unidirectionally nonlinearly coupled time-delayed chaotic systems with variable time delays. Based on the Krasovskii–Lyapunov approach, we find both the existence and sufficient stability conditions, using a general class of time-delayed chaotic systems related to optical bistable or hybrid optical bistable devices. Our method has the advantage that it requires only one nonlinearly coupled term to achieve different types of projective synchronization in time-delayed chaotic systems with variable time delays. Compared with other existing works, our result provides an easy way to achieve projective-anticipating, projective and projective-lag synchronization. Numerical simulations of the Ikeda system are given to demonstrate the validity of the proposed method. (paper)

  12. Studies of nonlinear and chaotic phenomena in solid state systems

    Energy Technology Data Exchange (ETDEWEB)

    Bryant, P.H.

    1987-09-01

    This thesis contains three sections discussing different areas. Spin wave interactions in iron garnets are described in section one. Mathematical analysis of a magnetic oscillator is presented in section two. In the final section, the source of noise in Josephson Junctions is investigated. The three sections are indexed separately. (JDH)

  13. Studies of nonlinear and chaotic phenomena in solid state systems

    International Nuclear Information System (INIS)

    Bryant, P.H.

    1987-09-01

    This thesis contains three sections discussing different areas. Spin wave interactions in iron garnets are described in section one. Mathematical analysis of a magnetic oscillator is presented in section two. In the final section, the source of noise in Josephson Junctions is investigated. The three sections are indexed separately

  14. Soliton solutions and chaotic motions of the Zakharov equations for the Langmuir wave in the plasma

    Energy Technology Data Exchange (ETDEWEB)

    Zhen, Hui-Ling; Tian, Bo, E-mail: tian-bupt@163.com; Wang, Yu-Feng; Liu, De-Yin [State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 (China)

    2015-03-15

    For the interaction between the high-frequency Langmuir waves and low-frequency ion-acoustic waves in the plasma, the Zakharov equations are studied in this paper. Via the Hirota method, we obtain the soliton solutions, based on which the soliton propagation is presented. It is found that with λ increasing, the amplitude of u decreases, whereas that of v remains unchanged, where λ is the ion-acoustic speed, u is the slowly-varying envelope of the Langmuir wave, and v is the fluctuation of the equilibrium ion density. Both the head-on and bound-state interactions between the two solitons are displayed. We observe that with λ decreasing, the interaction period of u decreases, while that of v keeps unchanged. It is found that the Zakharov equations cannot admit any chaotic motions. With the external perturbations taken into consideration, the perturbed Zakharov equations are studied for us to see the associated chaotic motions. Both the weak and developed chaotic motions are investigated, and the difference between them roots in the relative magnitude of the nonlinearities and perturbations. The chaotic motions are weakened with λ increasing, or else, strengthened. Periodic motion appears when the nonlinear terms and external perturbations are balanced. With such a balance kept, one period increases with λ increasing.

  15. Gyro-Landau fluid model of tokamak core fluctuations

    International Nuclear Information System (INIS)

    Leboeuf, J.N.; Carreras, B.A.; Dominguez, N.; Hedrick, C.L.; Sidikman, K.L.; Lynch, V.E.; Drake, J.B.; Walker, D.W.

    1992-01-01

    Dissipative trapped electron modes (DTEM) may be one of the causes of deterioration of confinement in tokamak and stellatator plasmas. We have implemented a fluid model to study DTEM turbulence in slab geometry. The electron dynamics include in addition to the adiabatic part, a non-adiabatic piece modeled with an i-delta-type response. The ion dynamics include Landau damping and FLR corrections through Landau fluid approximate techniques and Pade approximants for Γ 0 (b)=I 0 (b)e -b . The model follows from the gyrokinetic equation. Evolution equations, which closely resemble those used in standard reduced MHD, are presented since these are better suited to non-linear calculations. The numerical results of radially resolved calculations will be discussed. A recently developed hybrid model, which consists of a gyrokinetic implementation for the ions using particles and the same description for the electron dynamics as in the fluid model, will also be presented

  16. GyroBoy – a self-balancing robot programmed in JAVA with leJOS EV3

    DEFF Research Database (Denmark)

    Christensen, Bjørn Klint

    GyroBoy is a self-balancing robot created by LEGO as a demonstration of what you can build with the EV3 LEGO Mindstorms education kit. The kit includes building instructions as well as a control program for GyroBoy developed in LEGO´s so called block-programming language. In this article I will p...... will present a similar control program developed in Java using the leJOS EV3 class library.......GyroBoy is a self-balancing robot created by LEGO as a demonstration of what you can build with the EV3 LEGO Mindstorms education kit. The kit includes building instructions as well as a control program for GyroBoy developed in LEGO´s so called block-programming language. In this article I...

  17. Slewing maneuvers and vibration control of space structures by feedforward/feedback moment-gyro controls

    Science.gov (United States)

    Yang, Li-Farn; Mikulas, Martin M., Jr.; Park, K. C.; Su, Renjeng

    1993-01-01

    This paper presents a moment-gyro control approach to the maneuver and vibration suppression of a flexible truss arm undergoing a constant slewing motion. The overall slewing motion is triggered by a feedforward input, and a companion feedback controller is employed to augment the feedforward input and subsequently to control vibrations. The feedforward input for the given motion requirement is determined from the combined CMG (Control Momentum Gyro) devices and the desired rigid-body motion. The rigid-body dynamic model has enabled us to identify the attendant CMG momentum saturation constraints. The task for vibration control is carried out in two stages; first in the search of a suitable CMG placement along the beam span for various slewing maneuvers, and subsequently in the development of Liapunov-based control algorithms for CMG spin-stabilization. Both analytical and numerical results are presented to show the effectiveness of the present approach.

  18. An Outdoor Navigation Platform with a 3D Scanner and Gyro-assisted Odometry

    Science.gov (United States)

    Yoshida, Tomoaki; Irie, Kiyoshi; Koyanagi, Eiji; Tomono, Masahiro

    This paper proposes a light-weight navigation platform that consists of gyro-assisted odometry, a 3D laser scanner and map-based localization for human-scale robots. The gyro-assisted odometry provides highly accurate positioning only by dead-reckoning. The 3D laser scanner has a wide field of view and uniform measuring-point distribution. The map-based localization is robust and computationally inexpensive by utilizing a particle filter on a 2D grid map generated by projecting 3D points on to the ground. The system uses small and low-cost sensors, and can be applied to a variety of mobile robots in human-scale environments. Outdoor navigation experiments were conducted at the Tsukuba Challenge held in 2009 and 2010, which is an open proving ground for human-scale robots. Our robot successfully navigated the assigned 1-km courses in a fully autonomous mode multiple times.

  19. Auto Regressive Moving Average (ARMA) Modeling Method for Gyro Random Noise Using a Robust Kalman Filter

    Science.gov (United States)

    Huang, Lei

    2015-01-01

    To solve the problem in which the conventional ARMA modeling methods for gyro random noise require a large number of samples and converge slowly, an ARMA modeling method using a robust Kalman filtering is developed. The ARMA model parameters are employed as state arguments. Unknown time-varying estimators of observation noise are used to achieve the estimated mean and variance of the observation noise. Using the robust Kalman filtering, the ARMA model parameters are estimated accurately. The developed ARMA modeling method has the advantages of a rapid convergence and high accuracy. Thus, the required sample size is reduced. It can be applied to modeling applications for gyro random noise in which a fast and accurate ARMA modeling method is required. PMID:26437409

  20. On dynamics analysis of a new chaotic attractor

    International Nuclear Information System (INIS)

    Zhou Wuneng; Xu Yuhua; Lu Hongqian; Pan Lin

    2008-01-01

    In this Letter, a new chaotic system is discussed. Some basic dynamical properties, such as Lyapunov exponents, Poincare mapping, fractal dimension, bifurcation diagram, continuous spectrum and chaotic dynamical behaviors of the new chaotic system are studied, either numerically or analytically. The obtained results show clearly that the system discussed in this Letter is a new chaotic system and deserves a further detailed investigation

  1. The method of separation of variables for the Frobenius-Perron operator associated to a class of two dimensional chaotic maps

    International Nuclear Information System (INIS)

    Luevano, Jose-Ruben

    2011-01-01

    Analytical expressions for the invariant densities for a class of discrete two dimensional chaotic systems are given. The method of separation of variables for the associated Frobenius-Perron equation is introduced. These systems are related to nonlinear difference equations which are of the type x k+2 = T(x k ). The function T is a chaotic map of an interval whose chaotic behaviour is inherited to the two dimensional one. We work out in detail some examples, with T an expansive or intermittent map, in order to expose the method. Finally, we discuss how to generalize the method to higher dimensional maps.

