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
Synchronization of two different chaotic systems via nonlinear ...
African Journals Online (AJOL)
ADOWIE PERE
ABSTRACT: This work reports the synchronization of a pair of four chaotic systems via nonlinear control technique. This method has been found to be easy to implement and effective especially on two different chaotic systems. We paired four chaotic systems out of which one is new and we have six possible pairs.
Nonlinear observer based phase synchronization of chaotic systems
International Nuclear Information System (INIS)
Meng Juan; Wang Xingyuan
2007-01-01
This Letter analyzes the phase synchronization problem of autonomous chaotic systems. Based on the nonlinear state observer algorithm and the pole placement technique, a phase synchronization scheme is designed. The phase synchronization of a new chaotic system is achieved by using this observer controller. Numerical simulations further demonstrate the effectiveness of the proposed phase synchronization scheme
Chaos synchronization of a new chaotic system via nonlinear control
International Nuclear Information System (INIS)
Zhang Qunjiao; Lu Junan
2008-01-01
This paper investigates chaos synchronization of a new chaotic system [Lue J, Chen G, Cheng D. A new chaotic system and beyond: the generalized Lorenz-like system. Int J Bifurcat Chaos 2004;14:1507-37]. Two kinds of novel nonlinear controllers are designed based on the Lyapunov stability theory. It can be viewed as an improvement to the existing results of reference [Park JH. Chaos synchronization of a chaotic system via nonlinear control. Chaos, Solitons and Fractals 2005;25:579-84] because we use less controllers but realize a global and exponential asymptotical synchronization. Numerical simulations are provided to show the effectiveness and advantage of this method
Nonlinear PI control of chaotic systems using singular perturbation theory
International Nuclear Information System (INIS)
Wang Jiang; Wang Jing; Li Huiyan
2005-01-01
In this paper, we develop the nonlinear PI controllers for a class of chaotic systems based on singular perturbation theory. The original system is decomposed into two reduced order systems, to which the nonlinear uncertain terms belongs. In order to alleviate the deterioration of these nonlinear uncertainties, the nonlinear PI controllers are applied to each subsystem and combined to construct the composite controller for the full order system. The effectiveness and feasibility of the proposed control scheme is demonstrated through numerical simulations on the chaotic Chua's circuit
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)
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
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
Nonlinear Dynamics, Chaotic and Complex Systems
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
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
On nonlinear control design for autonomous chaotic systems of integer and fractional orders
International Nuclear Information System (INIS)
Ahmad, Wajdi M.; Harb, Ahmad M.
2003-01-01
In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive 'backstepping' method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an electronic chaotic oscillator model, and a mechanical chaotic 'jerk' model. We demonstrate the robustness of the derived controllers against system order reduction arising from the use of fractional integrators in the system models. Our results are validated via numerical simulations
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
Nonlinear Time-Reversal in a Wave Chaotic System
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)
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
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)
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.
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....
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.
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.
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.
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.
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
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.
Nonlinear dynamics non-integrable systems and chaotic dynamics
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.
Chaotic behaviour of nonlinear coupled reaction–diffusion system in ...
Indian Academy of Sciences (India)
chaos in four-dimensional space by the generalized definitions of spatial ... according to nonlinear noise in the real physical world, f(φ(x),ψ(x)) and g(φ(x) ... tion in ecological system, where φm,n(s) is the host density in generations s and s + 1,.
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.
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.
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
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.
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
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.
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
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.
Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity
Jeevarekha, A.; Paul Asir, M.; Philominathan, P.
2016-06-01
This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.
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.
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.
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.
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
Using Chaotic System in Encryption
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.
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.
Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system
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.
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
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.
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
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.
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.
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...
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.
Lectures on chaotic dynamical systems
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.
Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Gundara, G.; Mada Sanjaya, W. S.; Subiyanto
2018-03-01
A 3-D new chaotic attractor with two quadratic nonlinearities is proposed in this paper. The dynamical properties of the new chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new chaotic system has three unstable equilibrium points. The new chaotic attractor is dissipative in nature. As an engineering application, adaptive synchronization of identical new chaotic attractors is designed via nonlinear control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic attractor model.
International Nuclear Information System (INIS)
Emans, Joseph; Wiercigroch, Marian; Krivtsov, Anton M.
2005-01-01
The nonlinear analysis of a common beam system was performed, and the method for such, outlined and presented. Nonlinear terms for the governing dynamic equations were extracted and the behaviour of the system was investigated. The analysis was carried out with and without physically realistic parameters, to show the characteristics of the system, and the physically realistic responses. Also, the response as part of a more complex system was considered, in order to investigate the cumulative effects of nonlinearities. Chaos, as well as periodic motion was found readily for the physically unrealistic parameters. In addition, nonlinear behaviour such as co-existence of attractors was found even at modest oscillation levels during investigations with realistic parameters. When considered as part of a more complex system with further nonlinearities, comparisons with linear beam theory show the classical approach to be lacking in accuracy of qualitative predictions, even at weak oscillations
Experimental Observation of Chaotic Beats in Oscillators Sharing Nonlinearity
Paul Asir, M.; Jeevarekha, A.; Philominathan, P.
