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

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.

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.

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

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.

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.

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)

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.

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

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

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.

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.

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

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.

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.

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)

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

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

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)

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.

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

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....

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.

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

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.

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.

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.

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.

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

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.

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.

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.

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

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

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.

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)

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.

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.

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

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

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.

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.

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

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.)

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.)

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

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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.

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.

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.

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

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.

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.

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.

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

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).

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)

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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....

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

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.

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

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...

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

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)

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.

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)

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.

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.

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.

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

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

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

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

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.

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.

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.

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.

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

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.

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

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

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

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.

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.

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

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.

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 ...

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.

Chaos Synchronization Using Adaptive Dynamic Neural Network Controller with Variable Learning Rates

Directory of Open Access Journals (Sweden)

Chih-Hong Kao

2011-01-01

Full Text Available This paper addresses the synchronization of chaotic gyros with unknown parameters and external disturbance via an adaptive dynamic neural network control (ADNNC system. The proposed ADNNC system is composed of a neural controller and a smooth compensator. The neural controller uses a dynamic RBF (DRBF network to online approximate an ideal controller. The DRBF network can create new hidden neurons online if the input data falls outside the hidden layer and prune the insignificant hidden neurons online if the hidden neuron is inappropriate. The smooth compensator is designed to compensate for the approximation error between the neural controller and the ideal controller. Moreover, the variable learning rates of the parameter adaptation laws are derived based on a discrete-type Lyapunov function to speed up the convergence rate of the tracking error. Finally, the simulation results which verified the chaotic behavior of two nonlinear identical chaotic gyros can be synchronized using the proposed ADNNC scheme.

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.

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.

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

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

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

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.

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

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...

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

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).

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

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)

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

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...

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

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...

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.

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.

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.

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.

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.

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

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.

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.

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

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

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.

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.

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.

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.

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

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...

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

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

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.

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

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.

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.

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.

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 ...

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

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.

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.

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.

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)

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)

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.

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.

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.

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.

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

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.

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.

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...

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

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.

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.

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.

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.

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

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)

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 ...

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.

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.

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.

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.

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.

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

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)

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...

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

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

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

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

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.

Nonlinear dynamics of mini-satellite respinup by weak internal controllable torques

Science.gov (United States)

Somov, Yevgeny

2014-12-01

Contemporary space engineering advanced new problem before theoretical mechanics and motion control theory: a spacecraft directed respinup by the weak restricted control internal forces. The paper presents some results on this problem, which is very actual for energy supply of information mini-satellites (for communication, geodesy, radio- and opto-electronic observation of the Earth et al.) with electro-reaction plasma thrusters and gyro moment cluster based on the reaction wheels or the control moment gyros. The solution achieved is based on the methods for synthesis of nonlinear robust control and on rigorous analytical proof for the required spacecraft rotation stability by Lyapunov function method. These results were verified by a computer simulation of strongly nonlinear oscillatory processes at respinuping of a flexible spacecraft.

Nonlinear dynamics of mini-satellite respinup by weak internal controllable torques

Energy Technology Data Exchange (ETDEWEB)

Somov, Yevgeny, E-mail: e-somov@mail.ru [Samara State Technical University, Department for Guidance, Navigation and Control, 244 Molodogvardeyskaya Str., Samara 443100 (Russian Federation)

2014-12-10

Contemporary space engineering advanced new problem before theoretical mechanics and motion control theory: a spacecraft directed respinup by the weak restricted control internal forces. The paper presents some results on this problem, which is very actual for energy supply of information mini-satellites (for communication, geodesy, radio- and opto-electronic observation of the Earth et al.) with electro-reaction plasma thrusters and gyro moment cluster based on the reaction wheels or the control moment gyros. The solution achieved is based on the methods for synthesis of nonlinear robust control and on rigorous analytical proof for the required spacecraft rotation stability by Lyapunov function method. These results were verified by a computer simulation of strongly nonlinear oscillatory processes at respinuping of a flexible spacecraft.

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

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)

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

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.

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.

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

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.

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.

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

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.

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.

Predictable nonlinear dynamics: Advances and limitations

International Nuclear Information System (INIS)

Anosov, L.A.; Butkovskii, O.Y.; Kravtsov, Y.A.; Surovyatkina, E.D.

1996-01-01

Methods for reconstruction chaotic dynamical system structure directly from experimental time series are described. Effectiveness of general methods is illustrated with the results of numerical simulation. It is of common interest that from the single time series it is possible to reconstruct a set of interconnected variables. Predictive power of dynamical models, provided by the nonlinear dynamics inverse problem solution, is limited firstly by the noise level in the system under study and is characterized by the horizon of predictability. New physical results are presented, concerning nonstationary and bifurcation nonlinear systems: (1) algorithms for revealing of nonstationarity in random-like chaotic time-series are suggested based on discriminant analysis with nonlinear discriminant function; (2) an opportunity is established to predict the final state in bifurcation system with quickly varying control parameters; (3) hysteresis is founded out in bifurcation system with quickly varying parameters; (4) delayed correlation left-angle noise-prediction error right-angle in chaotic systems is revealed. copyright 1996 American Institute of Physics

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....

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

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

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)

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.

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.

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.

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.

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

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.

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

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.

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)

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...

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

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

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.

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

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...

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

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

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.

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

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

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.

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.

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.

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.

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.

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.

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...

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.

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)

Chaos resulting from nonlinear relations between different variables

International Nuclear Information System (INIS)

Dohtani, Akitaka

2011-01-01

Research highlights: → We prove a general result on the existence of chaos. → We focus on the cyclic composites of interdependent relations between different variables. → By considering several examples, we conclude that the cyclic composites play an important role in detecting chaotic dynamics. - Abstract: In this study, we further develop the perturbation method of Marotto and investigate the general mechanisms responsible for nonlinear dynamics, which are typical of multidimensional systems. We focus on the composites of interdependent relations between different variables. First, we prove a general result on chaos, which shows that the cyclic composites of nonlinear interdependent relations are sources of chaotic dynamics in multidimensional systems. By considering several examples, we conclude that the cyclic composites play an important role in detecting chaotic dynamics.

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.

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...

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)

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

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)

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.

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

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.

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.

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)

Nonlinear gyrokinetic simulations of the I-mode high confinement regime and comparisons with experiment

Energy Technology Data Exchange (ETDEWEB)

White, A. E., E-mail: whitea@mit.edu; Howard, N. T.; Creely, A. J.; Chilenski, M. A.; Greenwald, M.; Hubbard, A. E.; Hughes, J. W.; Marmar, E.; Rice, J. E.; Sierchio, J. M.; Sung, C.; Walk, J. R.; Whyte, D. G. [MIT Plasma Science and Fusion Center, Cambridge, Massachusetts 02139 (United States); Mikkelsen, D. R.; Edlund, E. M.; Kung, C. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08540 (United States); Holland, C. [University of California, San Diego (UCSD) San Diego, California 92093 (United States); Candy, J.; Petty, C. C. [General Atomics, P.O. Box 85608, San Diego, California 92186 (United States); Reinke, M. L. [York University, Heslington, York YO10 5DD (United Kingdom); and others

2015-05-15

For the first time, nonlinear gyrokinetic simulations of I-mode plasmas are performed and compared with experiment. I-mode is a high confinement regime, featuring energy confinement similar to H-mode, but without enhanced particle and impurity particle confinement [D. G. Whyte et al., Nucl. Fusion 50, 105005 (2010)]. As a consequence of the separation between heat and particle transport, I-mode exhibits several favorable characteristics compared to H-mode. The nonlinear gyrokinetic code GYRO [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] is used to explore the effects of E × B shear and profile stiffness in I-mode and compare with L-mode. The nonlinear GYRO simulations show that I-mode core ion temperature and electron temperature profiles are more stiff than L-mode core plasmas. Scans of the input E × B shear in GYRO simulations show that E × B shearing of turbulence is a stronger effect in the core of I-mode than L-mode. The nonlinear simulations match the observed reductions in long wavelength density fluctuation levels across the L-I transition but underestimate the reduction of long wavelength electron temperature fluctuation levels. The comparisons between experiment and gyrokinetic simulations for I-mode suggest that increased E × B shearing of turbulence combined with increased profile stiffness are responsible for the reductions in core turbulence observed in the experiment, and that I-mode resembles H-mode plasmas more than L-mode plasmas with regards to marginal stability and temperature profile stiffness.

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.

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.

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.

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.

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...

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

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

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.

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.

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

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.

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)

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).

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)

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.

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.

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

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.

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)

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

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.

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.

Spatiotemporal chaos in mixed linear-nonlinear two-dimensional coupled logistic map lattice

Science.gov (United States)

Zhang, Ying-Qian; He, Yi; Wang, Xing-Yuan

2018-01-01

We investigate a new spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps for spatial coupling connections based on 2DCML. Here, the coupling methods are including with linear neighborhood coupling and the nonlinear chaotic map coupling of lattices, and the former 2DCML system is only a special case in the proposed system. In this paper the criteria such Kolmogorov-Sinai entropy density and universality, bifurcation diagrams, space-amplitude and snapshot pattern diagrams are provided in order to investigate the chaotic behaviors of the proposed system. Furthermore, we also investigate the parameter ranges of the proposed system which holds those features in comparisons with those of the 2DCML system and the MLNCML system. Theoretical analysis and computer simulation indicate that the proposed system contains features such as the higher percentage of lattices in chaotic behaviors for most of parameters, less periodic windows in bifurcation diagrams and the larger range of parameters for chaotic behaviors, which is more suitable for cryptography.

Nonlinear dynamics as an engine of computation.

Science.gov (United States)

Kia, Behnam; Lindner, John F; Ditto, William L

2017-03-06

Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics-cybernetical physics-opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

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.