  2. One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order 1 < q < 2

    Science.gov (United States)

    Zhou, Ping; Bai, Rongji

    2014-01-01

    Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in 1 < q < 2, one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order 1 < q < 2 is considered. Numerical simulations show the validity and feasibility of the proposed scheme. PMID:25247207

  3. One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order 1

    Directory of Open Access Journals (Sweden)

    Ping Zhou

    2014-01-01

    Full Text Available Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in 1chaotic system with fractional-order 1

  4. ℋ∞ Adaptive observer for nonlinear fractional-order systems

    KAUST Repository

    Ndoye, Ibrahima; Laleg-Kirati, Taous-Meriem; Darouach, Mohamed; Voos, Holger

    2016-01-01

    inequalities (LMIs) by using an indirect Lyapunov method.The proposed ℋ∞ adaptive observer is also robust against Lipschitz additive nonlinear uncertainty. The performance of the observer is illustrated through some examples including the chaotic Lorenz and Lü

  5. Aerodynamic Drag Analysis of 3-DOF Flex-Gimbal GyroWheel System in the Sense of Ground Test

    Science.gov (United States)

    Huo, Xin; Feng, Sizhao; Liu, Kangzhi; Wang, Libin; Chen, Weishan

    2016-01-01

    GyroWheel is an innovative device that combines the actuating capabilities of a control moment gyro with the rate sensing capabilities of a tuned rotor gyro by using a spinning flex-gimbal system. However, in the process of the ground test, the existence of aerodynamic disturbance is inevitable, which hinders the improvement of the specification performance and control accuracy. A vacuum tank test is a possible candidate but is sometimes unrealistic due to the substantial increase in costs and complexity involved. In this paper, the aerodynamic drag problem with respect to the 3-DOF flex-gimbal GyroWheel system is investigated by simulation analysis and experimental verification. Concretely, the angular momentum envelope property of the spinning rotor system is studied and its integral dynamical model is deduced based on the physical configuration of the GyroWheel system with an appropriately defined coordinate system. In the sequel, the fluid numerical model is established and the model geometries are checked with FLUENT software. According to the diversity and time-varying properties of the rotor motions in three-dimensions, the airflow field around the GyroWheel rotor is analyzed by simulation with respect to its varying angular velocity and tilt angle. The IPC-based experimental platform is introduced, and the properties of aerodynamic drag in the ground test condition are obtained through comparing the simulation with experimental results. PMID:27941602

  6. Chaotic bubbling and nonstagnant foams.

    Science.gov (United States)

    Tufaile, Alberto; Sartorelli, José Carlos; Jeandet, Philippe; Liger-Belair, Gerard

    2007-06-01

    We present an experimental investigation of the agglomeration of bubbles obtained from a nozzle working in different bubbling regimes. This experiment consists of a continuous production of bubbles from a nozzle at the bottom of a liquid column, and these bubbles create a two-dimensional (2D) foam (or a bubble raft) at the top of this column. The bubbles can assemble in various dynamically stable arrangement, forming different kinds of foams in a liquid mixture of water and glycerol, with the effect that the bubble formation regimes influence the foam obtained from this agglomeration of bubbles. The average number of bubbles in the foam is related to the bubble formation frequency and the bubble mean lifetime. The periodic bubbling can generate regular or irregular foam, while a chaotic bubbling only generates irregular foam.

  7. Plasma parameter estimations for the Large Helical Device based on the gyro-reduced Bohm scaling

    International Nuclear Information System (INIS)

    Okamoto, Masao; Nakajima, Noriyoshi; Sugama, Hideo.

    1991-10-01

    A model of gyro-reduced Bohm scaling law is incorporated into a one-dimensional transport code to predict plasma parameters for the Large Helical Device (LHD). The transport code calculations reproduce well the LHD empirical scaling law and basic parameters and profiles of the LHD plasma are calculated. The amounts of toroidal currents (bootstrap current and beam-driven current) are also estimated. (author)

  8. The gyro-radius scaling of ion thermal transport from global numerical simulations of ITG turbulence

    International Nuclear Information System (INIS)

    Ottaviani, M.; Manfredi, G.

    1998-12-01

    A three-dimensional, fluid code is used to study the scaling of ion thermal transport caused by Ion-Temperature-Gradient-Driven (ITG) turbulence. The code includes toroidal effects and is capable of simulating the whole torus. It is found that both close to the ITG threshold and well above threshold, the thermal transport and the turbulence structures exhibit a gyro-Bohm scaling, at least for plasmas with moderate poloidal flow. (author)

  9. Terahertz radiation induced chaotic electron transport in semiconductor superlattices with a tilted magnetic field

    International Nuclear Information System (INIS)

    Wang, C.; Wang, F.; Cao, J. C.

    2014-01-01

    Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation

  10. Terahertz radiation induced chaotic electron transport in semiconductor superlattices with a tilted magnetic field.

    Science.gov (United States)

    Wang, C; Wang, F; Cao, J C

    2014-09-01

    Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation.

  11. Image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing

    Science.gov (United States)

    Zhou, Nanrun; Pan, Shumin; Cheng, Shan; Zhou, Zhihong

    2016-08-01

    Most image encryption algorithms based on low-dimensional chaos systems bear security risks and suffer encryption data expansion when adopting nonlinear transformation directly. To overcome these weaknesses and reduce the possible transmission burden, an efficient image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing is proposed. The original image is measured by the measurement matrices in two directions to achieve compression and encryption simultaneously, and then the resulting image is re-encrypted by the cycle shift operation controlled by a hyper-chaotic system. Cycle shift operation can change the values of the pixels efficiently. The proposed cryptosystem decreases the volume of data to be transmitted and simplifies the keys distribution simultaneously as a nonlinear encryption system. Simulation results verify the validity and the reliability of the proposed algorithm with acceptable compression and security performance.

  12. Terahertz radiation induced chaotic electron transport in semiconductor superlattices with a tilted magnetic field

    Energy Technology Data Exchange (ETDEWEB)

    Wang, C., E-mail: cwang@mail.sim.ac.cn; Wang, F.; Cao, J. C., E-mail: jccao@mail.sim.ac.cn [Key Laboratory of Terahertz Solid-State Technology, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050 (China)

    2014-09-01

    Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation.

  13. Internal crisis in a second-order non-linear non-autonomous electronic oscillator

    International Nuclear Information System (INIS)

    Stavrinides, S.G.; Deliolanis, N.C.; Miliou, A.N.; Laopoulos, Th.; Anagnostopoulos, A.N.

    2008-01-01

    The internal crisis of a second-order non-linear non-autonomous chaotic electronic circuit is studied. The phase portraits consist of two interacting sub-attractors, a chaotic and a periodic one. Maximal Lyapunov exponents were calculated, for both the periodic and the chaotic waveforms, in order to confirm their nature. Transitions between the chaotic and the periodic sub-attractors become more frequent by increasing the circuit driving frequency. The frequency distribution of the corresponding laminar lengths and their average values indicate that an internal crisis takes place in this circuit, manifested in the intermittent behaviour of the corresponding orbits

  14. Regular transport dynamics produce chaotic travel times.

    Science.gov (United States)

    Villalobos, Jorge; Muñoz, Víctor; Rogan, José; Zarama, Roberto; Johnson, Neil F; Toledo, Benjamín; Valdivia, Juan Alejandro

    2014-06-01

    In the hope of making passenger travel times shorter and more reliable, many cities are introducing dedicated bus lanes (e.g., Bogota, London, Miami). Here we show that chaotic travel times are actually a natural consequence of individual bus function, and hence of public transport systems more generally, i.e., chaotic dynamics emerge even when the route is empty and straight, stops and lights are equidistant and regular, and loading times are negligible. More generally, our findings provide a novel example of chaotic dynamics emerging from a single object following Newton's laws of motion in a regularized one-dimensional system.

  15. Chaotic inflation in models with flat directions

    International Nuclear Information System (INIS)

    Graziani, F.; Olive, K.

    1989-01-01

    We consider the chaotic inflationary scenario in models with flat directions. We find that unless the scalars along the flat directions have vacuum expectation values p or 10 14 M p 15 M p depending on the expectation values of the chaotic inflator, Ψ, one or two or more periods of inflation occur but with a resulting energy density perturbation δρ/ρ ≅ 10 -16 , far too small to be of any consequence for galaxy formation. Even with p only limited initial values of ≅ (3-200) M p result in inflation with reasonable density perturbations. Thus chaotic inflation in models with flat directions require rather special initial conditions. (orig.)

  16. Chaotic invasive weed optimization algorithm with application to parameter estimation of chaotic systems

    International Nuclear Information System (INIS)

    Ahmadi, Mohamadreza; Mojallali, Hamed

    2012-01-01

    Highlights: ► A new meta-heuristic optimization algorithm. ► Integration of invasive weed optimization and chaotic search methods. ► A novel parameter identification scheme for chaotic systems. - Abstract: This paper introduces a novel hybrid optimization algorithm by taking advantage of the stochastic properties of chaotic search and the invasive weed optimization (IWO) method. In order to deal with the weaknesses associated with the conventional method, the proposed chaotic invasive weed optimization (CIWO) algorithm is presented which incorporates the capabilities of chaotic search methods. The functionality of the proposed optimization algorithm is investigated through several benchmark multi-dimensional functions. Furthermore, an identification technique for chaotic systems based on the CIWO algorithm is outlined and validated by several examples. The results established upon the proposed scheme are also supplemented which demonstrate superior performance with respect to other conventional methods.

  17. Stimulated Brillouin scattering during electron gyro-harmonic heating at EISCAT

    Directory of Open Access Journals (Sweden)

    H. Y. Fu

    2015-08-01

    Full Text Available Observations of secondary radiation, stimulated electromagnetic emission (SEE, produced during ionospheric modification experiments using ground-based, high-power, high-frequency (HF radio waves are considered. The High Frequency Active Auroral Research Program (HAARP facility is capable of generating narrowband SEE in the form of stimulated Brillouin scatter (SBS and stimulated ion Bernstein scatter (SIBS in the SEE spectrum. Such narrowband SEE spectral lines have not been reported using the European Incoherent Scatter (EISCAT heater facility before. This work reports the first EISCAT results of narrowband SEE spectra and compares them to SEE previously observed at HAARP during electron gyro-harmonic heating. An analysis of experimental SEE data shows observations of emission lines within 100 Hz of the pump frequency, interpreted as SBS, during the 2012 July EISCAT campaign. Experimental results indicate that SBS strengthens as the pump frequency approaches the third electron gyro-harmonic. Also, for different heater antenna beam angles, the CUTLASS radar backscatter induced by HF radio pumping is suppressed near electron gyro-harmonics, whereas electron temperature enhancement weakens as measured by EISCAT/UHF radar. The main features of these new narrowband EISCAT observations are generally consistent with previous SBS measurements at HAARP.