This paper deals with the generation of chaotic beats in a system of two forced dissipative LCR oscillators sharing a nonlinear element. The presence of two external periodic excitations and a common nonlinear element in the chosen system enables the facile generation of chaotic beats. Thus rendered chaotic beats were characterized in both time domain and phase space. Lyapunov exponents and envelope of the beats were computed to diagnose the chaotic nature of the signals. The role of common nonlinearity on the complexity of the generated beats is discussed. Real-time experimental hardware implementation has also been done to confirm the subsistence of the phenomenon, for the first time. Extensive Multisim simulations were carried out to understand, a bit more about the shrinkage and revivals of state variables in phase space.
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.
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
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
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...
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.
Nonlinear chaotic model for predicting storm surges
Directory of Open Access Journals (Sweden)
M. Siek
2010-09-01
Full Text Available This paper addresses the use of the methods of nonlinear dynamics and chaos theory for building a predictive chaotic model from time series. The chaotic model predictions are made by the adaptive local models based on the dynamical neighbors found in the reconstructed phase space of the observables. We implemented the univariate and multivariate chaotic models with direct and multi-steps prediction techniques and optimized these models using an exhaustive search method. The built models were tested for predicting storm surge dynamics for different stormy conditions in the North Sea, and are compared to neural network models. The results show that the chaotic models can generally provide reliable and accurate short-term storm surge predictions.
International Nuclear Information System (INIS)
Ge Zhengming; Chang Chingming
2009-01-01
By applying pure error dynamics and elaborate nondiagonal Lyapunov function, the nonlinear generalized synchronization is studied in this paper. Instead of current mixed error dynamics in which master state variables and slave state variables are presented, the nonlinear generalized synchronization can be obtained by pure error dynamics without auxiliary numerical simulation. The elaborate nondiagonal Lyapunov function is applied rather than current monotonous square sum Lyapunov function deeply weakening the powerfulness of Lyapunov direct method. Both autonomous and nonautonomous double Mathieu systems are used as examples with numerical simulations.
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
Cascade Chaotic System With Applications.
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.
A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps
International Nuclear Information System (INIS)
Behnia, S.; Akhshani, A.; Ahadpour, S.; Mahmodi, H.; Akhavan, A.
2007-01-01
In recent years, a growing number of discrete chaotic cryptographic algorithms have been proposed. However, most of them encounter some problems such as the lack of robustness and security. In this Letter, we introduce a new image encryption algorithm based on one-dimensional piecewise nonlinear chaotic maps. The system is a measurable dynamical system with an interesting property of being either ergodic or having stable period-one fixed point. They bifurcate from a stable single periodic state to chaotic one and vice versa without having usual period-doubling or period-n-tippling scenario. Also, we present the KS-entropy of this maps with respect to control parameter. This algorithm tries to improve the problem of failure of encryption such as small key space, encryption speed and level of security
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
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.
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.
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)
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
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.
Min, Lequan; Chen, Guanrong
This paper establishes some generalized synchronization (GS) theorems for a coupled discrete array of difference systems (CDADS) and a coupled continuous array of differential systems (CCADS). These constructive theorems provide general representations of GS in CDADS and CCADS. Based on these theorems, one can design GS-driven CDADS and CCADS via appropriate (invertible) transformations. As applications, the results are applied to autonomous and nonautonomous coupled Chen cellular neural network (CNN) CDADS and CCADS, discrete bidirectional Lorenz CNN CDADS, nonautonomous bidirectional Chua CNN CCADS, and nonautonomously bidirectional Chen CNN CDADS and CCADS, respectively. Extensive numerical simulations show their complex dynamic behaviors. These theorems provide new means for understanding the GS phenomena of complex discrete and continuously differentiable networks.
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
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.
Hash function based on piecewise nonlinear chaotic map
International Nuclear Information System (INIS)
Akhavan, A.; Samsudin, A.; Akhshani, A.
2009-01-01
Chaos-based cryptography appeared recently in the early 1990s as an original application of nonlinear dynamics in the chaotic regime. In this paper, an algorithm for one-way hash function construction based on piecewise nonlinear chaotic map with a variant probability parameter is proposed. Also the proposed algorithm is an attempt to present a new chaotic hash function based on multithreaded programming. In this chaotic scheme, the message is connected to the chaotic map using probability parameter and other parameters of chaotic map such as control parameter and initial condition, so that the generated hash value is highly sensitive to the message. Simulation results indicate that the proposed algorithm presented several interesting features, such as high flexibility, good statistical properties, high key sensitivity and message sensitivity. These properties make the scheme a suitable choice for practical applications.
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 Motion of Nonlinearly Coupled Quintic Oscillators | Adeloye ...