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.

Nonlinear Analysis of Two-phase Circumferential Motion in the Ablation Circumstance

Science.gov (United States)

Xiao-liang, Xu; Hai-ming, Huang; Zi-mao, Zhang

2010-05-01

In aerospace craft reentry and solid rocket propellant nozzle, thermal chemistry ablation is a complex process coupling with convection, heat transfer, mass transfer and chemical reaction. Based on discrete vortex method (DVM), thermal chemical ablation model and particle kinetic model, a computational module dealing with the two-phase circumferential motion in ablation circumstance is designed, the ablation velocity and circumferential field can be thus calculated. The calculated nonlinear time series are analyzed in chaotic identification method: relative chaotic characters such as correlation dimension and the maximum Lyapunov exponent are calculated, fractal dimension of vortex bulbs and particles distributions are also obtained, thus the nonlinear ablation process can be judged as a spatiotemporal chaotic process.

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

Institute of Scientific and Technical Information of China (English)

无

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.

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)

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.

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...

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.

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.

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.

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

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.

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

Role of nonlinear dynamics and chaos in applied sciences

International Nuclear Information System (INIS)

Lawande, Quissan V.; Maiti, Nirupam

2000-02-01

Nonlinear dynamics manifests itself in a number of phenomena in both laboratory and day to day dealings. However, little attention was being paid to this dynamically rich field. With the advent of high speed computers with visual graphics, the field has proliferated over past few years. One of the most rewarding realization from nonlinear dynamics is the universally acclaimed field of chaos. Chaos has brought in order and has broken the disciplinary boundaries that existed until recently. With its universal phenomena, almost all disciplines following an evolutionary character can be treated on same footing. Chaotic dynamics has its grounding in the multidisciplinary field of synergetics founded by Professor Hermann Haken. In this report, we address some of the basics related to the field of chaos. We have discussed simple mechanisms for generating chaotic trajectories, ways and means of characterizing such systems and the manifestation of their signatures in the evolutions. We have mentioned the links of this field with other existing theories. We have outlined the topics on bifurcation and stability of dynamical systems. Information theoretic aspects and notions on fractal geometry are reviewed in the light of dynamical characterization of chaotic systems. Application oriented views of this novel dynamical phenomena are discussed through examples on simple nonlinear electronic circuits and a BWR reactor. Some ideas relating to control and synchronization in chaotic systems also addressed. In conclusion, we have explored the possibilities of exploiting nonlinear dynamics and chaos in the context of multidisciplinary character of BARC. (author)

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.

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.

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.

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)

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

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.

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.

Nonlinear wave chaos: statistics of second harmonic fields.

Science.gov (United States)

Zhou, Min; Ott, Edward; Antonsen, Thomas M; Anlage, Steven M

2017-10-01

Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.

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.

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.

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

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.

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.

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.

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

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.

Chaos control of third-order phase-locked loops using backstepping nonlinear controller

International Nuclear Information System (INIS)

Harb, Ahmad M.; Harb, Bassam A.

2004-01-01

Previous study showed that a third-order phase-locked loop (PLL) with sinusoidal phase detector characteristics experienced a Hopf bifurcation point as well as chaotic behavior. As a result, this behavior drives the PLL to the out-of-lock (unstable) state. The analysis was based on a modern nonlinear theory such as bifurcation and chaos. The main goal of this paper is to control this chaotic behavior. A nonlinear controller based on the theory of backstepping is designed. The study showed the effectiveness of the designed nonlinear controller in controlling the undesirable unstable behavior and pulling the PLL back to the in-lock state

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

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.

Nonlinear Multiuser Receiver for Optimized Chaos-Based DS-CDMA Systems

Directory of Open Access Journals (Sweden)

S. Shaerbaf

2011-09-01

Full Text Available Chaos based communications have drawn increasing attention over the past years. Chaotic signals are derived from non-linear dynamic systems. They are aperiodic, broadband and deterministic signals that appear random in the time domain. Because of these properties, chaotic signals have been proposed to generate spreading sequences for wide-band secure communication recently. Like conventional DS-CDMA systems, chaos-based CDMA systems suffer from multi-user interference (MUI due to other users transmitting in the cell. In this paper, we propose a novel method based on radial basis function (RBF for both blind and non-blind multiuser detection in chaos-based DS-CDMA systems. We also propose a new method for optimizing generation of binary chaotic sequences using Genetic Algorithm. Simulation results show that our proposed nonlinear receiver with optimized chaotic sequences outperforms in comparison to other conventional detectors such as a single-user detector, decorrelating detector and minimum mean square error detector, particularly for under-loaded CDMA condition, which the number of active users is less than processing gain.

Non-linear time series analysis on flow instability of natural circulation under rolling motion condition

International Nuclear Information System (INIS)

Zhang, Wenchao; Tan, Sichao; Gao, Puzhen; Wang, Zhanwei; Zhang, Liansheng; Zhang, Hong

2014-01-01

Highlights: • Natural circulation flow instabilities in rolling motion are studied. • The method of non-linear time series analysis is used. • Non-linear evolution characteristic of flow instability is analyzed. • Irregular complex flow oscillations are chaotic oscillations. • The effect of rolling parameter on the threshold of chaotic oscillation is studied. - Abstract: Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions were studied by the method of non-linear time series analysis. Experimental flow time series of different dimensionless power and rolling parameters were analyzed based on phase space reconstruction theory. Attractors which were reconstructed in phase space and the geometric invariants, including correlation dimension, Kolmogorov entropy and largest Lyapunov exponent, were determined. Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions was studied based on the results of the geometric invariant analysis. The results indicated that the values of the geometric invariants first increase and then decrease as dimensionless power increases which indicated the non-linear characteristics of the system first enhance and then weaken. The irregular complex flow oscillation is typical chaotic oscillation because the value of geometric invariants is at maximum. The threshold of chaotic oscillation becomes larger as the rolling frequency or rolling amplitude becomes big. The main influencing factors that influence the non-linear characteristics of the natural circulation system under rolling motion are thermal driving force, flow resistance and the additional forces caused by rolling motion. The non-linear characteristics of the natural circulation system under rolling motion changes caused by the change of the feedback and coupling degree among these influencing factors when the dimensionless power or rolling parameters changes

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.

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.

Scaling of chaos in strongly nonlinear lattices.

Science.gov (United States)

Mulansky, Mario

2014-06-01

Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.

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.

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.

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

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.

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

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...

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.

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.

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

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.

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.

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

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.

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

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

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

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

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

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

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.

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

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.

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.

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.

Sliding mode synchronization controller design with neural network for uncertain chaotic systems

Energy Technology Data Exchange (ETDEWEB)

Mou Chen [College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China)], E-mail: chenmou@nuaa.edu.cn; Jiang Changsheng; Bin Jiang; Wu Qingxian [College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China)

2009-02-28

A sliding mode synchronization controller is presented with RBF neural network for two chaotic systems in this paper. The compound disturbance of the synchronization error system consists of nonlinear uncertainties and exterior disturbances of chaotic systems. Based on RBF neural networks, a compound disturbance observer is proposed and the update law of parameters is given to monitor the compound disturbance. The synchronization controller is given based on the output of the compound disturbance observer. The designed controller can make the synchronization error convergent to zero and overcome the disruption of the uncertainty and the exterior disturbance of the system. Finally, an example is given to demonstrate the availability of the proposed synchronization control method.

Adaptive modified function projective synchronization of multiple time-delayed chaotic Rossler system

International Nuclear Information System (INIS)

Sudheer, K. Sebastian; Sabir, M.

2011-01-01

In this Letter we consider modified function projective synchronization of unidirectionally coupled multiple time-delayed Rossler chaotic systems using adaptive controls. Recently, delay differential equations have attracted much attention in the field of nonlinear dynamics. The high complexity of the multiple time-delayed systems can provide a new architecture for enhancing message security in chaos based encryption systems. Adaptive control can be used for synchronization when the parameters of the system are unknown. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two chaotic systems are function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.

Robust synchronization of drive-response chaotic systems via adaptive sliding mode control

International Nuclear Information System (INIS)

Li, W.-L.; Chang, K.-M.

2009-01-01

A robust adaptive sliding control scheme is developed in this study to achieve synchronization for two identical chaotic systems in the presence of uncertain system parameters, external disturbances and nonlinear control inputs. An adaptation algorithm is given based on the Lyapunov stability theory. Using this adaptation technique to estimate the upper-bounds of parameter variation and external disturbance uncertainties, an adaptive sliding mode controller is then constructed without requiring the bounds of parameter and disturbance uncertainties to be known in advance. It is proven that the proposed adaptive sliding mode controller can maintain the existence of sliding mode in finite time in uncertain chaotic systems. Finally, numerical simulations are presented to show the effectiveness of the proposed control scheme.

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

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).

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).

Multi-pulse chaotic motions of a rotor-active magnetic bearing system with time-varying stiffness

International Nuclear Information System (INIS)

Zhang, W.; Yao, M.H.; Zhan, X.P.

2006-01-01

In this paper, we investigate the Shilnikov type multi-pulse chaotic dynamics for a rotor-active magnetic bearings (AMB) system with 8-pole legs and the time-varying stiffness. The stiffness in the AMB is considered as the time-varying in a periodic form. The dimensionless equation of motion for the rotor-AMB system with the time-varying stiffness in the horizontal and vertical directions is a two-degree-of-freedom nonlinear system with quadratic and cubic nonlinearities and parametric excitation. The asymptotic perturbation method is used to obtain the averaged equations in the case of primary parametric resonance and 1/2 subharmonic resonance. It is found from the numerical results that there are the phenomena of the Shilnikov type multi-pulse chaotic motions for the rotor-AMB system. A new jumping phenomenon is discovered in the rotor-AMB system with the time-varying stiffness

NONLINEAR ACCELERATOR LATTICES WITH ONE AND TWO ANALYTIC INVARIANTS

International Nuclear Information System (INIS)

Danilov, Viatcheslav V.