  18. State-of-the-art of high power gyro-devices and free electron masers

    International Nuclear Information System (INIS)

    Thumm, M.

    1993-10-01

    At present, gyrotron oscillators are mainly used as high power millimeter wave sources for electron cyclotron resonance heating (ECRH) and diagnostics of magnetically confined plasmas for generation of energy by controlled thermonuclear fusion. 140 GHz gyrotrons with output power P out = 0.58 MW, pulse length τ = 2.0 s and efficiency η = 34% are commercially available. Diagnostic gyrotrons deliver P out = 40 kW with τ = 40 μs at frequencies up to 650 GHz (η ≥ 4%). Recently, gyrotron oscillators have also been successfully used in material processing and plasma chemistry. Such technological applications require gyrotrons with the following parameters: f ≥ 28 GHz, P out = 10-30 kW, CW, η ≥ 30%. This paper reports on achievements and problems related to the development of very high power mm-wave gyrotrons for long pulse or CW operation and describes the microwave technological pecularities of the different development steps. In addition, this work gives a short overview of the present development of gyrotrons for technological applications, quasi-optical gyrotrons, cyclotron autoresonance masers (CARMs), gyro-klystrons, gyro-TWT amplifiers, gyro-BWO's and free electron masers (FEMs). The most impressive FEM output parameters are: P out = 2 GW, τ = 20 ns, η = 13% at 140 GHz (LLNL) and P out = 15 kW, τ = 20 μs, η = 5% in the range from 120 to 900 GHz (UCSB). (orig.) [de

  19. Velocity ratio measurement using the frequency of gyro backward wave

    International Nuclear Information System (INIS)

    Muggli, P.; Tran, M.Q.; Tran, T.M.

    1990-10-01

    The operating diagram of a low quality factor, 8GHz TE 01 0 gyrotron exhibits oscillations between 6.8 and 7.3GHz. These oscillations are identified as the backward wave component of the TE 21 0 traveling mode. As the resonance condition of this mode depends on the average parallel velocity [ > of the beam electrons (ω BW ≅Ω C /γ - k [ [ >), the measurement of ω BW for given Ω C and γ, is used as a diagnostic for the beam electrons velocity ratio α= / [ >. The values of α, deduced from ω BW through the linear dispersion relation for the electron cyclotron instability in an infinite waveguide, are unrealistic. A non-linear simulation code gives α values which are in very good agreement with the ones predicted by a particle trajectory code (+10% to +20%). We find numerically that the particles' velocity dispersion in vperpendicular and v [ increases ω BW . This effect explains part of the discrepancy between the values of α inferred from ω BW without velocity dispersion and the expected values. (author) 10 refs., 6 figs., 1 tab

  20. Parametric Identification of Nonlinear Dynamical Systems

    Science.gov (United States)

    Feeny, Brian

    2002-01-01

    In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.

  1. Chaotic dynamics of flexible Euler-Bernoulli beams

    Energy Technology Data Exchange (ETDEWEB)

    Awrejcewicz, J., E-mail: awrejcew@p.lodz.pl [Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland and Department of Vehicles, Warsaw University of Technology, 84 Narbutta St., 02-524 Warsaw (Poland); Krysko, A. V., E-mail: anton.krysko@gmail.com [Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov (Russian Federation); Kutepov, I. E., E-mail: iekutepov@gmail.com; Zagniboroda, N. A., E-mail: tssrat@mail.ru; Dobriyan, V., E-mail: Dobriy88@yandex.ru; Krysko, V. A., E-mail: tak@san.ru [Department of Mathematics and Modeling, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov (Russian Federation)

    2013-12-15

    Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c{sup 2}) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions is carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q{sub 0} and frequency ω{sub p} of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.

  2. Chaos control and duration time of a class of uncertain chaotic systems

    International Nuclear Information System (INIS)

    Bowong, Samuel; Moukam Kakmeni, F.M.

    2003-01-01

    This Letter presents a robust control scheme for a class of uncertain chaotic systems in the canonical form, with unknown nonlinearities. To cope with the uncertainties, we combine Lyapunov methodology with observer design. The proposed strategy comprises an exponential linearizing feedback and an uncertainty estimator. The developed control scheme allows chaos suppression. The advantage of this method over the existing results is that the control time is explicitly computed. Simulations studies are conducted to verify the effectiveness of the scheme

  3. Model-free prediction of noisy chaotic time series by deep learning

    OpenAIRE

    Yeo, Kyongmin

    2017-01-01

    We present a deep neural network for a model-free prediction of a chaotic dynamical system from noisy observations. The proposed deep learning model aims to predict the conditional probability distribution of a state variable. The Long Short-Term Memory network (LSTM) is employed to model the nonlinear dynamics and a softmax layer is used to approximate a probability distribution. The LSTM model is trained by minimizing a regularized cross-entropy function. The LSTM model is validated against...

  4. Chaotic synchronization with gap junction of multi-neurons in external electrical stimulation

    International Nuclear Information System (INIS)

    Deng Bin; Wang Jiang; Fei Xiangyang

    2005-01-01

    The synchronization of n(n 3) neurons coupled with gap junction in external electrical stimulation is investigated. In this paper, the coupled model is established on the basis of nonlinear cable model, and then the relation between coupling strength of the gap junction and the synchronization is discussed in detail. The sufficient condition of complete synchronization is attained from rigorous mathematical derivation. The synchronizations of periodic neurons and chaotic neurons are studied respectively

  5. Modeling and Analysis of a Fractional-Order Generalized Memristor-Based Chaotic System and Circuit Implementation

    Science.gov (United States)

    Yang, Ningning; Xu, Cheng; Wu, Chaojun; Jia, Rong; Liu, Chongxin

    2017-12-01

    Memristor is a nonlinear “missing circuit element”, that can easily achieve chaotic oscillation. Memristor-based chaotic systems have received more and more attention. Research shows that fractional-order systems are more close to real systems. As an important parameter, the order can increase the flexibility and degree of freedom of the system. In this paper, a fractional-order generalized memristor, which consists of a diode bridge and a parallel circuit with an equivalent unit circuit and a linear resistance, is proposed. Frequency and electrical characteristics of the fractional-order memristor are analyzed. A chain structure circuit is used to implement the fractional-order unit circuit. Then replacing the conventional Chua’s diode by the fractional-order generalized memristor, a fractional-order memristor-based chaotic circuit is proposed. A large amount of research work has been done to investigate the influence of the order on the dynamical behaviors of the fractional-order memristor-based chaotic circuit. Varying with the order, the system enters the chaotic state from the periodic state through the Hopf bifurcation and period-doubling bifurcation. The chaotic state of the system has two types of attractors: single-scroll and double-scroll attractor. The stability theory of fractional-order systems is used to determine the minimum order occurring Hopf bifurcation. And the influence of the initial value on the system is analyzed. Circuit simulations are designed to verify the results of theoretical analysis and numerical simulation.

  6. Output Choice of a Chaotic Jerk Circuit Used as Transmitter in Data Secure Communications

    Directory of Open Access Journals (Sweden)

    DATCU, O.

    2015-11-01

    Full Text Available Usually, when analyzing a data series, dynamical systems theory is used to reconstruct the state space of the original system. This work aims to determine which of a chaotic system's states is best suited as output when transmitting secret messages. This is the first step prior to designing an actual communication scheme. As an example, the three states of Sprott's jerk circuit are analyzed in terms of the local observability they ensure for the original dynamics when transmitted as a scalar data series. Results show that its first two states enable accurate estimation of the transmitter's dynamics at the receiving end. However, its third state generates, in some regions of the state space, a non-invertible transformation between the original state space and the one the receiver sees. This is due to the exponential nonlinearities present in this state's derivatives. Given that these nonlinearities remain inaccessible to the receiver, they are neglected in order to allow the partial reconstruction of the dynamics of the transmitter. But, since these nonlinearities are essential for the chaotic behavior, this makes the third state unusable for cryptographic purposes. This analysis may be applied to any bipolar junction transistor or diode based chaotic circuit.

  7. Prediction and Geometry of Chaotic Time Series

    National Research Council Canada - National Science Library

    Leonardi, Mary

    1997-01-01

    This thesis examines the topic of chaotic time series. An overview of chaos, dynamical systems, and traditional approaches to time series analysis is provided, followed by an examination of state space reconstruction...

  8. Encryption in Chaotic Systems with Sinusoidal Excitations

    Directory of Open Access Journals (Sweden)

    G. Obregón-Pulido

    2014-01-01

    Full Text Available In this contribution an encryption method using a chaotic oscillator, excited by “n” sinusoidal signals, is presented. The chaotic oscillator is excited by a sum of “n” sinusoidal signals and a message. The objective is to encrypt such a message using the chaotic behavior and transmit it, and, as the chaotic system is perturbed by the sinusoidal signal, the transmission security could be increased due to the effect of such a perturbation. The procedure is based on the regulation theory and consider that the receiver knows the frequencies of the perturbing signal, with this considerations the algorithm estimates the excitation in such a way that the receiver can cancel out the perturbation and all the undesirable dynamics in order to produce only the message. In this way we consider that the security level is increased.