African Journals Online (AJOL)
With a fixed energy, we investigate the motion of two nonlinearly coupled quintic oscillators for various values of the coupling strength with the aid of the Poincare surface of section. It is observed that chaotic motion sets in for coupling strength as low as 0.001. The degree of chaoticity generally increases as the coupling ...
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 ...
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.
Nonlinear Time Series Prediction Using Chaotic Neural Networks
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 dynamics and chaotic phenomena an introduction
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...
Eigenfunctions in chaotic quantum systems
Energy Technology Data Exchange (ETDEWEB)
Baecker, Arnd
2007-07-01
The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)
Eigenfunctions in chaotic quantum systems
International Nuclear Information System (INIS)
Baecker, Arnd
2007-01-01
The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)
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.
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.
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
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)
Correlation control theory of chaotic laser systems
International Nuclear Information System (INIS)
Li Fuli.
1986-04-01
A novel control theory of chaotic systems is studied. The correlation functions are calculated and used as feedback signals of the chaotic lasers. Computer experiments have shown that in this way the chaotic systems can be controlled to have time-independent output when the external control parameters are in chaotic domain. (author)
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
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
Chaotic and steady state behaviour of a nonlinear controlled gyro subjected to harmonic disturbances
International Nuclear Information System (INIS)
Perez Polo, Manuel F.; Perez Molina, Manuel
2007-01-01
Chaotic and steady state motions of a nonlinear controlled gimbals suspension gyro used to stabilize an external body are studied in this paper. The equations of the gyro without nonlinear control are deduced from the Euler-Lagrange equations by using the nutation theory. The equations of the system show that a cyclic variable appears. Its elimination allows us to find an auxiliary nonlinear system from which it is possible to deduce a nonlinear control law in order to obtain a desired equilibrium point. From the analysis of the nonlinear control law it is possible to show that due to both harmonic disturbances in the platform of the gyro and in the body to stabilize, regular and chaotic motions can appear. The chaotic motion is researched by means of chaos maps, bifurcation diagrams, sensitivity to initial conditions, Lyapunov exponents and Fourier spectrum density. The transition from chaotic to steady state motion by eliminating the harmonic disturbances from the modification of the initial nonlinear control law is also researched. Next, the paper shows how to use the chaotic motion in order to obtain small input signals so that the desired equilibrium state of the gyro can be reached. The developed methodology and its compared performance are evaluated through analytical methods and numerical simulations
Chaotic and steady state behaviour of a nonlinear controlled gyro subjected to harmonic disturbances
Energy Technology Data Exchange (ETDEWEB)
Perez Polo, Manuel F. [Department of Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)]. E-mail: manolo@dfists.ua.es; Perez Molina, Manuel [Facultad de Ciencias Matematicas, Universidad Nacional de Educacion a Distancia, UNED, C/Boyero 12-1A, Alicante 03007 (Spain)]. E-mail: ma_perez_m@hotmail.com
2007-07-15
Chaotic and steady state motions of a nonlinear controlled gimbals suspension gyro used to stabilize an external body are studied in this paper. The equations of the gyro without nonlinear control are deduced from the Euler-Lagrange equations by using the nutation theory. The equations of the system show that a cyclic variable appears. Its elimination allows us to find an auxiliary nonlinear system from which it is possible to deduce a nonlinear control law in order to obtain a desired equilibrium point. From the analysis of the nonlinear control law it is possible to show that due to both harmonic disturbances in the platform of the gyro and in the body to stabilize, regular and chaotic motions can appear. The chaotic motion is researched by means of chaos maps, bifurcation diagrams, sensitivity to initial conditions, Lyapunov exponents and Fourier spectrum density. The transition from chaotic to steady state motion by eliminating the harmonic disturbances from the modification of the initial nonlinear control law is also researched. Next, the paper shows how to use the chaotic motion in order to obtain small input signals so that the desired equilibrium state of the gyro can be reached. The developed methodology and its compared performance are evaluated through analytical methods and numerical simulations.
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.
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
Nonlinear mode conversion with chaotic soliton generation at plasma resonance
International Nuclear Information System (INIS)
Pietsch, H.; Laedke, E.W.; Spatschek, K.H.
1993-01-01
The resonant absorption of electromagnetic waves near the critical density in inhomogeneous plasmas is studied. A driven nonlinear Schroedinger equation for the mode-converted oscillations is derived by multiple-scaling techniques. The model is simulated numerically. The generic transition from a stationary to a time-dependent solution is investigated. Depending on the parameters, a time-chaotic behavior is found. By a nonlinear analysis, based on the inverse scattering transform, solitons of a corresponding integrable equation are identified as the dominant coherent structures of the chaotic dynamics. Finally, a map is presented which predicts chaotic soliton generation and emission at the critical density. Its qualitative behavior, concerning the bifurcation points, is in excellent agreement with the numerical simulations
On synchronization of three chaotic systems
International Nuclear Information System (INIS)
Yan Jianping; Li Changpin
2005-01-01
In this paper, a simple but efficient method is applied to the synchronization of three chaotic systems, i.e., the chaotic Lorenz, Chua, and Chen systems. Numerical simulations show this method works very well
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...