2010-01-01

Integrable systems appeared in physics long ago at the onset of classical dynamics with examples being Kepler s and other famous problems. Unfortunately, the majority of nonlinear problems turned out to be nonintegrable. In accelerator terms, any 2D nonlinear map produces a chaotic motion and a complex network of stable and unstable resonances with the unit probability. Nevertheless, in the proximity of an integrable system the full volume of such a chaotic network is small. Thus, the integrable nonlinear motion in accelerators has the potential to introduce a large betatron tune spread to suppress instabilities and to mitigate space charge effects with relatively small resonances and particle loss. To create such an accelerator lattice one has to find magnetic and electrtic field combinations leading to a stable integrable motion. This paper presents families of lattices with one invariant where bounded motion can be easily created in large volumes of the phase space. In addition, it presents 3 families of integrable nonlinear accelerator lattices, relizable with longitudinal-coordinate-dependent magnetic or electric fields with the stable nonlinear motion, which can be solved in terms of separable variables.

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.

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.

Nonlinear dynamics of the relativistic standard map

International Nuclear Information System (INIS)

Nomura, Y.; Ichikawa, Y.H.; Horton, W.

1991-01-01

Heating and acceleration of charged particles by RF fields have been extensively investigated by the standard map (ST). Thus, it is natural to pose the question asking how the relativistic effects change the nonlinear dynamical behavior described by the classical ST map. The authors show that the speed of light limits the rate of advance of the phase in the relativistic standard map (RST) and introduces KAM surfaces persisting in the high momentum region. The RST map is a two parameter (k, β = ω/kc) family of dynamics reducing to the ST map when β → 0. For β ≠ 0 the relativity suppresses the onset of stochasticity. Chernikov et al. has also reported this effect. They have carried out extensive studies of nonlinear dynamics of the RST map and found very intricate structure of mixing of the higher order periodic orbits and chaotic orbits. They have shown that no matter how its gets chaotic the symmetry properties of the RST map determines its nonlinear dynamical behavior. 1 ref

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

Observer-based adaptive control of chaos in nonlinear discrete-time systems using time-delayed state feedback

International Nuclear Information System (INIS)

Goharrizi, Amin Yazdanpanah; Khaki-Sedigh, Ali; Sepehri, Nariman

2009-01-01

A new approach to adaptive control of chaos in a class of nonlinear discrete-time-varying systems, using a delayed state feedback scheme, is presented. It is discussed that such systems can show chaotic behavior as their parameters change. A strategy is employed for on-line calculation of the Lyapunov exponents that will be used within an adaptive scheme that decides on the control effort to suppress the chaotic behavior once detected. The scheme is further augmented with a nonlinear observer for estimation of the states that are required by the controller but are hard to measure. Simulation results for chaotic control problem of Jin map are provided to show the effectiveness of the proposed scheme.

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.

Application of nonlinear forecasting techniques for meteorological modeling

Directory of Open Access Journals (Sweden)

V. Pérez-Muñuzuri

2000-10-01

Full Text Available A nonlinear forecasting method was used to predict the behavior of a cloud coverage time series several hours in advance. The method is based on the reconstruction of a chaotic strange attractor using four years of cloud absorption data obtained from half-hourly Meteosat infrared images from Northwestern Spain. An exhaustive nonlinear analysis of the time series was carried out to reconstruct the phase space of the underlying chaotic attractor. The forecast values are used by a non-hydrostatic meteorological model ARPS for daily weather prediction and their results compared with surface temperature measurements from a meteorological station and a vertical sounding. The effect of noise in the time series is analyzed in terms of the prediction results.Key words: Meterology and atmospheric dynamics (mesoscale meteorology; general – General (new fields

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.

A novel adaptive-impulsive synchronization of fractional-order chaotic systems

International Nuclear Information System (INIS)

Andrew, Leung Y. T.; Xian-Feng, Li; Yan-Dong, Chu; Hui, Zhang

2015-01-01

A novel adaptive–impulsive scheme is proposed for synchronizing fractional-order chaotic systems without the necessity of knowing the attractors’ bounds in priori. The nonlinear functions in these systems are supposed to satisfy local Lipschitz conditions but which are estimated with adaptive laws. The novelty is that the combination of adaptive control and impulsive control offers a control strategy gathering the advantages of both. In order to guarantee the convergence is no less than an expected exponential rate, a combined feedback strength design is created such that the symmetric axis can shift freely according to the updated transient feedback strength. All of the unknown Lipschitz constants are also updated exponentially in the meantime of achieving synchronization. Two different fractional-order chaotic systems are employed to demonstrate the effectiveness of the novel adaptive–impulsive control scheme. (paper)

Nonlinear dynamics in the Einstein-Friedmann equation

International Nuclear Information System (INIS)

Tanaka, Yosuke; Mizuno, Yuji; Ohta, Shigetoshi; Mori, Keisuke; Horiuchi, Tanji

2009-01-01

We have studied the gravitational field equations on the basis of general relativity and nonlinear dynamics. The space component of the Einstein-Friedmann equation shows the chaotic behaviours in case the following conditions are satisfied: (i)the expanding ratio: h=x . /x max = +0.14) for the occurrence of the chaotic behaviours in the Einstein-Friedmann equation (0 ≤ λ ≤ +0.14). The numerical calculations are performed with the use of the Microsoft EXCEL(2003), and the results are shown in the following cases; λ = 2b = +0.06 and +0.14.

Robust Synchronization of Delayed Chaotic FitzHugh-Nagumo Neurons under External Electrical Stimulation

Directory of Open Access Journals (Sweden)

Muhammad Rehan

2012-01-01

Full Text Available Synchronization of chaotic neurons under external electrical stimulation (EES is studied in order to understand information processing in the brain and to improve the methodologies employed in the treatment of cognitive diseases. This paper investigates the dynamics of uncertain coupled chaotic delayed FitzHugh-Nagumo (FHN neurons under EES for incorporated parametric variations. A global nonlinear control law for synchronization of delayed neurons with known parameters is developed. Based on local and global Lipschitz conditions, knowledge of the bounds on the neuronal states, the Lyapunov-Krasovskii functional, and the L2 gain reduction, a less conservative local robust nonlinear control law is formulated to address the problem of robust asymptotic synchronization of delayed FHN neurons under parametric uncertainties. The proposed local control law guarantees both robust stability and robust performance and provides the L2 bound for uncertainty rejection in the synchronization error dynamics. Separate conditions for single-input and multiple-input control schemes for synchronization of a wide class of FHN systems are provided. The results of the proposed techniques are verified through numerical simulations.

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.

A chaotic view of behavior change: a quantum leap for health promotion.

Science.gov (United States)

Resnicow, Ken; Vaughan, Roger

2006-09-12

The study of health behavior change, including nutrition and physical activity behaviors, has been rooted in a cognitive-rational paradigm. Change is conceptualized as a linear, deterministic process where individuals weigh pros and cons, and at the point at which the benefits outweigh the cost change occurs. Consistent with this paradigm, the associated statistical models have almost exclusively assumed a linear relationship between psychosocial predictors and behavior. Such a perspective however, fails to account for non-linear, quantum influences on human thought and action. Consider why after years of false starts and failed attempts, a person succeeds at increasing their physical activity, eating healthier or losing weight. Or, why after years of success a person relapses. This paper discusses a competing view of health behavior change that was presented at the 2006 annual ISBNPA meeting in Boston. Rather than viewing behavior change from a linear perspective it can be viewed as a quantum event that can be understood through the lens of Chaos Theory and Complex Dynamic Systems. Key principles of Chaos Theory and Complex Dynamic Systems relevant to understanding health behavior change include: 1) Chaotic systems can be mathematically modeled but are nearly impossible to predict; 2) Chaotic systems are sensitive to initial conditions; 3) Complex Systems involve multiple component parts that interact in a nonlinear fashion; and 4) The results of Complex Systems are often greater than the sum of their parts. Accordingly, small changes in knowledge, attitude, efficacy, etc may dramatically alter motivation and behavioral outcomes. And the interaction of such variables can yield almost infinite potential patterns of motivation and behavior change. In the linear paradigm unaccounted for variance is generally relegated to the catch all "error" term, when in fact such "error" may represent the chaotic component of the process. The linear and chaotic paradigms are

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.

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.

Asynchronous error-correcting secure communication scheme based on fractional-order shifting chaotic system

Science.gov (United States)

Chao, Luo

2015-11-01

In this paper, a novel digital secure communication scheme is firstly proposed. Different from the usual secure communication schemes based on chaotic synchronization, the proposed scheme employs asynchronous communication which avoids the weakness of synchronous systems and is susceptible to environmental interference. Moreover, as to the transmission errors and data loss in the process of communication, the proposed scheme has the ability to be error-checking and error-correcting in real time. In order to guarantee security, the fractional-order complex chaotic system with the shifting of order is utilized to modulate the transmitted signal, which has high nonlinearity and complexity in both frequency and time domains. The corresponding numerical simulations demonstrate the effectiveness and feasibility of the scheme.

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.

A new method to determine magnetic properties of the unsaturated-magnetized rotor of a novel gyro

Science.gov (United States)

Li, Hai; Liu, Xiaowei; Dong, Changchun; Zhang, Haifeng

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.