  9. Chaotic Zones around Rotating Small Bodies

    Energy Technology Data Exchange (ETDEWEB)

    Lages, José; Shevchenko, Ivan I. [Institut UTINAM, Observatoire des Sciences de l’Univers THETA, CNRS, Université de Franche-Comté, Besançon F-25030 (France); Shepelyansky, Dima L., E-mail: jose.lages@utinam.cnrs.fr [Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, Toulouse F-31062 (France)

    2017-06-01

    Small bodies of the solar system, like asteroids, trans-Neptunian objects, cometary nuclei, and planetary satellites, with diameters smaller than 1000 km usually have irregular shapes, often resembling dumb-bells or contact binaries. The spinning of such a gravitating dumb-bell creates around it a zone of chaotic orbits. We determine its extent analytically and numerically. We find that the chaotic zone swells significantly if the rotation rate is decreased; in particular, the zone swells more than twice if the rotation rate is decreased 10 times with respect to the “centrifugal breakup” threshold. We illustrate the properties of the chaotic orbital zones in examples of the global orbital dynamics about asteroid 243 Ida (which has a moon, Dactyl, orbiting near the edge of the chaotic zone) and asteroid 25143 Itokawa.

  10. Globally Coupled Chaotic Maps with Constant Force

    International Nuclear Information System (INIS)

    Li Jinghui

    2008-01-01

    We investigate the motion of the globally coupled maps (logistic map) with a constant force. It is shown that the constant force can cause multi-synchronization for the globally coupled chaotic maps studied by us.

  11. Multiswitching compound antisynchronization of four chaotic systems

    Indian Academy of Sciences (India)

    Ayub Khan

    2017-11-28

    Nov 28, 2017 ... systems, electrical engineering, information process- ... model. The synchronization problem among three or more chaotic ...... we perform numerical simulations in MATLAB using ... In the simulation process we assume α1 =.

  12. Prediction of the Reference Evapotranspiration Using a Chaotic Approach

    Science.gov (United States)

    Wang, Wei-guang; Zou, Shan; Luo, Zhao-hui; Zhang, Wei; Kong, Jun

    2014-01-01

    Evapotranspiration is one of the most important hydrological variables in the context of water resources management. An attempt was made to understand and predict the dynamics of reference evapotranspiration from a nonlinear dynamical perspective in this study. The reference evapotranspiration data was calculated using the FAO Penman-Monteith equation with the observed daily meteorological data for the period 1966–2005 at four meteorological stations (i.e., Baotou, Zhangbei, Kaifeng, and Shaoguan) representing a wide range of climatic conditions of China. The correlation dimension method was employed to investigate the chaotic behavior of the reference evapotranspiration series. The existence of chaos in the reference evapotranspiration series at the four different locations was proved by the finite and low correlation dimension. A local approximation approach was employed to forecast the daily reference evapotranspiration series. Low root mean square error (RSME) and mean absolute error (MAE) (for all locations lower than 0.31 and 0.24, resp.), high correlation coefficient (CC), and modified coefficient of efficiency (for all locations larger than 0.97 and 0.8, resp.) indicate that the predicted reference evapotranspiration agrees well with the observed one. The encouraging results indicate the suitableness of chaotic approach for understanding and predicting the dynamics of the reference evapotranspiration. PMID:25133221

  13. Prediction of the Reference Evapotranspiration Using a Chaotic Approach

    Directory of Open Access Journals (Sweden)

    Wei-guang Wang

    2014-01-01

    Full Text Available Evapotranspiration is one of the most important hydrological variables in the context of water resources management. An attempt was made to understand and predict the dynamics of reference evapotranspiration from a nonlinear dynamical perspective in this study. The reference evapotranspiration data was calculated using the FAO Penman-Monteith equation with the observed daily meteorological data for the period 1966–2005 at four meteorological stations (i.e., Baotou, Zhangbei, Kaifeng, and Shaoguan representing a wide range of climatic conditions of China. The correlation dimension method was employed to investigate the chaotic behavior of the reference evapotranspiration series. The existence of chaos in the reference evapotranspiration series at the four different locations was proved by the finite and low correlation dimension. A local approximation approach was employed to forecast the daily reference evapotranspiration series. Low root mean square error (RSME and mean absolute error (MAE (for all locations lower than 0.31 and 0.24, resp., high correlation coefficient (CC, and modified coefficient of efficiency (for all locations larger than 0.97 and 0.8, resp. indicate that the predicted reference evapotranspiration agrees well with the observed one. The encouraging results indicate the suitableness of chaotic approach for understanding and predicting the dynamics of the reference evapotranspiration.

  14. A chaotic system with a single unstable node

    Energy Technology Data Exchange (ETDEWEB)

    Sprott, J.C. [Department of Physics, University of Wisconsin, Madison, WI 53706 (United States); Jafari, Sajad, E-mail: sajadjafari@aut.ac.ir [Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413 (Iran, Islamic Republic of); Pham, Viet-Thanh [School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi (Viet Nam); Hosseini, Zahra Sadat [Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413 (Iran, Islamic Republic of)

    2015-09-25

    This paper describes an unusual example of a three-dimensional dissipative chaotic flow with quadratic nonlinearities in which the only equilibrium is an unstable node. The region of parameter space with bounded solutions is relatively small as is the basin of attraction, which accounts for the difficulty of its discovery. Furthermore, for some values of the parameters, the system has an attracting torus, which is uncommon in three-dimensional systems, and this torus can coexist with a strange attractor or with a limit cycle. The limit cycle and strange attractor exhibit symmetry breaking and attractor merging. All the attractors appear to be hidden in that they cannot be found by starting with initial conditions in the vicinity of the equilibrium, and thus they represent a new type of hidden attractor with important and potentially problematic engineering consequences. - Highlights: • An unusual example of a three-dimensional dissipative chaotic flow is introduced. • In this system the only equilibrium is an unstable node. • For some values of the parameters, the system has an attracting torus. • This torus can coexist with a strange attractor or with a limit cycle. • These properties are uncommon in three-dimensional systems.

  15. Fuzzy logic controllers and chaotic natural convection loops

    International Nuclear Information System (INIS)

    Theler, German

    2007-01-01

    The study of natural circulation loops is a subject of special concern for the engineering design of advanced nuclear reactors, as natural convection provides an efficient and completely passive heat removal system. However, under certain circumstances thermal-fluid-dynamical instabilities may appear, threatening the reactor safety as a whole.On the other hand, fuzzy logic controllers provide an ideal framework to approach highly non-linear control problems. In the present work, we develop a software-based fuzzy logic controller and study its application to chaotic natural convection loops.We numerically analyse the linguistic control of the loop known as the Welander problem in such conditions that, if the controller were not present, the circulation flow would be non-periodic unstable.We also design a Taka gi-Sugeno fuzzy controller based on a fuzzy model of a natural convection loop with a toroidal geometry, in order to stabilize a Lorenz-chaotic behaviour.Finally, we show experimental results obtained in a rectangular natural circulation loop [es

  16. Controlling chaotic behavior in CO2 and other lasers

    Science.gov (United States)

    1993-06-01

    Additional substantial experimental progress has been made, in the third month of the project, in setting up equipment and testing for producing chaotic behavior with a CO2 laser. The project goal is to synchronize and control chaos in CO2 and other lasers, and thereby increase the power in ensembles of coupled laser sources. Numerous investigations into the chaos regime have been made, a second CO2 laser has been brought on stream, and work is progressing in the fourth month toward coupling the two lasers and control of the first laser. It is also intended to submit at least two papers to the Second Experimental Chaos Conference which is supported by the Office of Naval Research. Abstracts to those two papers are attached. Last month's report discussed the experimental investigation of nonlinear dynamics of CO2 lasers which involved a new technique of inducing chaos. In this new technique, an acoustically modulated feedback of the laser light was used and led to chaotic dynamics at a very low modulation frequency of 375 Hz. Since then, new results have been obtained by an Electro-Optical Modulation (EOM) technique. In the new setup, the electro-optical modulator is placed in an external cavity outside the laser.

  17. Synchronizing a class of uncertain chaotic systems

    International Nuclear Information System (INIS)

    Chen Maoyin; Zhou Donghua; Shang Yun

    2005-01-01

    This Letter deals with the synchronization of a class of uncertain chaotic systems in the drive-response framework. A robust adaptive observer based response system is designed to synchronize a given chaotic system with unknown parameters and external disturbances. Lyapunov stability ensures the global synchronization between the drive and response systems even if Lipschitz constants on function matrices and bounds on uncertainties are unknown. Numerical simulation of Genesio-Tesi system verifies the effectiveness of this scheme

  18. Anti-synchronization of chaotic oscillators

    International Nuclear Information System (INIS)

    Kim, Chil-Min; Rim, Sunghwan; Kye, Won-Ho; Ryu, Jung-Wan; Park, Young-Jai

    2003-01-01

    We have observed anti-synchronization phenomena in coupled identical chaotic oscillators. Anti-synchronization can be characterized by the vanishing of the sum of relevant variables. We have qualitatively analyzed its base mechanism by using the dynamics of the difference and the sum of the relevant variables in coupled chaotic oscillators. Near the threshold of the synchronization and anti-synchronization transition, we have obtained the novel characteristic relation

  19. Improvement on generalised synchronisation of chaotic systems

    International Nuclear Information System (INIS)

    Hui-Bin, Zhu; Fang, Qiu; Bao-Tong, Cui

    2010-01-01

    In this paper, the problem of generalised synchronisation of two different chaotic systems is investigated. Some less conservative conditions are derived using linear matrix inequality other than existing results. Furthermore, a simple adaptive control scheme is proposed to achieve the generalised synchronisation of chaotic systems. The proposed method is simple and easy to implement in practice and can be applied to secure communications. Numerical simulations are also given to demonstrate the effectiveness and feasibility of the theoretical analysis

  20. Chaotic behavior in a relativistic electron beam interacting with a transverse slow electromagnetic wave

    International Nuclear Information System (INIS)

    Serbeto, A.; Alves, M.V.