Advances and applications in chaotic systems
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.
Targeting engineering synchronization in chaotic systems
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.
Controller Synthesis for Periodically Forced Chaotic Systems
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.
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.
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)
Dynamics and Control of a Chaotic Electromagnetic System
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...
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
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
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.
A nonlinear optimal control approach for chaotic finance dynamics
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.
Dynamic Parameter-Control Chaotic System.
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.
Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator
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.
Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator
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.
Robust synchronization of chaotic systems via feedback
Energy Technology Data Exchange (ETDEWEB)
Femat, Ricardo [IPICYT, San Luis Potosi (Mexico). Dept. de Matematicas Aplicadas; Solis-Perales, Gualberto [Universidad de Guadalajara, Centro Univ. de Ciencias Exactas e Ingenierias (Mexico). Div. de Electronica y Computacion
2008-07-01
This volume includes the results derived during last ten years about both suppression and synchronization of chaotic -continuous time- systems. Along this time, the concept was to study how the intrinsic properties of dynamical systems can be exploited to suppress and to synchronize the chaotic behaviour and what synchronization phenomena can be found under feedback interconnection. A compilation of these findings is described in this book. This book shows a perspective on synchronization of chaotic systems. (orig.)
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.
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.
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.
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
Jiang, Xingxing; Cheng, Mengfan; Luo, Fengguang; Deng, Lei; Fu, Songnian; Ke, Changjian; Zhang, Minming; Tang, Ming; Shum, Ping; Liu, Deming
2016-12-12
A novel electro-optic chaos source is proposed on the basis of the reverse-time chaos theory and an analog-digital hybrid feedback loop. The analog output of the system can be determined by the numeric states of shift registers, which makes the system robust and easy to control. The dynamical properties as well as the complexity dependence on the feedback parameters are investigated in detail. The correlation characteristics of the system are also studied. Two improving strategies which were established in digital field and analog field are proposed to conceal the time-delay signature. The proposed scheme has the potential to be used in radar and optical secure communication systems.
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
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
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.
Localization of Stable and Chaotic Nonpropagating Structures in Nonlinear Mesoscopic Lattices.
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.
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
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
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
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
Synchronizing a class of uncertain chaotic systems
International Nuclear Information System (INIS)
Chen Maoyin; Zhou Donghua; Shang Yun
2005-01-01
This Letter deals with the synchronization of a class of uncertain chaotic systems in the drive-response framework. A robust adaptive observer based response system is designed to synchronize a given chaotic system with unknown parameters and external disturbances. Lyapunov stability ensures the global synchronization between the drive and response systems even if Lipschitz constants on function matrices and bounds on uncertainties are unknown. Numerical simulation of Genesio-Tesi system verifies the effectiveness of this scheme
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
Multiswitching compound antisynchronization of four chaotic systems
Indian Academy of Sciences (India)
Ayub Khan
2017-11-28
Nov 28, 2017 ... systems, electrical engineering, information process- ... model. The synchronization problem among three or more chaotic ...... we perform numerical simulations in MATLAB using ... In the simulation process we assume α1 =.
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).
Improvement on generalised synchronisation of chaotic systems
International Nuclear Information System (INIS)
Hui-Bin, Zhu; Fang, Qiu; Bao-Tong, Cui
2010-01-01
In this paper, the problem of generalised synchronisation of two different chaotic systems is investigated. Some less conservative conditions are derived using linear matrix inequality other than existing results. Furthermore, a simple adaptive control scheme is proposed to achieve the generalised synchronisation of chaotic systems. The proposed method is simple and easy to implement in practice and can be applied to secure communications. Numerical simulations are also given to demonstrate the effectiveness and feasibility of the theoretical analysis
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.
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
Experimental chaotic quantification in bistable vortex induced vibration systems
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
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.
Encryption in Chaotic Systems with Sinusoidal Excitations
Directory of Open Access Journals (Sweden)
G. Obregón-Pulido
2014-01-01
Full Text Available In this contribution an encryption method using a chaotic oscillator, excited by “n” sinusoidal signals, is presented. The chaotic oscillator is excited by a sum of “n” sinusoidal signals and a message. The objective is to encrypt such a message using the chaotic behavior and transmit it, and, as the chaotic system is perturbed by the sinusoidal signal, the transmission security could be increased due to the effect of such a perturbation. The procedure is based on the regulation theory and consider that the receiver knows the frequencies of the perturbing signal, with this considerations the algorithm estimates the excitation in such a way that the receiver can cancel out the perturbation and all the undesirable dynamics in order to produce only the message. In this way we consider that the security level is increased.
Chaotic mechanics in systems with impacts and friction
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.
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.
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.
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
Qualitative feature extractions of chaotic systems
International Nuclear Information System (INIS)
Vicha, T.; Dohnal, M.