Comparison of low confinement mode transport simulations using the mixed Bohm/gyro-Bohm and the Multi-Mode-95 transport model

International Nuclear Information System (INIS)

Onjun, Thawatchai; Bateman, Glenn; Kritz, Arnold H.; Hannum, David

2001-01-01

Predictive transport simulations using the mixed Bohm/gyro-Bohm (JET) transport model [M. Erba , Plasma Phys. Controlled Fusion 39, 261 (1997)] are compared with simulations using the Multi-Mode-95 (MMM95) transport model [G. Bateman , Phys. Plasmas 5, 1793 (1998)]. Temperature and density profiles from these simulations are compared with experimental data for 13 low confinement mode (L-mode) discharges from the Doublet III-D Tokamak (DIII-D) [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] and the Tokamak Fusion Test Reactor (TFTR) [D. Grove and D. M. Meade, Nucl. Fusion 25, 1167 (1985)]. The selected discharges include systematic scans over gyro-radius, plasma power, current, and density. It is found that simulations using the two models match experimental data equally well, in spite of the fact that the JET model has predominantly Bohm scaling (proportional to gyro-radius) while the MMM95 model has a purely gyro-Bohm scaling (proportional to gyro-radius squared)

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.

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.

Application of nonlinear forecasting techniques for meteorological modeling

Directory of Open Access Journals (Sweden)

V. Pérez-Muñuzuri

Full Text Available A nonlinear forecasting method was used to predict the behavior of a cloud coverage time series several hours in advance. The method is based on the reconstruction of a chaotic strange attractor using four years of cloud absorption data obtained from half-hourly Meteosat infrared images from Northwestern Spain. An exhaustive nonlinear analysis of the time series was carried out to reconstruct the phase space of the underlying chaotic attractor. The forecast values are used by a non-hydrostatic meteorological model ARPS for daily weather prediction and their results compared with surface temperature measurements from a meteorological station and a vertical sounding. The effect of noise in the time series is analyzed in terms of the prediction results.

Key words: Meterology and atmospheric dynamics (mesoscale meteorology; general – General (new fields

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

Resonant responses and chaotic dynamics of composite laminated circular cylindrical shell with membranes

Science.gov (United States)

Zhang, W.; Liu, T.; Xi, A.; Wang, Y. N.

2018-06-01

This paper is focused on the resonant responses and chaotic dynamics of a composite laminated circular cylindrical shell with radially pre-stretched membranes at both ends and clamped along a generatrix. Based on the two-degree-of-freedom non-autonomous nonlinear equations of this system, the method of multiple scales is employed to obtain the four-dimensional nonlinear averaged equation. The resonant case considered here is the primary parametric resonance-1/2 subharmonic resonance and 1:1 internal resonance. Corresponding to several selected parameters, the frequency-response curves are obtained. From the numerical results, we find that the hardening-spring-type behaviors and jump phenomena are exhibited. The jump phenomena also occur in the amplitude curves of the temperature parameter excitation. Moreover, it is found that the temperature parameter excitation, the coupling degree of two order modes and the detuning parameters can effect the nonlinear oscillations of this system. The periodic and chaotic motions of the composite laminated circular cylindrical shell clamped along a generatrix are demonstrated by the bifurcation diagrams, the maximum Lyapunov exponents, the phase portraits, the waveforms, the power spectrums and the Poincaré map. The temperature parameter excitation shows that the Pomeau-Manneville type intermittent chaos occur under the certain initial conditions. It is also found that there exist the twin phenomena between the Pomeau-Manneville type intermittent chaos and the period-doubling bifurcation.

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.

Robust digital controllers for uncertain chaotic systems: A digital redesign approach

Energy Technology Data Exchange (ETDEWEB)

Ababneh, Mohammad [Department of Controls, FMC Kongsberg Subsea, FMC Energy Systems, Houston, TX 77067 (United States); Barajas-Ramirez, Juan-Gonzalo [CICESE, Depto. De Electronica y Telecomunicaciones, Ensenada, BC, 22860 (Mexico); Chen Guanrong [Centre for Chaos Control and Synchronization, Department of Electronic Engineering, City University of Hong Kong (China); Shieh, Leang S. [Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204-4005 (United States)

2007-03-15

In this paper, a new and systematic method for designing robust digital controllers for uncertain nonlinear systems with structured uncertainties is presented. In the proposed method, a controller is designed in terms of the optimal linear model representation of the nominal system around each operating point of the trajectory, while the uncertainties are decomposed such that the uncertain nonlinear system can be rewritten as a set of local linear models with disturbed inputs. Applying conventional robust control techniques, continuous-time robust controllers are first designed to eliminate the effects of the uncertainties on the underlying system. Then, a robust digital controller is obtained as the result of a digital redesign of the designed continuous-time robust controller using the state-matching technique. The effectiveness of the proposed controller design method is illustrated through some numerical examples on complex nonlinear systems--chaotic systems.

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.

Dynamic Analysis and Adaptive Sliding Mode Controller for a Chaotic Fractional Incommensurate Order Financial System

Science.gov (United States)

Hajipour, Ahmad; Tavakoli, Hamidreza

2017-12-01

In this study, the dynamic behavior and chaos control of a chaotic fractional incommensurate-order financial system are investigated. Using well-known tools of nonlinear theory, i.e. Lyapunov exponents, phase diagrams and bifurcation diagrams, we observe some interesting phenomena, e.g. antimonotonicity, crisis phenomena and route to chaos through a period doubling sequence. Adopting largest Lyapunov exponent criteria, we find that the system yields chaos at the lowest order of 2.15. Next, in order to globally stabilize the chaotic fractional incommensurate order financial system with uncertain dynamics, an adaptive fractional sliding mode controller is designed. Numerical simulations are used to demonstrate the effectiveness of the proposed control method.

Nonlinear chaos-dynamical approach to analysis of atmospheric ...

Indian Academy of Sciences (India)

false nearest neighbors, Lyapunov's exponents, surrogate data, nonlinear prediction ... Chaotic dynamics; time series of the 222Rn concentration; universal complex ... tems is due to a number of applications, including the ..... Computer Engineering. ... Ternovsky,Quantum Systems in Physics, Chemistry, and. Biology, pp.

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...

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.

Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations

International Nuclear Information System (INIS)

Udaltsov, Vladimir S.; Goedgebuer, Jean-Pierre; Larger, Laurent; Cuenot, Jean-Baptiste; Levy, Pascal; Rhodes, William T.

2003-01-01

We report that signal encoding with high-dimensional chaos produced by delayed feedback systems with a strong nonlinearity can be broken. We describe the procedure and illustrate the method with chaotic waveforms obtained from a strongly nonlinear optical system that we used previously to demonstrate signal encryption/decryption with chaos in wavelength. The method can be extended to any systems ruled by nonlinear time-delayed differential equations

Chaos control for a class of chaotic systems using PI-type state observer approach

International Nuclear Information System (INIS)

Jiang Guoping; Zheng Weixing

2004-01-01

In this paper, by using the PI-type state observer design approach and the characteristic of ergodicity of chaos, a new method is presented for controlling chaos, including the stabilization of unstable equilibrium points and set-point tracking, for a class of chaotic systems. Based on the theory of nonlinear ordinary differential equations, a simple criterion is derived for designing the controller gains for stabilization and tracking, in which control parameters can be selected via the pole placement technique of linear control theory. More importantly, this control method has a simple controller structure, high robustness against system parametric variations, and strong rejection of external constant disturbances. The method is applied to the chaotic Lorenz system for demonstration

Study of possible chaotic, quasi-periodic and periodic structures in quantum dusty plasma

International Nuclear Information System (INIS)

Ghosh, Uday Narayan; Chatterjee, Prasanta; Roychoudhury, Rajkumar

2014-01-01

Existence of chaotic, quasi-periodic, and periodic structures of dust-ion acoustic waves is studied in quantum dusty plasmas through dynamical system approach. A system of coupled differential equations is derived from the fluid model and subsequently, variational matrix is obtained. The characteristic equation is obtained at the equilibrium point, and the behavior of nonlinear waves is studied numerically using Runge-Kutta method. The behavior of the dynamical system changes significantly when any of plasma parameters, such as the dust concentration parameter, temperature ratio, or the quantum diffraction parameter, is varied. The change of the characteristic of solution of the system is extensively studied. It is found that the system changes its behavior from chaotic pattern to limit cycle behavior

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)

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.

Applications of Nonlinear Dynamics Model and Design of Complex Systems

CERN Document Server

In, Visarath; Palacios, Antonio

2009-01-01

This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.

Nonlinear dynamics new directions models and applications

CERN Document Server

Ugalde, Edgardo

2015-01-01

This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: ·         Develops applications of nonlinear dynamics on a diversity of topics such as patterns of synchrony in neuronal networks, laser synchronization, control of chaotic systems, and the study of transient dynam...

Reconstruction of chaotic signals with applications to chaos-based communications

CERN Document Server

Feng, Jiu Chao

2008-01-01

This book provides a systematic review of the fundamental theory of signal reconstruction and the practical techniques used in reconstructing chaotic signals. Specific applications of signal reconstruction methods in chaos-based communications are expounded in full detail, along with examples illustrating the various problems associated with such applications.The book serves as an advanced textbook for undergraduate and graduate courses in electronic and information engineering, automatic control, physics and applied mathematics. It is also highly suited for general nonlinear scientists who wi

An efficient three-party password-based key agreement protocol using extended chaotic maps

International Nuclear Information System (INIS)

Shu Jian

2015-01-01

Three-party password-based key agreement protocols allow two users to authenticate each other via a public channel and establish a session key with the aid of a trusted server. Recently, Farash et al. [Farash M S, Attari M A 2014 “An efficient and provably secure three-party password-based authenticated key exchange protocol based on Chebyshev chaotic maps”, Nonlinear Dynamics 77(7): 399–411] proposed a three-party key agreement protocol by using the extended chaotic maps. They claimed that their protocol could achieve strong security. In the present paper, we analyze Farash et al.’s protocol and point out that this protocol is vulnerable to off-line password guessing attack and suffers communication burden. To handle the issue, we propose an efficient three-party password-based key agreement protocol using extended chaotic maps, which uses neither symmetric cryptosystems nor the server’s public key. Compared with the relevant schemes, our protocol provides better performance in terms of computation and communication. Therefore, it is suitable for practical applications. (paper)

Manual Optical Attitude Re-initialization of a Crew Vehicle in Space Using Bias Corrected Gyro Data

Science.gov (United States)

Gioia, Christopher J.