    1993-01-01

    Using a nonlinear set of equations which describes the excitation of a purely transverse slow electromagnetic wave by a relativistic electron beam, it is shown that the system runs from chaotic behavior to a regular stable state due to crisis phenomenon and from stabilized soliton and repeated stabilized explosive solutions to a temporal chaos. These behaviors suggest that the primary mechanism for the saturation of the explosive instability is not only the cubic nonlinear frequency shift as pointed out by many authors until now. The inclusion of the velocity perturbation in the beam charge initial equilibrium state leads the system to these strange behaviors. (author)

  1. Qualitative dynamical analysis of chaotic plasma perturbations model

    Science.gov (United States)

    Elsadany, A. A.; Elsonbaty, Amr; Agiza, H. N.

    2018-06-01

    In this work, an analytical framework to understand nonlinear dynamics of plasma perturbations model is introduced. In particular, we analyze the model presented by Constantinescu et al. [20] which consists of three coupled ODEs and contains three parameters. The basic dynamical properties of the system are first investigated by the ways of bifurcation diagrams, phase portraits and Lyapunov exponents. Then, the normal form technique and perturbation methods are applied so as to the different types of bifurcations that exist in the model are investigated. It is proved that pitcfork, Bogdanov-Takens, Andronov-Hopf bifurcations, degenerate Hopf and homoclinic bifurcation can occur in phase space of the model. Also, the model can exhibit quasiperiodicity and chaotic behavior. Numerical simulations confirm our theoretical analytical results.

  2. Detecting malicious chaotic signals in wireless sensor network

    Science.gov (United States)

    Upadhyay, Ranjit Kumar; Kumari, Sangeeta

    2018-02-01

    In this paper, an e-epidemic Susceptible-Infected-Vaccinated (SIV) model has been proposed to analyze the effect of node immunization and worms attacking dynamics in wireless sensor network. A modified nonlinear incidence rate with cyrtoid type functional response has been considered using sleep and active mode approach. Detailed stability analysis and the sufficient criteria for the persistence of the model system have been established. We also established different types of bifurcation analysis for different equilibria at different critical points of the control parameters. We performed a detailed Hopf bifurcation analysis and determine the direction and stability of the bifurcating periodic solutions using center manifold theorem. Numerical simulations are carried out to confirm the theoretical results. The impact of the control parameters on the dynamics of the model system has been investigated and malicious chaotic signals are detected. Finally, we have analyzed the effect of time delay on the dynamics of the model system.

  3. Collection of master-slave synchronized chaotic systems

    International Nuclear Information System (INIS)

    Lerescu, A.I.; Constandache, N.; Oancea, S.; Grosu, I.

    2004-01-01

    In this work the open-plus-closed-loop (OPCL) method of synchronization is used in order to synchronize the systems from the Sprott's collection of the simplest chaotic systems. The method is general and we looked for the simplest coupling between master and slave. The main result is that for the systems that contains one nonlinear term and that term contains one variable then the coupling consists of one term. The numerical intervals of parameters where the synchronization is achieved are obtained analytically by applying Routh-Hurwitz conditions. Detailed calculations and numerical results are given for the system I from the Sprott's collection. Working in the same manner for many systems this method can be adopted for the teaching of the topic

  4. Finite-Time Synchronizing Control for Chaotic Neural Networks

    Directory of Open Access Journals (Sweden)

    Chao Zhang

    2014-01-01

    Full Text Available This paper addresses the finite-time synchronizing problem for a class of chaotic neural networks. In a real communication network, parameters of the master system may be time-varying and the system may be perturbed by external disturbances. A simple high-gain observer is designed to track all the nonlinearities, unknown system functions, and disturbances. Then, a dynamic active compensatory controller is proposed and by using the singular perturbation theory, the control method can guarantee the finite-time stability of the error system between the master system and the slave system. Finally, two illustrative examples are provided to show the effectiveness and applicability of the proposed scheme.

  5. Neural network modeling of chaotic dynamics in nuclear reactor flows

    International Nuclear Information System (INIS)

    Welstead, S.T.

    1992-01-01

    Neural networks have many scientific applications in areas such as pattern classification and time series prediction. The universal approximation property of these networks, however, can also be exploited to provide researchers with tool for modeling observed nonlinear phenomena. It has been shown that multilayer feed forward networks can capture important global nonlinear properties, such as chaotic dynamics, merely by training the network on a finite set of observed data. The network itself then provides a model of the process that generated the data. Characterizations such as the existence and general shape of a strange attractor and the sign of the largest Lyapunov exponent can then be extracted from the neural network model. In this paper, the author applies this idea to data generated from a nonlinear process that is representative of convective flows that can arise in nuclear reactor applications. Such flows play a role in forced convection heat removal from pressurized water reactors and boiling water reactors, and decay heat removal from liquid-metal-cooled reactors, either by natural convection or by thermosyphons

  6. Blended particle filters for large-dimensional chaotic dynamical systems

    Science.gov (United States)

    Majda, Andrew J.; Qi, Di; Sapsis, Themistoklis P.

    2014-01-01

    A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase space are introduced here. These blended particle filters are constructed in this paper through a mathematical formalism involving conditional Gaussian mixtures combined with statistically nonlinear forecast models compatible with this structure developed recently with high skill for uncertainty quantification. Stringent test cases for filtering involving the 40-dimensional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents are used here. These cases demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations. The formalism developed here is also useful for multiscale filtering of turbulent systems and a simple application is sketched below. PMID:24825886

  7. Chaotic dynamic and control for micro-electro-mechanical systems of massive storage with harmonic base excitation

    International Nuclear Information System (INIS)

    Perez Polo, Manuel F.; Perez Molina, Manuel; Gil Chica, Javier

    2009-01-01

    This paper explores chaotic behaviour and control of micro-electro-mechanical systems (MEMS), which consist of thousands of small read/write probe tips that access gigabytes of data stored in a non-volatile magnetic surface. The model of the system is formed by two masses connected by a nonlinear spring and a viscous damping. The paper shows that, by means of an adequate feedback law, the masses can behave as two coupled Duffing's oscillators, which may reach chaotic behaviour when harmonic forces are applied. The chaotic motion is destroyed by applying the following control strategies: (i) static output feedback control law with constant forces and (ii) geometric nonlinear control. The aim is to drive the masses to a set point even with harmonic base excitation, by using chaotic dynamics and nonlinear control. The paper shows that it is possible to obtain a positioning time around a few ms with sub-nanometre accuracy, velocities, accelerations and forces, as it appears in the design of present MEMS devices. Numerical simulations are used to verify the mathematical discussions.

  8. Chaotic dynamic and control for micro-electro-mechanical systems of massive storage with harmonic base excitation

    Energy Technology Data Exchange (ETDEWEB)

    Perez Polo, Manuel F. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)], E-mail: manolo@dfists.ua.es; Perez Molina, Manuel [Facultad de Ciencias Matematicas, Universidad Nacional de Educacion a Distancia. UNED, C/Boyero 12-1A, Alicante 03007 (Spain)], E-mail: ma_perez_m@hotmail.com; Gil Chica, Javier [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)], E-mail: gil@dfists.ua.es

    2009-02-15

    This paper explores chaotic behaviour and control of micro-electro-mechanical systems (MEMS), which consist of thousands of small read/write probe tips that access gigabytes of data stored in a non-volatile magnetic surface. The model of the system is formed by two masses connected by a nonlinear spring and a viscous damping. The paper shows that, by means of an adequate feedback law, the masses can behave as two coupled Duffing's oscillators, which may reach chaotic behaviour when harmonic forces are applied. The chaotic motion is destroyed by applying the following control strategies: (i) static output feedback control law with constant forces and (ii) geometric nonlinear control. The aim is to drive the masses to a set point even with harmonic base excitation, by using chaotic dynamics and nonlinear control. The paper shows that it is possible to obtain a positioning time around a few ms with sub-nanometre accuracy, velocities, accelerations and forces, as it appears in the design of present MEMS devices. Numerical simulations are used to verify the mathematical discussions.

  9. A novel image block cryptosystem based on a spatiotemporal chaotic system and a chaotic neural network

    International Nuclear Information System (INIS)

    Wang Xing-Yuan; Bao Xue-Mei

    2013-01-01

    In this paper, we propose a novel block cryptographic scheme based on a spatiotemporal chaotic system and a chaotic neural network (CNN). The employed CNN comprises a 4-neuron layer called a chaotic neuron layer (CNL), where the spatiotemporal chaotic system participates in generating its weight matrix and other parameters. The spatiotemporal chaotic system used in our scheme is the typical coupled map lattice (CML), which can be easily implemented in parallel by hardware. A 160-bit-long binary sequence is used to generate the initial conditions of the CML. The decryption process is symmetric relative to the encryption process. Theoretical analysis and experimental results prove that the block cryptosystem is secure and practical, and suitable for image encryption. (general)

  10. Composing chaotic music from the letter m

    Science.gov (United States)

    Sotiropoulos, Anastasios D.