2008-01-01
The theory of chaos offers useful tools for systems analysis. However, models of complex systems are based on a network of inconsistent, space and uncertain knowledge items. Traditional quantitative methods of chaos analysis are therefore not applicable. The paper by the same authors [Vicha T, Dohnal M. Qualitative identification of chaotic systems behaviours. Chaos, Solitons and Fractals, in press, [Log. No. 601019] ] presents qualitative interpretation of some chaos concepts. There are only three qualitative values positive/increasing, negative/decreasing and zero/constant. It means that any set of qualitative multidimensional descriptions of unsteady state behaviours is discrete and finite. A finite upper limit exists for the total number of qualitatively distinguishable scenarios. A set of 21 published chaotic models is solved qualitatively and 21 sets of all existing qualitative scenarios are presented. The intersection of all 21 scenario sets is empty. There is no such a behaviour which is common for all 21 models. The set of 21 qualitative models (e.g. Lorenz, Roessler) can be used to compare chaotic behaviours of an unknown qualitative model with them to evaluate if its chaotic behaviours is close to e.g. Lorenz chaotic model and how much
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)
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)
Study of chaos in chaotic satellite systems
Indian Academy of Sciences (India)
Lyapunov exponents are estimated. From these studies, chaosin satellite system has been established. Solution of equations of motion of the satellite system are drawn in the form of three-dimensional, two-dimensional and time series phase portraits. Phase portraits and time series display the chaotic nature of the ...
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.
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.
Generalized projective synchronization of a unified chaotic system
International Nuclear Information System (INIS)
Yan Jianping; Li Changpin
2005-01-01
In the present paper, a simple but efficient control technique of the generalized projective synchronization is applied to a unified chaotic system. Numerical simulations show that this method works very well, which can also be applied to other chaotic systems
Entanglement production in quantized chaotic systems
Indian Academy of Sciences (India)
Abstract. Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical ...
Entanglement production in quantized chaotic systems
Indian Academy of Sciences (India)
Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical studies.
Cryptanalysis of a chaotic secure communication system
International Nuclear Information System (INIS)
Alvarez, G.; Montoya, F.; Romera, M.; Pastor, G.
2003-01-01
Recently a chaotic encryption system has been proposed by P. Garcia et al. It represents an improvement over an algorithm previously presented by some of the same authors. In this Letter, several weaknesses of the new cryptosystem are pointed out and four successful cryptanalytic attacks are described
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
Nonlinear dynamics of drops and bubbles and chaotic phenomena
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
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.
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.
Generalized projective synchronization of chaotic nonlinear gyros coupled with dead-zone input
International Nuclear Information System (INIS)
Hung, M.-L.; Yan, J.-J.; Liao, T.-L.
2008-01-01
This paper addresses the synchronization problem of drive-response chaotic gyros coupled with dead-zone nonlinear input. Using the sliding mode control technique, a novel control law is established which guarantees generalized projective synchronization even when the dead-zone nonlinearity is present. Numerical simulations are presented to verify that the synchronization can be achieved by using the proposed synchronization scheme
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.
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
Exact solutions to chaotic and stochastic systems
González, J. A.; Reyes, L. I.; Guerrero, L. E.
2001-03-01
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.
Chaos control of Chen chaotic dynamical system
International Nuclear Information System (INIS)
Yassen, M.T.
2003-01-01
This paper is devoted to study the problem of controlling chaos in Chen chaotic dynamical system. Two different methods of control, feedback and nonfeedback methods are used to suppress chaos to unstable equilibria or unstable periodic orbits (UPO). The Lyapunov direct method and Routh-Hurwitz criteria are used to study the conditions of the asymptotic stability of the steady states of the controlled system. Numerical simulations are presented to show these results
New robust chaotic system with exponential quadratic term
International Nuclear Information System (INIS)
Bao Bocheng; Li Chunbiao; Liu Zhong; Xu Jianping
2008-01-01
This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller. (general)
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)
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.
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.
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.
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.
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.
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.
Fractional order control and synchronization of chaotic systems
Vaidyanathan, Sundarapandian; Ouannas, Adel
2017-01-01
The book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining the concepts involved in a clear, matter-of-fact style. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories, methods and applications in a number of research areas related to fractional order control and synchronization of chaotic systems, such as: fractional chaotic systems, hyperchaotic systems, complex systems, fractional order discrete chaotic systems, chaos control, chaos synchronization, jerk circuits, fractional chaotic systems with hidden attractors, neural network, fuzzy logic controllers, behavioral modeling, robust and adaptive control, sliding mode control, different types of synchronization, circuit realization of chaotic systems, etc. In addition to providing readers extensive information on chaos fundamentals, fractional calculus, fractional differential equations, fractional contro...