NASA and other space agencies have shown interest in sending humans on missions beyond low Earth orbit. Proposed is an algorithm that estimates the attitude of a manned spacecraft using measured line-of-sight (LOS) vectors to stars and gyroscope measurements. The Manual Optical Attitude Reinitialization (MOAR) algorithm and corresponding device draw inspiration from existing technology from the Gemini, Apollo and Space Shuttle programs. The improvement over these devices is the capability of estimating gyro bias completely independent from re-initializing attitude. It may be applied to the lost-in-space problem, where the spacecraft's attitude is unknown. In this work, a model was constructed that simulated gyro data using the Farrenkopf gyro model, and LOS measurements from a spotting scope were then computed from it. Using these simulated measurements, gyro bias was estimated by comparing measured interior star angles to those derived from a star catalog and then minimizing the difference using an optimization technique. Several optimization techniques were analyzed, and it was determined that the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm performed the best when combined with a grid search technique. Once estimated, the gyro bias was removed and attitude was determined by solving the Wahba Problem via the Singular Value Decomposition (SVD) approach. Several Monte Carlo simulations were performed that looked at different operating conditions for the MOAR algorithm. These included the effects of bias instability, using different constellations for data collection, sampling star measurements in different orders, and varying the time between measurements. A common method of estimating gyro bias and attitude in a Multiplicative Extended Kalman Filter (MEKF) was also explored and disproven for use in the MOAR algorithm. A prototype was also constructed to validate the proposed concepts. It was built using a simple spotting scope, MEMS grade IMU, and a Raspberry

Exact results for quantum chaotic systems and one-dimensional fermions from matrix models

International Nuclear Information System (INIS)

Simons, B.D.; Lee, P.A.; Altshuler, B.L.

1993-01-01

We demonstrate a striking connection between the universal parametric correlations of the spectra of quantum chaotic systems and a class of integrable quantum hamiltonians. We begin by deriving a non-perturbative expression for the universal m-point correlation function of the spectra of random matrix ensembles in terms of a non-linear supermatrix σ-model. These results are shown to coincide with those from previous studies of weakly disordered metallic systems. We then introduce a continuous matrix model which describes the quantum mechanics of the Sutherland hamiltonian describing particles interacting through an inverse-square pairwise potential. We demonstrate that a field theoretic approach can be employed to determine exact analytical expressions for correlations of the quantum hamiltonian. The results, which are expressed in terms of a non-linear σ-model, are shown to coincide with those for analogous correlation functions of random matrix ensembles after an appropriate change of variables. We also discuss possible generalizations of the matrix model to higher dimensions. These results reveal a common mathematical structure which underlies branches of theoretical physics ranging from continuous matrix models to strongly interacting quantum hamiltonians, and universalities in the spectra of quantum chaotic systems. (orig.)

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...

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

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)

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

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.

Model-free adaptive control optimization using a chaotic particle swarm approach

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; Rodrigues Coelho, Antonio Augusto [Department of Automation and Systems, Federal University of Santa Catarina, Box 476, 88040-900 Florianopolis, Santa Catarina (Brazil)], E-mail: aarc@das.ufsc.br

2009-08-30

It is well known that conventional control theories are widely suited for applications where the processes can be reasonably described in advance. However, when the plant's dynamics are hard to characterize precisely or are subject to environmental uncertainties, one may encounter difficulties in applying the conventional controller design methodologies. Despite the difficulty in achieving high control performance, the fine tuning of controller parameters is a tedious task that always requires experts with knowledge in both control theory and process information. Nowadays, more and more studies have focused on the development of adaptive control algorithms that can be directly applied to complex processes whose dynamics are poorly modeled and/or have severe nonlinearities. In this context, the design of a Model-Free Learning Adaptive Control (MFLAC) based on pseudo-gradient concepts and optimization procedure by a Particle Swarm Optimization (PSO) approach using constriction coefficient and Henon chaotic sequences (CPSOH) is presented in this paper. PSO is a stochastic global optimization technique inspired by social behavior of bird flocking. The PSO models the exploration of a problem space by a population of particles. Each particle in PSO has a randomized velocity associated to it, which moves through the space of the problem. Since chaotic mapping enjoys certainty, ergodicity and the stochastic property, the proposed CPSOH introduces chaos mapping which introduces some flexibility in particle movements in each iteration. The chaotic sequences allow also explorations at early stages and exploitations at later stages during the search procedure of CPSOH. Motivation for application of CPSOH approach is to overcome the limitation of the conventional MFLAC design, which cannot guarantee satisfactory control performance when the plant has different gains for the operational range when designed by trial-and-error by user. Numerical results of the MFLAC with

Model-free adaptive control optimization using a chaotic particle swarm approach

International Nuclear Information System (INIS)

Santos Coelho, Leandro dos; Rodrigues Coelho, Antonio Augusto

2009-01-01

It is well known that conventional control theories are widely suited for applications where the processes can be reasonably described in advance. However, when the plant's dynamics are hard to characterize precisely or are subject to environmental uncertainties, one may encounter difficulties in applying the conventional controller design methodologies. Despite the difficulty in achieving high control performance, the fine tuning of controller parameters is a tedious task that always requires experts with knowledge in both control theory and process information. Nowadays, more and more studies have focused on the development of adaptive control algorithms that can be directly applied to complex processes whose dynamics are poorly modeled and/or have severe nonlinearities. In this context, the design of a Model-Free Learning Adaptive Control (MFLAC) based on pseudo-gradient concepts and optimization procedure by a Particle Swarm Optimization (PSO) approach using constriction coefficient and Henon chaotic sequences (CPSOH) is presented in this paper. PSO is a stochastic global optimization technique inspired by social behavior of bird flocking. The PSO models the exploration of a problem space by a population of particles. Each particle in PSO has a randomized velocity associated to it, which moves through the space of the problem. Since chaotic mapping enjoys certainty, ergodicity and the stochastic property, the proposed CPSOH introduces chaos mapping which introduces some flexibility in particle movements in each iteration. The chaotic sequences allow also explorations at early stages and exploitations at later stages during the search procedure of CPSOH. Motivation for application of CPSOH approach is to overcome the limitation of the conventional MFLAC design, which cannot guarantee satisfactory control performance when the plant has different gains for the operational range when designed by trial-and-error by user. Numerical results of the MFLAC with CPSOH

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.

Linearly and nonlinearly bidirectionally coupled synchronization of hyperchaotic systems

International Nuclear Information System (INIS)

Zhou Jin; Lu Junan; Wu Xiaoqun

2007-01-01

To date, there have been many results about unidirectionally coupled synchronization of chaotic systems. However, much less work is reported on bidirectionally-coupled synchronization. In this paper, we investigate the synchronization of two bidirectionally coupled Chen hyperchaotic systems, which are coupled linearly and nonlinearly respectively. Firstly, linearly coupled synchronization of two hyperchaotic Chen systems is investigated, and a theorem on how to choose the coupling coefficients are developed to guarantee the global asymptotical synchronization of two coupled hyperchaotic systems. Analysis shows that the choice of the coupling coefficients relies on the bound of the chaotic system. Secondly, the nonlinearly coupled synchronization is studied; a sufficient condition for the locally asymptotical synchronization is derived, which is independent of the bound of the hyperchaotic system. Finally, numerical simulations are included to verify the effectiveness and feasibility of the developed theorems

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity.

Science.gov (United States)

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

Science.gov (United States)

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K.; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

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...

A chaotic view of behavior change: a quantum leap for health promotion

Directory of Open Access Journals (Sweden)

Vaughan Roger

2006-09-01

Full Text Available Abstract Background The study of health behavior change, including nutrition and physical activity behaviors, has been rooted in a cognitive-rational paradigm. Change is conceptualized as a linear, deterministic process where individuals weigh pros and cons, and at the point at which the benefits outweigh the cost change occurs. Consistent with this paradigm, the associated statistical models have almost exclusively assumed a linear relationship between psychosocial predictors and behavior. Such a perspective however, fails to account for non-linear, quantum influences on human thought and action. Consider why after years of false starts and failed attempts, a person succeeds at increasing their physical activity, eating healthier or losing weight. Or, why after years of success a person relapses. This paper discusses a competing view of health behavior change that was presented at the 2006 annual ISBNPA meeting in Boston. Discussion Rather than viewing behavior change from a linear perspective it can be viewed as a quantum event that can be understood through the lens of Chaos Theory and Complex Dynamic Systems. Key principles of Chaos Theory and Complex Dynamic Systems relevant to understanding health behavior change include: 1 Chaotic systems can be mathematically modeled but are nearly impossible to predict; 2 Chaotic systems are sensitive to initial conditions; 3 Complex Systems involve multiple component parts that interact in a nonlinear fashion; and 4 The results of Complex Systems are often greater than the sum of their parts. Accordingly, small changes in knowledge, attitude, efficacy, etc may dramatically alter motivation and behavioral outcomes. And the interaction of such variables can yield almost infinite potential patterns of motivation and behavior change. In the linear paradigm unaccounted for variance is generally relegated to the catch all "error" term, when in fact such "error" may represent the chaotic component of the

Hysteresis compensation of the Prandtl-Ishlinskii model for piezoelectric actuators using modified particle swarm optimization with chaotic map.