    Chaotic music is composed from a proposed iterative map depicting the letter m, relating the pitch, duration and loudness of successive steps. Each of the two curves of the letter m is based on the classical logistic map. Thus, the generating map is xn+1 = r xn(1/2 - xn) for xn between 0 and 1/2 defining the first curve, and xn+1 = r (xn - 1/2)(1 - xn) for xn between 1/2 and 1 representing the second curve. The parameter r which determines the height(s) of the letter m varies from 2 to 16, the latter value ensuring fully developed chaotic solutions for the whole letter m; r = 8 yielding full chaotic solutions only for its first curve. The m-model yields fixed points, bifurcation points and chaotic regions for each separate curve, as well as values of the parameter r greater than 8 which produce inter-fixed points, inter-bifurcation points and inter-chaotic regions from the interplay of the two curves. Based on this, music is composed from mapping the m- recurrence model solutions onto actual notes. The resulting musical score strongly depends on the sequence of notes chosen by the composer to define the musical range corresponding to the range of the chaotic mathematical solutions x from 0 to 1. Here, two musical ranges are used; one is the middle chromatic scale and the other is the seven- octaves range. At the composer's will and, for aesthetics, within the same composition, notes can be the outcome of different values of r and/or shifted in any octave. Compositions with endings of non-repeating note patterns result from values of r in the m-model that do not produce bifurcations. Scores of chaotic music composed from the m-model and the classical logistic model are presented.

  11. Dynamics of Nonlinear Time-Delay Systems

    CERN Document Server

    Lakshmanan, Muthusamy

    2010-01-01

    Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different bran...

  12. A new method to determine magnetic properties of the unsaturated-magnetized rotor of a novel gyro

    Energy Technology Data Exchange (ETDEWEB)

    Li, Hai, E-mail: lihai7772006@126.com [MEMS Center, Harbin Institution of Technology, Harbin, 150001 (China); Liu, Xiaowei [MEMS Center, Harbin Institution of Technology, Harbin, 150001 (China); Key Laboratory of Micro-Systems and Micro-Structures Manufacturing, Ministry of Education, Harbin, 150001 (China); Dong, Changchun [School of Software, Harbin University of Science and Technology, Harbin, 150001 (China); Zhang, Haifeng [MEMS Center, Harbin Institution of Technology, Harbin, 150001 (China)

    2016-06-01

    A new method is proposed to determine magnetic properties of the unsaturated-magnetized, small and irregular shaped rotor of a novel gyro. The method is based on finite-element analysis and the measurements of the magnetic flux density distribution, determining magnetic parameters by comparing the magnetic flux intensity distribution differences between the modeling results under different parameters and the measured ones. Experiment on a N30 Grade NdFeB magnet shows that its residual magnetic flux density is 1.10±0.01 T, and coercive field strength is 801±3 kA/m, which are consistent with the given parameters of the material. The method was applied to determine the magnetic properties of the rotor of the gyro, and the magnetic properties acquired were used to predict the open-loop gyro precession frequency. The predicted precession frequency should be larger than 12.9 Hz, which is close to the experimental result 13.5 Hz. The result proves that the method is accurate in estimating the magnetic properties of the rotor of the gyro. - Highlights: • A new method to determine the magnetic properties of a gyro’s rotor is proposed. • The method is based on FEA and magnetic flux density distributions near magnets. • The result is determined by the distribution and values of all the measured points. • Using the result, the open-loop gyro precession frequency is precisely predicted.

  13. A new method to determine magnetic properties of the unsaturated-magnetized rotor of a novel gyro

    International Nuclear Information System (INIS)

    Li, Hai; Liu, Xiaowei; Dong, Changchun; Zhang, Haifeng

    2016-01-01

    A new method is proposed to determine magnetic properties of the unsaturated-magnetized, small and irregular shaped rotor of a novel gyro. The method is based on finite-element analysis and the measurements of the magnetic flux density distribution, determining magnetic parameters by comparing the magnetic flux intensity distribution differences between the modeling results under different parameters and the measured ones. Experiment on a N30 Grade NdFeB magnet shows that its residual magnetic flux density is 1.10±0.01 T, and coercive field strength is 801±3 kA/m, which are consistent with the given parameters of the material. The method was applied to determine the magnetic properties of the rotor of the gyro, and the magnetic properties acquired were used to predict the open-loop gyro precession frequency. The predicted precession frequency should be larger than 12.9 Hz, which is close to the experimental result 13.5 Hz. The result proves that the method is accurate in estimating the magnetic properties of the rotor of the gyro. - Highlights: • A new method to determine the magnetic properties of a gyro’s rotor is proposed. • The method is based on FEA and magnetic flux density distributions near magnets. • The result is determined by the distribution and values of all the measured points. • Using the result, the open-loop gyro precession frequency is precisely predicted.

  14. Breaking of ensembles of linear and nonlinear oscillators

    International Nuclear Information System (INIS)

    Buts, V.A.

    2016-01-01

    Some results concerning the study of the dynamics of ensembles of linear and nonlinear oscillators are stated. It is shown that, in general, a stable ensemble of linear oscillator has a limited number of oscillators. This number has been defined for some simple models. It is shown that the features of the dynamics of linear oscillators can be used for conversion of the low-frequency energy oscillations into high frequency oscillations. The dynamics of coupled nonlinear oscillators in most cases is chaotic. For such a case, it is shown that the statistical characteristics (moments) of chaotic motion can significantly reduce potential barriers that keep the particles in the capture region

  15. Chaotic artificial immune approach applied to economic dispatch of electric energy using thermal units

    International Nuclear Information System (INIS)

    Santos Coelho, Leandro dos; Mariani, Viviana Cocco

    2009-01-01

    The economic dispatch problem (EDP) is an optimization problem useful in power systems operation. The objective of the EDP of electric power generation, whose characteristics are complex and highly non-linear, is to schedule the committed generating unit outputs so as to meet the required load demand at minimum operating cost while satisfying system constraints. Recently, as an alternative to the conventional mathematical approaches, modern heuristic optimization techniques have been given much attention by many researchers due to their ability to find an almost global optimal solution in EDPs. As special mechanism to avoid being trapped in local minimum, the ergodicity property of chaotic sequences has been used as optimization technique in EDPs. Based on the chaos theory, this paper discusses the design and validation of an optimization procedure based on a chaotic artificial immune network approach based on Zaslavsky's map. The optimization approach based on chaotic artificial immune network is validated for a test system consisting of 13 thermal units whose incremental fuel cost function takes into account the valve-point loading effects. Simulation results and comparisons show that the chaotic artificial immune network approach is competitive in performance with other optimization approaches presented in literature and is also an attractive tool to be used on applications in the power systems field.

  16. Chaotic behavior in a hydrodynamic model of a fluidized bed reactor

    International Nuclear Information System (INIS)

    Schouten, J.C.; van den Bleek, C.M.

    1991-01-01

    Recent preliminary experimental studies using time-series analysis have demonstrated that the multi-phase flow in fluidized bed reactors can be characterized as chaotic. In the present paper, it is therefore argued that the chaotic time-dependence of fluidization is a characteristic feature which should be included in scaling rules for fluidized bed reactors. For example, the similarity groups applied in dimensionless fluidized bed scaling should be improved by extending them with functions of the relevant numbers from chaos theory, such as the correlation and embedding dimension or the maximum Lyapunov exponent. This requires that the dependence of these numbers on fluidization parameters must be theoretically and experimentally investigated. The concept of chaos in fluidization also requires that the classical, empirically developed, hydrodynamic models that are applied in fluidized bed scaling are amended to include time-dependence, non-linearity as well as a sufficient level of complexity before they can predict any chaotic behavior. An example is given of chaotic behavior generated in the classical counter-current flow model according to Van Deemter by writing the upwards solids velocity as a harmonic oscillating function of time. A low-dimensional strange attractor is found, embedded in two-dimensional phase space, of which the correlation dimension depends on the solids exchange coefficient

  17. State-of-the-art of high power gyro-devices and free electron masers 1994

    International Nuclear Information System (INIS)

    Thumm, M.

    1995-04-01

    At present, gyrotron oscillators are mainly used as high power millimeter wave sources for electron cyclotron resonance heating (ECRH) and diagnostics of magnetically confined plasmas for generation of energy by controlled thermonuclear fusion. 140 GHz gyrotrons with output power P out =0.54 MW, pulse length τ=3.0 s and efficiency η=42% are commercially available. Total efficiencies around 50% have been achieved using single-stage depressed collectors. Diagnostic gyrotrons deliver P out =40 kW with τ=40 μs at frequencies up to 650 GHz (η≥4%). Recently, gyrotron oscillators have also been successfully used in material processing and plasma chemistry. Such technological applications require gyrotrons with the following parameters: f≥24 GHz, P out =10-50 kW, CW, η≥30%. This paper reports on achievements and problems related to the development of very high power mm-wave gyrotrons for long pulse or CW operation and describes the microwave technological pecularities of the different development steps. In addition, this work gives a short overview of the present development of gyrotrons for technological applications, relativistic gyrotrons, quasi-optical gyrotrons, cyclotron autoresonance masers (CARMs), gyro klystrons, gyro-TWT amplifiers, gyrotwystron amplifiers, gyro-BWO's, peniotrons and free electron masers (FEMs). The most impressive FEM output parameters are: P out =2 GW, τ=20 ns, η=13% at 140 GHz (LLNL) and P out =15 kW, τ=20 μs, η=5% in the range from 120 to 900 GHz (UCSB). (orig.) [de

  18. A study of discrete nonlinear systems

    International Nuclear Information System (INIS)

    Dhillon, H.S.

    2001-04-01

    An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)

  19. Analytical theory of frequency-multiplying gyro-traveling-wave-tubes

    International Nuclear Information System (INIS)

    Nusinovich, G.S.; Chen, W.; Granatstein, V.L.