Mechanical analysis of Chen chaotic system
International Nuclear Information System (INIS)
Liang, Xiyin; Qi, Guoyuan
2017-01-01
The Chen chaotic system is transformed into Kolmogorov type system, which is decomposed into four types of torques: inertial torque, internal torque, dissipation and external torque. By the combinations of different torques, five cases are studied to discover key factors of chaos generation and the physical meaning. The conversion among Hamiltonian energy, kinetic energy and potential energy is investigated in these five cases. The relationship between the energies and the parameters is studied. It concludes that the combination of these four types of torques is necessary conditions to produce chaos, and any combination of three types of torques cannot produce chaos in Chen system.
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.
A combination chaotic system and application in color image encryption
Parvaz, R.; Zarebnia, M.
2018-05-01
In this paper, by using Logistic, Sine and Tent systems we define a combination chaotic system. Some properties of the chaotic system are studied by using figures and numerical results. A color image encryption algorithm is introduced based on new chaotic system. Also this encryption algorithm can be used for gray scale or binary images. The experimental results of the encryption algorithm show that the encryption algorithm is secure and practical.
National Research Council Canada - National Science Library
Drazin, P. G
1992-01-01
This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...
Normal form and synchronization of strict-feedback chaotic systems
International Nuclear Information System (INIS)
Wang, Feng; Chen, Shihua; Yu Minghai; Wang Changping
2004-01-01
This study concerns the normal form and synchronization of strict-feedback chaotic systems. We prove that, any strict-feedback chaotic system can be rendered into a normal form with a invertible transform and then a design procedure to synchronize the normal form of a non-autonomous strict-feedback chaotic system is presented. This approach needs only a scalar driving signal to realize synchronization no matter how many dimensions the chaotic system contains. Furthermore, the Roessler chaotic system is taken as a concrete example to illustrate the procedure of designing without transforming a strict-feedback chaotic system into its normal form. Numerical simulations are also provided to show the effectiveness and feasibility of the developed methods
Chaos synchronization of a unified chaotic system via partial linearization
International Nuclear Information System (INIS)
Yu Yongguang; Li Hanxiong; Duan Jian
2009-01-01
A partial linearization method is proposed for realizing the chaos synchronization of an unified chaotic system. Through synchronizing partial state of the chaotic systems can result in the synchronization of their entire states, and the resulting controller is singularity free. The results can be easily extended to the synchronization of other similar chaotic systems. Simulation results are conducted to show the effectiveness of the method.
Collection of master-slave synchronized chaotic systems
International Nuclear Information System (INIS)
Lerescu, A.I.; Constandache, N.; Oancea, S.; Grosu, I.
2004-01-01
In this work the open-plus-closed-loop (OPCL) method of synchronization is used in order to synchronize the systems from the Sprott's collection of the simplest chaotic systems. The method is general and we looked for the simplest coupling between master and slave. The main result is that for the systems that contains one nonlinear term and that term contains one variable then the coupling consists of one term. The numerical intervals of parameters where the synchronization is achieved are obtained analytically by applying Routh-Hurwitz conditions. Detailed calculations and numerical results are given for the system I from the Sprott's collection. Working in the same manner for many systems this method can be adopted for the teaching of the topic
Nonlinear and Complex Dynamics in Real Systems
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...
Noise-Induced Riddling in Chaotic Systems
International Nuclear Information System (INIS)
Lai, Y.; Grebogi, C.
1996-01-01
Recent works have considered the situation of riddling where, when a chaotic attractor lying in an invariant subspace is transversely stable, the basin of the attractor can be riddled with holes that belong to the basin of another attractor. We show that riddling can be induced by arbitrarily small random noise even if the attractor is transversely unstable, and we obtain universal scaling laws for noise-induced riddling. Our results imply that the phenomenon of riddling can be more prevalent than expected before, as noise is practically inevitable in dynamical systems. copyright 1996 The American Physical Society
Unitarity and irreversibility in chaotic systems
International Nuclear Information System (INIS)
Hasegawa, H.H.; Saphir, W.C.
1992-01-01
We analyze the spectral properties of the Perron-Frobenius operator U, associated with some simple highly chaotic maps. We obtain a spectral decomposition of U in terms of generalized eigenfunctions of U and its adjoint. The corresponding eigenvalues are related to the decay rates of correlation functions and have magnitude less than one, so that physically measurable quantities manifestly approach equilibrium. To obtain decaying eigenstates of unitary and isometric operators it is necessary to extend the Hilbert-space formulation of dynamical systems. We describe and illustrate a method to obtain the decomposition explicitly
On the quantization of classically chaotic system
International Nuclear Information System (INIS)
Godoy, N.F. de.
1988-01-01
Some propeties of a quantization in terms of observables of a classically chaotic system, which exhibits a strange are studied. It is shown in particular that convenient expected values of some observables have the correct classical limit and that in these cases the limits ℎ → O and t → ∞ (t=time) rigorously comute. This model was alternatively quantized by R.Graham in terms of Wigner function. The Graham's analysis is completed a few points, in particular, we find out a remarkable analogy with general results about the semi-classical limit of Wigner function. Finally the expected values obtained by both methods of quantization were compared. (author) [pt
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.