Science.gov (United States)

Long, Zhili; Wang, Rui; Fang, Jiwen; Dai, Xufei; Li, Zuohua

2017-07-01

Piezoelectric actuators invariably exhibit hysteresis nonlinearities that tend to become significant under the open-loop condition and could cause oscillations and errors in nanometer-positioning tasks. Chaotic map modified particle swarm optimization (MPSO) is proposed and implemented to identify the Prandtl-Ishlinskii model for piezoelectric actuators. Hysteresis compensation is attained through application of an inverse Prandtl-Ishlinskii model, in which the parameters are formulated based on the original model with chaotic map MPSO. To strengthen the diversity and improve the searching ergodicity of the swarm, an initial method of adaptive inertia weight based on a chaotic map is proposed. To compare and prove that the swarm's convergence occurs before stochastic initialization and to attain an optimal particle swarm optimization algorithm, the parameters of a proportional-integral-derivative controller are searched using self-tuning, and the simulated results are used to verify the search effectiveness of chaotic map MPSO. The results show that chaotic map MPSO is superior to its competitors for identifying the Prandtl-Ishlinskii model and that the inverse Prandtl-Ishlinskii model can provide hysteresis compensation under different conditions in a simple and effective manner.

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)

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

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...

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.

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.

Modified Levenberg-Marquardt Method for RÖSSLER Chaotic System Fuzzy Modeling Training

Science.gov (United States)

Wang, Yu-Hui; Wu, Qing-Xian; Jiang, Chang-Sheng; Xue, Ya-Li; Fang, Wei

Generally, fuzzy approximation models require some human knowledge and experience. Operator's experience is involved in the mathematics of fuzzy theory as a collection of heuristic rules. The main goal of this paper is to present a new method for identifying unknown nonlinear dynamics such as Rössler system without any human knowledge. Instead of heuristic rules, the presented method uses the input-output data pairs to identify the Rössler chaotic system. The training algorithm is a modified Levenberg-Marquardt (L-M) method, which can adjust the parameters of each linear polynomial and fuzzy membership functions on line, and do not rely on experts' experience excessively. Finally, it is applied to training Rössler chaotic system fuzzy identification. Comparing this method with the standard L-M method, the convergence speed is accelerated. The simulation results demonstrate the effectiveness of the proposed method.

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

The variation of the density functions on chaotic spheres in chaotic space-like Minkowski space time

International Nuclear Information System (INIS)

El-Ahmady, A.E.

2007-01-01

In this article we introduce types of chaotic spheres in chaotic space-like Minkowski space time M n+1 . The variations of the density functions under the folding of these chaotic spheres are defined. The foldings restriction imposed on the density function are also discussed. The relations between the folding of geometry and pure chaotic manifolds are deduced. Some theorems concerning these relations are presented

A Novel Approach Based on MEMS-Gyro's Data Deep Coupling for Determining the Centroid of Star Spot

Directory of Open Access Journals (Sweden)

Xing Fei

2012-01-01

Full Text Available The traditional approach of star tracker for determining the centroid of spot requires enough energy and good shape, so a relatively long exposure time and stable three-axis state become necessary conditions to maintain high accuracy, these limit its update rate and dynamic performance. In view of these issues, this paper presents an approach for determining the centroid of star spot which based on MEMS-Gyro's data deep coupling, it achieves the deep fusion of the data of star tracker and MEMS-Gyro at star map level through the introduction of EKF. The trajectory predicted by using the angular velocity of three axes can be used to set the extraction window, this enhances the dynamic performance because of the accurate extraction when the satellite has angular speed. The optimal estimations of the centroid position and the drift in the output signal of MEMS-Gyro through this approach reduce the influence of noise of the detector on accuracy of the traditional approach for determining the centroid and effectively correct the output signal of MEMS-Gyro. At the end of this paper, feasibility of this approach is verified by simulation.

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

Applicability of Time-Averaged Holography for Micro-Electro-Mechanical System Performing Non-Linear Oscillations

Directory of Open Access Journals (Sweden)

Paulius Palevicius

2014-01-01

Full Text Available Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms.

Applicability of Time-Averaged Holography for Micro-Electro-Mechanical System Performing Non-Linear Oscillations

Science.gov (United States)

Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas

2014-01-01

Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms. PMID:24451467

Applicability of time-averaged holography for micro-electro-mechanical system performing non-linear oscillations.

Science.gov (United States)

Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas

2014-01-21

Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms.

Nonlinear Dynamics Analysis of the Semiactive Suspension System with Magneto-Rheological Damper

Directory of Open Access Journals (Sweden)

Hailong Zhang

2015-01-01

Full Text Available This paper examines dynamical behavior of a nonlinear oscillator which models a quarter-car forced by the road profile. The magneto-rheological (MR suspension system has been established, by employing the modified Bouc-Wen force-velocity (F-v model of magneto-rheological damper (MRD. The possibility of chaotic motions in MR suspension is discovered by employing the method of nonlinear stability analysis. With the bifurcation diagrams and corresponding Lyapunov exponent (LE spectrum diagrams detected through numerical calculation, we can observe the complex dynamical behaviors and oscillating mechanism of alternating periodic oscillations, quasiperiodic oscillations, and chaotic oscillations with different profiles of road excitation, as well as the dynamical evolutions to chaos through period-doubling bifurcations, saddle-node bifurcations, and reverse period-doubling bifurcations.

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.

Detecting dynamic causal inference in nonlinear two-phase fracture flow

Science.gov (United States)

Faybishenko, Boris

2017-08-01

Identifying dynamic causal inference involved in flow and transport processes in complex fractured-porous media is generally a challenging task, because nonlinear and chaotic variables may be positively coupled or correlated for some periods of time, but can then become spontaneously decoupled or non-correlated. In his 2002 paper (Faybishenko, 2002), the author performed a nonlinear dynamical and chaotic analysis of time-series data obtained from the fracture flow experiment conducted by Persoff and Pruess (1995), and, based on the visual examination of time series data, hypothesized that the observed pressure oscillations at both inlet and outlet edges of the fracture result from a superposition of both forward and return waves of pressure propagation through the fracture. In the current paper, the author explores an application of a combination of methods for detecting nonlinear chaotic dynamics behavior along with the multivariate Granger Causality (G-causality) time series test. Based on the G-causality test, the author infers that his hypothesis is correct, and presents a causation loop diagram of the spatial-temporal distribution of gas, liquid, and capillary pressures measured at the inlet and outlet of the fracture. The causal modeling approach can be used for the analysis of other hydrological processes, for example, infiltration and pumping tests in heterogeneous subsurface media, and climatic processes, for example, to find correlations between various meteorological parameters, such as temperature, solar radiation, barometric pressure, etc.

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.

Nonlinear dynamics of homeothermic temperature control in skunk cabbage, Symplocarpus foetidus

Science.gov (United States)

Ito, Takanori; Ito, Kikukatsu

2005-11-01

Certain primitive plants undergo orchestrated temperature control during flowering. Skunk cabbage, Symplocarpus foetidus, has been demonstrated to maintain an internal temperature of around 20 °C even when the ambient temperature drops below freezing. However, it is not clear whether a unique algorithm controls the homeothermic behavior of S. foetidus, or whether such an algorithm might exhibit linear or nonlinear thermoregulatory dynamics. Here we report the underlying dynamics of temperature control in S. foetidus using nonlinear forecasting, attractor and correlation dimension analyses. It was shown that thermoregulation in S. foetidus was governed by low-dimensional chaotic dynamics, the geometry of which showed a strange attractor named the “Zazen attractor.” Our data suggest that the chaotic thermoregulation in S. foetidus is inherent and that it is an adaptive response to the natural environment.

Correlation dimension based nonlinear analysis of network traffics with different application protocols

International Nuclear Information System (INIS)

Wang Jun-Song; Yuan Jing; Li Qiang; Yuan Rui-Xi

2011-01-01

This paper uses a correlation dimension based nonlinear analysis approach to analyse the dynamics of network traffics with three different application protocols—HTTP, FTP and SMTP. First, the phase space is reconstructed and the embedding parameters are obtained by the mutual information method. Secondly, the correlation dimensions of three different traffics are calculated and the results of analysis have demonstrated that the dynamics of the three different application protocol traffics is different from each other in nature, i.e. HTTP and FTP traffics are chaotic, furthermore, the former is more complex than the later; on the other hand, SMTP traffic is stochastic. It is shown that correlation dimension approach is an efficient method to understand and to characterize the nonlinear dynamics of HTTP, FTP and SMTP protocol network traffics. This analysis provided insight into and a more accurate understanding of nonlinear dynamics of internet traffics which have a complex mixture of chaotic and stochastic components. (general)

A novel method for designing S-boxes based on chaotic maps

International Nuclear Information System (INIS)

Tang Guoping; Liao Xiaofeng; Chen Yong

2005-01-01

A method for obtaining cryptographically strong 8 x 8 S-boxes based on chaotic maps is presented and the cryptographical properties such as bijection, nonlinearity, strict avalanche criterion, output bits independence criterion and equiprobable input/output XOR distribution of these S-boxes are analyzed in detail. The results of numerical analysis also show that the S-boxes proposed are of the above properties and can resist the differential attack. Furthermore, our approach is suitable for practical application in designing cryptosystem

On nonlinear dynamics and control of a robotic arm with chaos

Directory of Open Access Journals (Sweden)

Felix J. L. P.