    2001-01-01

    The theory is developed which describes analytically the gain and bandwidth in frequency-multiplying gyro-traveling-wave-tubes. In this theory the input waveguide is considered in the small-signal approximation. Then, in the drift region separating the input and output waveguides, the electron ballistic bunching evolves which causes the appearance in the electron current density of the harmonics of the signal frequency. The excitation of the output waveguide by one of these harmonics is considered in a specified current approximation. This makes the analytical study of a large-signal operation possible. The theory is illustrated by using it to analyze the performance of an existing experimental tube

  20. Chaotic interactions of self-replicating RNA.

    Science.gov (United States)

    Forst, C V

    1996-03-01

    A general system of high-order differential equations describing complex dynamics of replicating biomolecules is given. Symmetry relations and coordinate transformations of general replication systems leading to topologically equivalent systems are derived. Three chaotic attractors observed in Lotka-Volterra equations of dimension n = 3 are shown to represent three cross-sections of one and the same chaotic regime. Also a fractal torus in a generalized three-dimensional Lotka-Volterra Model has been linked to one of the chaotic attractors. The strange attractors are studied in the equivalent four-dimensional catalytic replicator network. The fractal torus has been examined in adapted Lotka-Volterra equations. Analytic expressions are derived for the Lyapunov exponents of the flow in the replicator system. Lyapunov spectra for different pathways into chaos has been calculated. In the generalized Lotka-Volterra system a second inner rest point--coexisting with (quasi)-periodic orbits--can be observed; with an abundance of different bifurcations. Pathways from chaotic tori, via quasi-periodic tori, via limit cycles, via multi-periodic orbits--emerging out of periodic doubling bifurcations--to "simple" chaotic attractors can be found.

  1. Image Encryption and Chaotic Cellular Neural Network

    Science.gov (United States)

    Peng, Jun; Zhang, Du

    Machine learning has been playing an increasingly important role in information security and assurance. One of the areas of new applications is to design cryptographic systems by using chaotic neural network due to the fact that chaotic systems have several appealing features for information security applications. In this chapter, we describe a novel image encryption algorithm that is based on a chaotic cellular neural network. We start by giving an introduction to the concept of image encryption and its main technologies, and an overview of the chaotic cellular neural network. We then discuss the proposed image encryption algorithm in details, which is followed by a number of security analyses (key space analysis, sensitivity analysis, information entropy analysis and statistical analysis). The comparison with the most recently reported chaos-based image encryption algorithms indicates that the algorithm proposed in this chapter has a better security performance. Finally, we conclude the chapter with possible future work and application prospects of the chaotic cellular neural network in other information assurance and security areas.

  2. Qualitative feature extractions of chaotic systems

    International Nuclear Information System (INIS)

    Vicha, T.; Dohnal, M.

    2008-01-01

    The theory of chaos offers useful tools for systems analysis. However, models of complex systems are based on a network of inconsistent, space and uncertain knowledge items. Traditional quantitative methods of chaos analysis are therefore not applicable. The paper by the same authors [Vicha T, Dohnal M. Qualitative identification of chaotic systems behaviours. Chaos, Solitons and Fractals, in press, [Log. No. 601019] ] presents qualitative interpretation of some chaos concepts. There are only three qualitative values positive/increasing, negative/decreasing and zero/constant. It means that any set of qualitative multidimensional descriptions of unsteady state behaviours is discrete and finite. A finite upper limit exists for the total number of qualitatively distinguishable scenarios. A set of 21 published chaotic models is solved qualitatively and 21 sets of all existing qualitative scenarios are presented. The intersection of all 21 scenario sets is empty. There is no such a behaviour which is common for all 21 models. The set of 21 qualitative models (e.g. Lorenz, Roessler) can be used to compare chaotic behaviours of an unknown qualitative model with them to evaluate if its chaotic behaviours is close to e.g. Lorenz chaotic model and how much

  3. Temporal chaotic behaviour of vortex motion in a type-II superconductors with periodically-distributed pinning centres

    International Nuclear Information System (INIS)

    Lin, H.T.; Ke, C.; Cheng, C.H.

    2010-01-01

    Temporal chaotic character of vortex motion in systems where defects are arranged in periodic arrays has been investigated by computer simulation. Due to the high nonlinearity of the vortex-defect interaction, the temporal evolution of the vortex motion is chaotic with a power spectrum similar to what have been observed in the experiments. It is found that the strength of both the vortex-vortex and vortex-defect interactions have no significant effects on the chaotic motion of the vortices, however, the mismatch between these two interactions causes attractor crisis of the system. Different from them, the Lorentz force is not the origin of the attractor crisis, but it causes a divergent motion of the vortex (i.e., the flux flow).

  4. Temporal chaotic behaviour of vortex motion in a type-II superconductors with periodically-distributed pinning centres

    Energy Technology Data Exchange (ETDEWEB)

    Lin, H.T. [Faculty of Information Management, Cheng Shiu University, Kaoshuing, Taiwan (China); Ke, C. [Key Laboratory of Magnetic Levitation and Maglev Trains (Ministry of Education of China), Superconductivity R and D Center (SRDC), Mail Stop 165, Southwest Jiaotong University, Chengdu, Sichuan 610031 (China); Cheng, C.H., E-mail: c.cheng@unsw.edu.a [Key Laboratory of Magnetic Levitation and Maglev Trains (Ministry of Education of China), Superconductivity R and D Center (SRDC), Mail Stop 165, Southwest Jiaotong University, Chengdu, Sichuan 610031 (China); School of Materials Science and Engineering, University of New South Wale, Sydney, 2052 NSW (Australia)

    2010-11-01

    Temporal chaotic character of vortex motion in systems where defects are arranged in periodic arrays has been investigated by computer simulation. Due to the high nonlinearity of the vortex-defect interaction, the temporal evolution of the vortex motion is chaotic with a power spectrum similar to what have been observed in the experiments. It is found that the strength of both the vortex-vortex and vortex-defect interactions have no significant effects on the chaotic motion of the vortices, however, the mismatch between these two interactions causes attractor crisis of the system. Different from them, the Lorentz force is not the origin of the attractor crisis, but it causes a divergent motion of the vortex (i.e., the flux flow).

  5. From determinism and probability to chaos: chaotic evolution towards philosophy and methodology of chaotic optimization.

    Science.gov (United States)

    Pei, Yan

    2015-01-01

    We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.

  6. From Determinism and Probability to Chaos: Chaotic Evolution towards Philosophy and Methodology of Chaotic Optimization

    Science.gov (United States)

    2015-01-01

    We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed. PMID:25879067

  7. From Determinism and Probability to Chaos: Chaotic Evolution towards Philosophy and Methodology of Chaotic Optimization

    Directory of Open Access Journals (Sweden)

    Yan Pei

    2015-01-01

    Full Text Available We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC algorithm, interactive chaotic evolution (ICE that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.

  8. Generalized projective synchronization of a unified chaotic system

    International Nuclear Information System (INIS)

    Yan Jianping; Li Changpin

    2005-01-01

    In the present paper, a simple but efficient control technique of the generalized projective synchronization is applied to a unified chaotic system. Numerical simulations show that this method works very well, which can also be applied to other chaotic systems

  9. The Hausdorff measure of chaotic sets of adjoint shift maps

    Energy Technology Data Exchange (ETDEWEB)

    Wang Huoyun [Department of Mathematics of Guangzhou University, Guangzhou 510006 (China)]. E-mail: wanghuoyun@sina.com; Song Wangan [Department of Computer, Huaibei Coal Industry Teacher College, Huaibei 235000 (China)

    2006-11-15

    In this paper, the size of chaotic sets of adjoint shift maps is estimated by Hausdorff measure. We prove that for any adjoint shift map there exists a finitely chaotic set with full Hausdorff measure.

  10. Deep coupling of star tracker and MEMS-gyro data under highly dynamic and long exposure conditions

    International Nuclear Information System (INIS)

    Sun, Ting; Xing, Fei; You, Zheng; Wang, Xiaochu; Li, Bin

    2014-01-01

    Star trackers and gyroscopes are the two most widely used attitude measurement devices in spacecrafts. The star tracker is supposed to have the highest accuracy in stable conditions among different types of attitude measurement devices. In general, to detect faint stars and reduce the size of the star tracker, a method with long exposure time method is usually used. Thus, under dynamic conditions, smearing of the star image may appear and result in decreased accuracy or even failed extraction of the star spot. This may cause inaccuracies in attitude measurement. Gyros have relatively good dynamic performance and are usually used in combination with star trackers. However, current combination methods focus mainly on the data fusion of the output attitude data levels, which are inadequate for utilizing and processing internal blurred star image information. A method for tracking deep coupling stars and MEMS-gyro data is proposed in this work. The method achieves deep fusion at the star image level. First, dynamic star image processing is performed based on the angular velocity information of the MEMS-gyro. Signal-to-noise ratio (SNR) of the star spot could be improved, and extraction is achieved more effectively. Then, a prediction model for optimal estimation of the star spot position is obtained through the MEMS-gyro, and an extended Kalman filter is introduced. Meanwhile, the MEMS-gyro drift can be estimated and compensated though the proposed method. These enable the star tracker to achieve high star centroid determination accuracy under dynamic conditions. The MEMS-gyro drift can be corrected even when attitude data of the star tracker are unable to be solved and only one navigation star is captured in the field of view. Laboratory experiments were performed to verify the effectiveness of the proposed method and the whole system. (paper)

  11. Deep coupling of star tracker and MEMS-gyro data under highly dynamic and long exposure conditions

    Science.gov (United States)

    Sun, Ting; Xing, Fei; You, Zheng; Wang, Xiaochu; Li, Bin

    2014-08-01

    Star trackers and gyroscopes are the two most widely used attitude measurement devices in spacecrafts. The star tracker is supposed to have the highest accuracy in stable conditions among different types of attitude measurement devices. In general, to detect faint stars and reduce the size of the star tracker, a method with long exposure time method is usually used. Thus, under dynamic conditions, smearing of the star image may appear and result in decreased accuracy or even failed extraction of the star spot. This may cause inaccuracies in attitude measurement. Gyros have relatively good dynamic performance and are usually used in combination with star trackers. However, current combination methods focus mainly on the data fusion of the output attitude data levels, which are inadequate for utilizing and processing internal blurred star image information. A method for tracking deep coupling stars and MEMS-gyro data is proposed in this work. The method achieves deep fusion at the star image level. First, dynamic star image processing is performed based on the angular velocity information of the MEMS-gyro. Signal-to-noise ratio (SNR) of the star spot could be improved, and extraction is achieved more effectively. Then, a prediction model for optimal estimation of the star spot position is obtained through the MEMS-gyro, and an extended Kalman filter is introduced. Meanwhile, the MEMS-gyro drift can be estimated and compensated though the proposed method. These enable the star tracker to achieve high star centroid determination accuracy under dynamic conditions. The MEMS-gyro drift can be corrected even when attitude data of the star tracker are unable to be solved and only one navigation star is captured in the field of view. Laboratory experiments were performed to verify the effectiveness of the proposed method and the whole system.