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
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.
Study of chaos in chaotic satellite systems
Khan, Ayub; Kumar, Sanjay
2018-01-01
In this paper, we study the qualitative behaviour of satellite systems using bifurcation diagrams, Poincaré section, Lyapunov exponents, dissipation, equilibrium points, Kaplan-Yorke dimension etc. Bifurcation diagrams with respect to the known parameters of satellite systems are analysed. Poincaré sections with different sowing axes of the satellite are drawn. Eigenvalues of Jacobian matrices for the satellite system at different equilibrium points are calculated to justify the unstable regions. Lyapunov exponents are estimated. From these studies, chaos in satellite system has been established. Solution of equations of motion of the satellite system are drawn in the form of three-dimensional, two-dimensional and time series phase portraits. Phase portraits and time series display the chaotic nature of the considered system.
Stages of chaotic synchronization.
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.
Adaptive Synchronization of Memristor-based Chaotic Neural Systems
Directory of Open Access Journals (Sweden)
Xiaofang Hu
2014-11-01
Full Text Available Chaotic neural networks consisting of a great number of chaotic neurons are able to reproduce the rich dynamics observed in biological nervous systems. In recent years, the memristor has attracted much interest in the efficient implementation of artificial synapses and neurons. This work addresses adaptive synchronization of a class of memristor-based neural chaotic systems using a novel adaptive backstepping approach. A systematic design procedure is presented. Simulation results have demonstrated the effectiveness of the proposed adaptive synchronization method and its potential in practical application of memristive chaotic oscillators in secure communication.
Towards generalized synchronization of strictly different chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Femat, R. [Matematicas Aplicadas y Sistemas Computacionales, IPICYT, Apdo. Postal 3-90, 78291 Tangamanga, San Luis Potosi S.L.P. (Mexico)]. E-mail: rfemat@ipicyt.edu.mx; Kocarev, L. [Institute for Nonlinear Science, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0402 (United States)]. E-mail: lkocarev@ucsd.edu; Gerven, L. van [Department of Mechanical Engineering, Technische Universiteit Eindhoven (Netherlands); Monsivais-Perez, M.E. [Matematicas Aplicadas y Sistemas Computacionales, IPICYT, Camino a la Presa San Jose 2055, 78216 Lomas 4a Sec., San Luis Potosi S.L.P. (Mexico)
2005-07-11
This contribution addresses the problem of the generalized synchronization (GS) in different chaotic systems, and departs from chaotic systems in a triangular from, which can be derived from Lie derivatives. A state-feedback (full knowledge of both master and slave systems) scheme is designed, which achieves GS. The work includes illustrative examples; moreover an experimental setup is used to corroborate the obtained results.
Chaotic Phenomena in Technical Control Systems
DEFF Research Database (Denmark)
Mosekilde, Erik
1997-01-01
The paper discusses a number of examples of technical control systems that can exhibit deterministic chaos and other forms of complex nonlinear behavior. These examples include thermostatically regulated radiators, closely placed refrigirators, and industrial cooling compressors. The paper contin...
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)
Chaotic Behavior in a Switched Dynamical System
Directory of Open Access Journals (Sweden)
Fatima El Guezar
2008-01-01
Full Text Available We present a numerical study of an example of piecewise linear systems that constitute a class of hybrid systems. Precisely, we study the chaotic dynamics of the voltage-mode controlled buck converter circuit in an open loop. By considering the voltage input as a bifurcation parameter, we observe that the obtained simulations show that the buck converter is prone to have subharmonic behavior and chaos. We also present the corresponding bifurcation diagram. Our modeling techniques are based on the new French native modeler and simulator for hybrid systems called Scicos (Scilab connected object simulator which is a Scilab (scientific laboratory package. The followed approach takes into account the hybrid nature of the circuit.
Quantization rules for strongly chaotic systems
International Nuclear Information System (INIS)
Aurich, R.; Bolte, J.
1992-09-01
We discuss the quantization of strongly chaotic systems and apply several quantization rules to a model system given by the unconstrained motion of a particle on a compact surface of constant negative Gaussian curvature. We study the periodic-orbit theory for distinct symmetry classes corresponding to a parity operation which is always present when such a surface has genus two. Recently, several quantization rules based on periodic orbit theory have been introduced. We compare quantizations using the dynamical zeta function Z(s) with the quantization condition cos(π N(E)) = 0, where a periodix-orbit expression for the spectral staircase N(E) is used. A general discussion of the efficiency of periodic-orbit quantization then allows us to compare the different methods. The system dependence of the efficiency, which is determined by the topological entropy τ and the mean level density anti d(E), is emphasized. (orig.)