2014-01-01

Full Text Available In this paper a robotic arm is modelled by a double pendulum excited in its base by a DC motor of limited power via crank mechanism and elastic connector. In the mathematical model, a chaotic motion was identified, for a wide range of parameters. Controlling of the chaotic behaviour of the system, were implemented using, two control techniques, the nonlinear saturation control (NSC and the optimal linear feedback control (OLFC. The actuator and sensor of the device are allowed in the pivot and joints of the double pendulum. The nonlinear saturation control (NSC is based in the order second differential equations and its action in the pivot/joint of the robotic arm is through of quadratic nonlinearities feedback signals. The optimal linear feedback control (OLFC involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system to a desired periodic orbit, and control a feedback control to bring the trajectory of the system to the desired orbit. Simulation results, including of uncertainties show the feasibility of the both methods, for chaos control of the considered system.

Motif distributions in phase-space networks for characterizing experimental two-phase flow patterns with chaotic features.

Science.gov (United States)

Gao, Zhong-Ke; Jin, Ning-De; Wang, Wen-Xu; Lai, Ying-Cheng

2010-07-01

The dynamics of two-phase flows have been a challenging problem in nonlinear dynamics and fluid mechanics. We propose a method to characterize and distinguish patterns from inclined water-oil flow experiments based on the concept of network motifs that have found great usage in network science and systems biology. In particular, we construct from measured time series phase-space complex networks and then calculate the distribution of a set of distinct network motifs. To gain insight, we first test the approach using time series from classical chaotic systems and find a universal feature: motif distributions from different chaotic systems are generally highly heterogeneous. Our main finding is that the distributions from experimental two-phase flows tend to be heterogeneous as well, suggesting the underlying chaotic nature of the flow patterns. Calculation of the maximal Lyapunov exponent provides further support for this. Motif distributions can thus be a feasible tool to understand the dynamics of realistic two-phase flow patterns.

Non-linear partial differential equations an algebraic view of generalized solutions

CERN Document Server

Rosinger, Elemer E

1990-01-01

A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomen

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.

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

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.

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.

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...

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.)

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.

Dynamic analysis, circuit implementation and passive control of a novel four-dimensional chaotic system with multiscroll attractor and multiple coexisting attractors

Science.gov (United States)

Lai, Bang-Cheng; He, Jian-Jun

2018-03-01

In this paper, we construct a novel 4D autonomous chaotic system with four cross-product nonlinear terms and five equilibria. The multiple coexisting attractors and the multiscroll attractor of the system are numerically investigated. Research results show that the system has various types of multiple attractors, including three strange attractors with a limit cycle, three limit cycles, two strange attractors with a pair of limit cycles, two coexisting strange attractors. By using the passive control theory, a controller is designed for controlling the chaos of the system. Both analytical and numerical studies verify that the designed controller can suppress chaotic motion and stabilise the system at the origin. Moreover, an electronic circuit is presented for implementing the chaotic system.

A chaos-based evolutionary algorithm for general nonlinear programming problems

International Nuclear Information System (INIS)

El-Shorbagy, M.A.; Mousa, A.A.; Nasr, S.M.

2016-01-01

In this paper we present a chaos-based evolutionary algorithm (EA) for solving nonlinear programming problems named chaotic genetic algorithm (CGA). CGA integrates genetic algorithm (GA) and chaotic local search (CLS) strategy to accelerate the optimum seeking operation and to speed the convergence to the global solution. The integration of global search represented in genetic algorithm and CLS procedures should offer the advantages of both optimization methods while offsetting their disadvantages. By this way, it is intended to enhance the global convergence and to prevent to stick on a local solution. The inherent characteristics of chaos can enhance optimization algorithms by enabling it to escape from local solutions and increase the convergence to reach to the global solution. Twelve chaotic maps have been analyzed in the proposed approach. The simulation results using the set of CEC’2005 show that the application of chaotic mapping may be an effective strategy to improve the performances of EAs.

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

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

Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

Science.gov (United States)

Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

2018-01-01

In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

Design of a Double Anode Magnetron Injection Gun for Q-band Gyro-TWT Using Boundary Element Method

Science.gov (United States)

Li, Zhiliang; Feng, Jinjun; Liu, Bentian

2018-04-01

This paper presents a novel design code for double anode magnetron injection guns (MIGs) in gyro-devices based on boundary element method (BEM). The physical and mathematical models were constructed, and then the code using BEM for MIG's calculation was developed. Using the code, a double anode MIG for a Q-band gyrotron traveling-wave tube (gyro-TWT) amplifier operating in the circular TE01 mode at the fundamental cyclotron harmonic was designed. In order to verify the reliability of this code, velocity spread and guiding center radius of the MIG simulated by the BEM code were compared with these from the commonly used EGUN code, showing a reasonable agreement. Then, a Q-band gyro-TWT was fabricated and tested. The testing results show that the device has achieved an average power of 5kW and peak power ≥ 150 kW at a 3% duty cycle within bandwidth of 2 GHz, and maximum output peak power of 220 kW, with a corresponding saturated gain of 50.9 dB and efficiency of 39.8%. This paper demonstrates that the BEM code can be used as an effective approach for analysis of electron optics system in gyro-devices.

Chaotic particle swarm optimization algorithm in a support vector regression electric load forecasting model

International Nuclear Information System (INIS)

Hong, W.-C.

2009-01-01

Accurate forecasting of electric load has always been the most important issues in the electricity industry, particularly for developing countries. Due to the various influences, electric load forecasting reveals highly nonlinear characteristics. Recently, support vector regression (SVR), with nonlinear mapping capabilities of forecasting, has been successfully employed to solve nonlinear regression and time series problems. However, it is still lack of systematic approaches to determine appropriate parameter combination for a SVR model. This investigation elucidates the feasibility of applying chaotic particle swarm optimization (CPSO) algorithm to choose the suitable parameter combination for a SVR model. The empirical results reveal that the proposed model outperforms the other two models applying other algorithms, genetic algorithm (GA) and simulated annealing algorithm (SA). Finally, it also provides the theoretical exploration of the electric load forecasting support system (ELFSS)

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.

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)

DRIRU I/SKIRU - The application of the DTG to spacecraft attitude control. [Dynamically-Tuned Gyro for Inertial Reference Unit systems

Science.gov (United States)

Swanson, C. O.

1982-01-01

The dynamically tuned gyro (DTG) was developed to replace the floated, rate integrating gyro used for space attitude control, as the DTG fulfills cost, performance, and reliability requirements not satisfied by its predecessor. The use of this gyro in the Dry Gyro Inertial Reference Unit I (DRIRU I) marked the first application of a DTG in a spacecraft attitude reference unit. Design and performance characteristics of DTG application in the Singer-Kearfott Inertial Reference Unit (SKIRU) are outlined, for example its minimal weight (7 lb), and operational reliability. The DTG has accomplished 156,000 failure-free hours, and a chart, logging test performance, indicates that this and other requirements were more than sufficiently satisfied. The unit has an unparalleled life span, with several units still operating after 70,000 to 130,000 hours, and a random drift which always remains under 0.0005 deg/h. Potential for improvements, such as drift performance, are considered.

Weak chaos in the disordered nonlinear Schroedinger chain: Destruction of Anderson localization by Arnold diffusion

International Nuclear Information System (INIS)

Basko, D.M.

2011-01-01

Research highlights: → In a one-dimensional disordered chain of oscillators all normal modes are localized. → Nonlinearity leads to chaotic dynamics. → Chaos is concentrated on rare chaotic spots. → Chaotic spots drive energy exchange between oscillators. → Macroscopic transport coefficients are obtained. - Abstract: The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is shown that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots. Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization. The most important mechanism of equilibration at long distances is provided by random migration of the chaotic spots along the chain, which bears analogy with variable-range hopping of electrons in strongly disordered solids. The corresponding macroscopic transport equations are obtained.

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.

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

Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation

CERN Document Server

Petráš, Ivo

2011-01-01

"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...

Nonlinear dynamics in the relativistic field equation

International Nuclear Information System (INIS)

Tanaka, Yosuke; Mizuno, Yuji; Kado, Tatsuhiko; Zhao, Hua-An

2007-01-01

We have investigated relativistic equations and chaotic behaviors of the gravitational field with the use of general relativity and nonlinear dynamics. The space component of the Friedmann equation shows chaotic behaviors in case of the inflation (h=G-bar /G>0) and open (ζ=-1) universe. In other cases (h= 0 andx-bar 0 ) and the parameters (a, b, c and d); (2) the self-similarity of solutions in the x-x-bar plane and the x-ρ plane. We carried out the numerical calculations with the use of the microsoft EXCEL. The self-similarity and the hierarchy structure of the universe have been also discussed on the basis of E-infinity theory

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

The application of nonlinear dynamics in the study of ferroelectric materials

International Nuclear Information System (INIS)

Blochwitz, S.; Habel, R.; Diestelhorst, M.; Beige, H.

1996-01-01

It is well known that the structural phase transitions in ferroelectric materials are connected with strong nonlinear properties. So we can expect all features of nonlinear dynamical systems such as period-doubling cascades and chaos in a dynamical system that contains ferroelectric materials. Therefore we can apply nonlinear dynamics to these ferroelectric materials and we are doing it in two directions: (i) We study the structural phase transitions by analyzing the large signal behaviour with means of nonlinear dynamics. (ii) We control the chaotic behaviour of the system with the method proposed by Ott, Grebogi and Yorke. (authors)

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.

Linear and nonlinear verification of gyrokinetic microstability codes

Science.gov (United States)

Bravenec, R. V.; Candy, J.; Barnes, M.; Holland, C.