  12. HIGH-PRECISION ATTITUDE ESTIMATION METHOD OF STAR SENSORS AND GYRO BASED ON COMPLEMENTARY FILTER AND UNSCENTED KALMAN FILTER

    Directory of Open Access Journals (Sweden)

    C. Guo

    2017-07-01

    Full Text Available Determining the attitude of satellite at the time of imaging then establishing the mathematical relationship between image points and ground points is essential in high-resolution remote sensing image mapping. Star tracker is insensitive to the high frequency attitude variation due to the measure noise and satellite jitter, but the low frequency attitude motion can be determined with high accuracy. Gyro, as a short-term reference to the satellite’s attitude, is sensitive to high frequency attitude change, but due to the existence of gyro drift and integral error, the attitude determination error increases with time. Based on the opposite noise frequency characteristics of two kinds of attitude sensors, this paper proposes an on-orbit attitude estimation method of star sensors and gyro based on Complementary Filter (CF and Unscented Kalman Filter (UKF. In this study, the principle and implementation of the proposed method are described. First, gyro attitude quaternions are acquired based on the attitude kinematics equation. An attitude information fusion method is then introduced, which applies high-pass filtering and low-pass filtering to the gyro and star tracker, respectively. Second, the attitude fusion data based on CF are introduced as the observed values of UKF system in the process of measurement updating. The accuracy and effectiveness of the method are validated based on the simulated sensors attitude data. The obtained results indicate that the proposed method can suppress the gyro drift and measure noise of attitude sensors, improving the accuracy of the attitude determination significantly, comparing with the simulated on-orbit attitude and the attitude estimation results of the UKF defined by the same simulation parameters.

  13. Describing chaotic attractors: Regular and perpetual points

    Science.gov (United States)

    Dudkowski, Dawid; Prasad, Awadhesh; Kapitaniak, Tomasz

    2018-03-01

    We study the concepts of regular and perpetual points for describing the behavior of chaotic attractors in dynamical systems. The idea of these points, which have been recently introduced to theoretical investigations, is thoroughly discussed and extended into new types of models. We analyze the correlation between regular and perpetual points, as well as their relation with phase space, showing the potential usefulness of both types of points in the qualitative description of co-existing states. The ability of perpetual points in finding attractors is indicated, along with its potential cause. The location of chaotic trajectories and sets of considered points is investigated and the study on the stability of systems is shown. The statistical analysis of the observing desired states is performed. We focus on various types of dynamical systems, i.e., chaotic flows with self-excited and hidden attractors, forced mechanical models, and semiconductor superlattices, exhibiting the universality of appearance of the observed patterns and relations.

  14. Chaotic behavior learning of Chua's circuit

    International Nuclear Information System (INIS)

    Sun Jian-Cheng

    2012-01-01

    Least-square support vector machines (LS-SVM) are applied for learning the chaotic behavior of Chua's circuit. The system is divided into three multiple-input single-output (MISO) structures and the LS-SVM are trained individually. Comparing with classical approaches, the proposed one reduces the structural complexity and the selection of parameters is avoided. Some parameters of the attractor are used to compare the chaotic behavior of the reconstructed and the original systems for model validation. Results show that the LS-SVM combined with the MISO can be trained to identify the underlying link among Chua's circuit state variables, and exhibit the chaotic attractors under the autonomous working mode

  15. Semi-classical quantization of chaotic billiards

    International Nuclear Information System (INIS)

    Smilansky, U.

    1992-02-01

    The semi-classical quantization of chaotic billiards will be developed using scattering theory approach. This will be used to introduce and explain the inherent difficulties in the semi-classical quantization of chaos, and to show some of the modern tools which were developed recently to overcome these difficulties. To this end, we shall first obtain a semi-classical secular equation which is based on a finite number of classical periodic orbits. We shall use it to derive some spectral properties, and in particular to investigate the relationship between spectral statistics of quantum chaotic systems and the predictions of random-matrix theory. We shall finally discuss an important family of chaotic billiard, whose statistics does not follow any of the canonical ensembles, (GOE,GUE,...) but rather, corresponds to a new universality class. (author)

  16. Chaotic Dynamics of the Partially Follower-Loaded Elastic Double Pendulum

    DEFF Research Database (Denmark)

    Thomsen, Jon Juel

    1995-01-01

    The non-linear dynamics of the elastically restrained double pendulum, with non-conservative follower-type loading and linear damping, is re-examined with specific reference to the occurrence of chaotic motion. A local non-linear perturbation analysis is performed, showing that in three distinct ...... by both linear and non-linear forces. Although heuristically based, this may be used as a practical and rather accurate predictive criterion for chaos to appear in the specific system. Copyright © 1995 Academic Press. All rights reserved....... regions of loading parameter space, small initial disturbances will result in, respectively, (1) static equilibrium solutions, (2) stable periodic motion, and (3) initially large changes in amplitude due to a destabilizing effect of both linear and non-linear forces. A global numerical analysis confirms...... the theoretical findings for regions (1) and (2), and shows that in region (3) almost all solutions are chaotic. It is suggested that chaos is triggered by a bifurcating cascade of large amplitude stable and unstable equilibrium points, which may be explored by orbits only when the zero-solution is destabilized...

  17. Chaotic Flows Correlation effects and coherent structures

    CERN Document Server

    Bakunin, Oleg G

    2011-01-01

    The book introduces readers to and summarizes the current ideas and theories about the basic mechanisms for transport in chaotic flows. Typically no single paradigmatic approach exists as this topic is relevant for fields as diverse as plasma physics, geophysical flows and various branches of engineering. Accordingly, the dispersion of matter in chaotic or turbulent flows is analyzed from different perspectives. Partly based on lecture courses given by the author, this book addresses both graduate students and researchers in search of a high-level but approachable and broad introduction to the topic.

  18. Higgs vacuum stability and modified chaotic inflation

    Energy Technology Data Exchange (ETDEWEB)

    Saha, Abhijit Kumar, E-mail: abhijit.saha@iitg.ernet.in; Sil, Arunansu, E-mail: asil@iitg.ernet.in

    2017-02-10

    The issue of electroweak vacuum stability is studied in presence of a scalar field which participates in modifying the minimal chaotic inflation model. It is shown that the threshold effect on the Higgs quartic coupling originating from the Higgs–inflaton sector interaction can essentially make the electroweak vacuum stable up to the Planck scale. On the other hand we observe that the new physics parameters in this combined framework are enough to provide deviation from the minimal chaotic inflation predictions so as to keep it consistent with recent observation by Planck 2015.

  19. Chaotic behavior of a quantum waveguide

    Energy Technology Data Exchange (ETDEWEB)

    Pérez-Aguilar, H., E-mail: hiperezag@yahoo.com [Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Av. Francisco J. Mújica S/N 58030, Morelia, Michoacán (Mexico); Mendoza-Suárez, A.; Tututi, E.S. [Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Av. Francisco J. Mújica S/N 58030, Morelia, Michoacán (Mexico); Herrera-González, I.F. [Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570 Puebla (Mexico)

    2013-02-15

    In this work we consider an infinite quantum waveguide composed of two periodic, hard walls, one-dimensional rippled surfaces. We find that, under certain conditions, the proposed system presents some traces of quantum chaos, when the corresponding classical limit has chaotic behavior. Thus, it is possible to obtain disordered probability densities in a system with smooth surfaces. When the system has chaotic behavior we show numerically that the correlation length of the autocorrelation function of the probability density goes to zero. To corroborate some properties obtained for infinite waveguide that are physically admissible, we study the corresponding finite version of this system.

  20. Chaotic behavior of a quantum waveguide

    International Nuclear Information System (INIS)

    Pérez-Aguilar, H.; Mendoza-Suárez, A.; Tututi, E.S.; Herrera-González, I.F.

    2013-01-01

    In this work we consider an infinite quantum waveguide composed of two periodic, hard walls, one-dimensional rippled surfaces. We find that, under certain conditions, the proposed system presents some traces of quantum chaos, when the corresponding classical limit has chaotic behavior. Thus, it is possible to obtain disordered probability densities in a system with smooth surfaces. When the system has chaotic behavior we show numerically that the correlation length of the autocorrelation function of the probability density goes to zero. To corroborate some properties obtained for infinite waveguide that are physically admissible, we study the corresponding finite version of this system