2011-12-01

Verification of nonlinear microstability codes is a necessary step before comparisons or predictions of turbulent transport in toroidal devices can be justified. By verification we mean demonstrating that a code correctly solves the mathematical model upon which it is based. Some degree of verification can be accomplished indirectly from analytical instability threshold conditions, nonlinear saturation estimates, etc., for relatively simple plasmas. However, verification for experimentally relevant plasma conditions and physics is beyond the realm of analytical treatment and must rely on code-to-code comparisons, i.e., benchmarking. The premise is that the codes are verified for a given problem or set of parameters if they all agree within a specified tolerance. True verification requires comparisons for a number of plasma conditions, e.g., different devices, discharges, times, and radii. Running the codes and keeping track of linear and nonlinear inputs and results for all conditions could be prohibitive unless there was some degree of automation. We have written software to do just this and have formulated a metric for assessing agreement of nonlinear simulations. We present comparisons, both linear and nonlinear, between the gyrokinetic codes GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and GS2 [W. Dorland, F. Jenko, M. Kotschenreuther, and B. N. Rogers, Phys. Rev. Lett. 85, 5579 (2000)]. We do so at the mid-radius for the same discharge as in earlier work [C. Holland, A. E. White, G. R. McKee, M. W. Shafer, J. Candy, R. E. Waltz, L. Schmitz, and G. R. Tynan, Phys. Plasmas 16, 052301 (2009)]. The comparisons include electromagnetic fluctuations, passing and trapped electrons, plasma shaping, one kinetic impurity, and finite Debye-length effects. Results neglecting and including electron collisions (Lorentz model) are presented. We find that the linear frequencies with or without collisions agree well between codes, as do the time averages of

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)

Design and Numerical Simulation of Unidirectional Chaotic Synchronization and its Application in Secure Communication System

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A. Sambas

2013-09-01

Full Text Available Chaotic systems are characterized by sensitive dependence on initial conditions, similar to random behavior, and continuous broad-band power spectrum. Chaos is a good potential to be used in secure communications system. In this paper, in order to show some interesting phenomena of three-order Jerk circuit with modulus nonlinearity, the chaotic behavior as a function of a variable control parameter, has been studied. The initial study in this paper is to analyze the phase portraits, the Poincaré maps, the bifurcation diagrams, while the analysis of the synchronization in the case of unidirectional coupling between two identical generated chaotic systems, has been presented. Moreover, some appropriate comparisons are made to contrast some of the existing results. Finally, the effectiveness of the unidirectional coupling scheme between two identical Jerk circuits in a secure communication system is presented in details. Integration of theoretical physics, the numerical simulation by using MATLAB 2010, as well as the implementation of circuit simulations by using MultiSIM 10.0 has been performed in this study

Transition from Exponential to Power Law Income Distributions in a Chaotic Market

Science.gov (United States)

Pellicer-Lostao, Carmen; Lopez-Ruiz, Ricardo

Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the interaction of many agents at micro-level. One of these models is the gas-like model for trading markets. This tries to predict money distributions in closed economies and quite simply, obtains the ones observed in real economies. However, it reveals technical hitches to explain the power law distribution, observed in individuals with high incomes. In this work, nonlinear dynamics is introduced in the gas-like model in an effort to overcomes these flaws. A particular chaotic dynamics is used to break the pairing symmetry of agents (i, j) ⇔ (j, i). The results demonstrate that a "chaotic gas-like model" can reproduce the Exponential and Power law distributions observed in real economies. Moreover, it controls the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear and doom the market to extreme inequality.

Nonlinear analysis of the occurrence of hurricanes in the Gulf of Mexico and the Caribbean Sea

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B. Rojo-Garibaldi

2018-04-01

Full Text Available Hurricanes are complex systems that carry large amounts of energy. Their impact often produces natural disasters involving the loss of human lives and materials, such as infrastructure, valued at billions of US dollars. However, not everything about hurricanes is negative, as hurricanes are the main source of rainwater for the regions where they develop. This study shows a nonlinear analysis of the time series of the occurrence of hurricanes in the Gulf of Mexico and the Caribbean Sea obtained from 1749 to 2012. The construction of the hurricane time series was carried out based on the hurricane database of the North Atlantic basin hurricane database (HURDAT and the published historical information. The hurricane time series provides a unique historical record on information about ocean–atmosphere interactions. The Lyapunov exponent indicated that the system presented chaotic dynamics, and the spectral analysis and nonlinear analyses of the time series of the hurricanes showed chaotic edge behavior. One possible explanation for this chaotic edge is the individual chaotic behavior of hurricanes, either by category or individually regardless of their category and their behavior on a regular basis.

Nonlinear analysis of the occurrence of hurricanes in the Gulf of Mexico and the Caribbean Sea

Science.gov (United States)

Rojo-Garibaldi, Berenice; Salas-de-León, David Alberto; Adela Monreal-Gómez, María; Sánchez-Santillán, Norma Leticia; Salas-Monreal, David

2018-04-01

Hurricanes are complex systems that carry large amounts of energy. Their impact often produces natural disasters involving the loss of human lives and materials, such as infrastructure, valued at billions of US dollars. However, not everything about hurricanes is negative, as hurricanes are the main source of rainwater for the regions where they develop. This study shows a nonlinear analysis of the time series of the occurrence of hurricanes in the Gulf of Mexico and the Caribbean Sea obtained from 1749 to 2012. The construction of the hurricane time series was carried out based on the hurricane database of the North Atlantic basin hurricane database (HURDAT) and the published historical information. The hurricane time series provides a unique historical record on information about ocean-atmosphere interactions. The Lyapunov exponent indicated that the system presented chaotic dynamics, and the spectral analysis and nonlinear analyses of the time series of the hurricanes showed chaotic edge behavior. One possible explanation for this chaotic edge is the individual chaotic behavior of hurricanes, either by category or individually regardless of their category and their behavior on a regular basis.

Nonlinear dynamics of regenerative cutting processes-Comparison of two models

International Nuclear Information System (INIS)

Wang, X.S.; Hu, J.; Gao, J.B.

2006-01-01

Understanding the nonlinear dynamics of cutting processes is essential for the improvement of machining technology. We study machine cutting processes by two different models, one has been recently introduced by Litak [Litak G. Chaotic vibrations in a regenerative cutting process. Chaos, Solitons and Fractals 2002;13:1531-5] and the other is the classic delay differential equation model. Although chaotic solutions have been found in both models, well known routes to chaos, such as period-doubling or quasi-periodic motion to chaos are not observed in either model. Careful analysis shows that the chaotic motion from the Litak's model has sharper spectral peaks, a smaller correlation dimension and a smaller value for the largest positive Lyapunov exponent. Implications to the control of chaos in cutting processes are discussed

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...

Higher-Order Spectrum in Understanding Nonlinearity in EEG Rhythms

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Cauchy Pradhan

2012-01-01

Full Text Available The fundamental nature of the brain's electrical activities recorded as electroencephalogram (EEG remains unknown. Linear stochastic models and spectral estimates are the most common methods for the analysis of EEG because of their robustness, simplicity of interpretation, and apparent association with rhythmic behavioral patterns in nature. In this paper, we extend the use of higher-order spectrum in order to indicate the hidden characteristics of EEG signals that simply do not arise from random processes. The higher-order spectrum is an extension Fourier spectrum that uses higher moments for spectral estimates. This essentially nullifies all Gaussian random effects, therefore, can reveal non-Gaussian and nonlinear characteristics in the complex patterns of EEG time series. The paper demonstrates the distinguishing features of bispectral analysis for chaotic systems, filtered noises, and normal background EEG activity. The bispectrum analysis detects nonlinear interactions; however, it does not quantify the coupling strength. The squared bicoherence in the nonredundant region has been estimated to demonstrate nonlinear coupling. The bicoherence values are minimal for white Gaussian noises (WGNs and filtered noises. Higher bicoherence values in chaotic time series and normal background EEG activities are indicative of nonlinear coupling in these systems. The paper shows utility of bispectral methods as an analytical tool in understanding neural process underlying human EEG patterns.

Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic Chaos

Science.gov (United States)

Deissler, Robert G.

1996-01-01

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.

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

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...

SU-E-J-261: Statistical Analysis and Chaotic Dynamics of Respiratory Signal of Patients in BodyFix

Energy Technology Data Exchange (ETDEWEB)

Michalski, D; Huq, M; Bednarz, G; Lalonde, R; Yang, Y; Heron, D [University of Pittsburgh Medical Center, Pittsburgh, PA (United States)

2014-06-01

Purpose: To quantify respiratory signal of patients in BodyFix undergoing 4DCT scan with and without immobilization cover. Methods: 20 pairs of respiratory tracks recorded with RPM system during 4DCT scan were analyzed. Descriptive statistic was applied to selected parameters of exhale-inhale decomposition. Standardized signals were used with the delay method to build orbits in embedded space. Nonlinear behavior was tested with surrogate data. Sample entropy SE, Lempel-Ziv complexity LZC and the largest Lyapunov exponents LLE were compared. Results: Statistical tests show difference between scans for inspiration time and its variability, which is bigger for scans without cover. The same is for variability of the end of exhalation and inhalation. Other parameters fail to show the difference. For both scans respiratory signals show determinism and nonlinear stationarity. Statistical test on surrogate data reveals their nonlinearity. LLEs show signals chaotic nature and its correlation with breathing period and its embedding delay time. SE, LZC and LLE measure respiratory signal complexity. Nonlinear characteristics do not differ between scans. Conclusion: Contrary to expectation cover applied to patients in BodyFix appears to have limited effect on signal parameters. Analysis based on trajectories of delay vectors shows respiratory system nonlinear character and its sensitive dependence on initial conditions. Reproducibility of respiratory signal can be evaluated with measures of signal complexity and its predictability window. Longer respiratory period is conducive for signal reproducibility as shown by these gauges. Statistical independence of the exhale and inhale times is also supported by the magnitude of LLE. The nonlinear parameters seem more appropriate to gauge respiratory signal complexity since its deterministic chaotic nature. It contrasts with measures based on harmonic analysis that are blind for nonlinear features. Dynamics of breathing, so crucial for

SU-E-J-261: Statistical Analysis and Chaotic Dynamics of Respiratory Signal of Patients in BodyFix

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