Designing synchronization schemes for chaotic fractional-order unified systems
International Nuclear Information System (INIS)
Wang Junwei; Zhang Yanbin
2006-01-01
Synchronization in chaotic fractional-order differential systems is studied both theoretically and numerically. Two schemes are designed to achieve chaos synchronization of so-called unified chaotic systems and the corresponding numerical algorithms are established. Some sufficient conditions on synchronization are also derived based on the Laplace transformation theory. Computer simulations are used for demonstration
Modification for collection of master-slave synchronized chaotic systems
International Nuclear Information System (INIS)
Guo Rongwei; Li Gang
2009-01-01
In this paper, based on the adaptive-feedback control method, we synchronize two identical chaotic systems. In comparison with the previous methods such as the open-plus-closed-loop (OPCL) method, the present control scheme is simple, and therefore it is easily implemented in practice. At last, a group of chaotic systems are used to demonstrate the effectiveness of this method.
Lag synchronization of chaotic systems with time-delayed linear
Indian Academy of Sciences (India)
In this paper, the lag synchronization of chaotic systems with time-delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differential equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic systems.
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
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.
Dynamics of Nonlinear Time-Delay Systems
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...
Parametric Identification of Nonlinear Dynamical Systems
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.
Regularized forecasting of chaotic dynamical systems
International Nuclear Information System (INIS)
Bollt, Erik M.
2017-01-01
While local models of dynamical systems have been highly successful in terms of using extensive data sets observing even a chaotic dynamical system to produce useful forecasts, there is a typical problem as follows. Specifically, with k-near neighbors, kNN method, local observations occur due to recurrences in a chaotic system, and this allows for local models to be built by regression to low dimensional polynomial approximations of the underlying system estimating a Taylor series. This has been a popular approach, particularly in context of scalar data observations which have been represented by time-delay embedding methods. However such local models can generally allow for spatial discontinuities of forecasts when considered globally, meaning jumps in predictions because the collected near neighbors vary from point to point. The source of these discontinuities is generally that the set of near neighbors varies discontinuously with respect to the position of the sample point, and so therefore does the model built from the near neighbors. It is possible to utilize local information inferred from near neighbors as usual but at the same time to impose a degree of regularity on a global scale. We present here a new global perspective extending the general local modeling concept. In so doing, then we proceed to show how this perspective allows us to impose prior presumed regularity into the model, by involving the Tikhonov regularity theory, since this classic perspective of optimization in ill-posed problems naturally balances fitting an objective with some prior assumed form of the result, such as continuity or derivative regularity for example. This all reduces to matrix manipulations which we demonstrate on a simple data set, with the implication that it may find much broader context.
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.
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.
Blended particle filters for large-dimensional chaotic dynamical systems
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
Horseshoes in a Chaotic System with Only One Stable Equilibrium
Huan, Songmei; Li, Qingdu; Yang, Xiao-Song
To confirm the numerically demonstrated chaotic behavior in a chaotic system with only one stable equilibrium reported by Wang and Chen, we resort to Poincaré map technique and present a rigorous computer-assisted verification of horseshoe chaos by virtue of topological horseshoes theory.
Partial synchronization and spontaneous spatial ordering in coupled chaotic systems
International Nuclear Information System (INIS)
Ying Zhang; Gang Hu; Cerdeira, Hilda A.; Shigang Chen; Braun, Thomas; Yugui Yao
2000-11-01
A model of many symmetrically and locally coupled chaotic oscillators is studied. Partial chaotic synchronizations associated with spontaneous spatial ordering are demonstrated. Very rich patterns of the system are revealed, based on partial synchronization analysis. The stabilities of different partially synchronous spatiotemporal structures and some novel dynamical behaviors of these states are discussed both numerically and analytically. (author)
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.
Adaptive control of chaotic continuous-time systems with delay
Tian, Yu-Chu; Gao, Furong
1998-06-01
A simple delay system governed by a first-order differential-delay equation may behave chaotically, but the conditions for the system to have such behaviors have not been well recognized. In this paper, a set of rules is postulated first for the conditions for the delay system to display chaos. A model-reference adaptive control scheme is then proposed to control the chaotic system state to converge to an arbitrarily given reference trajectory with certain and uncertain system parameters. Numerical examples are given to analyze the chaotic behaviors of the delay system and to demonstrate the effectiveness of the proposed adaptive control scheme.
Discontinuity and complexity in nonlinear physical systems
Baleanu, Dumitru; Luo, Albert
2014-01-01
This unique book explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed....
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.
Non-reversible evolution of quantum chaotic system. Kinetic description
International Nuclear Information System (INIS)
Chotorlishvili, L.; Skrinnikov, V.
2008-01-01
It is well known that the appearance of non-reversibility in classical chaotic systems is connected with a local instability of phase trajectories relatively to a small change of initial conditions and parameters of the system. Classical chaotic systems reveal an exponential sensitivity to these changes. This leads to an exponential growth of initial error with time, and as the result after the statistical averaging over this error, the dynamics of the system becomes non-reversible. In spite of this, the question about the origin of non-reversibility in quantum case remains actual. The point is that the classical notion of instability of phase trajectories loses its sense during quantum consideration. The current work is dedicated to the clarification of the origin of non-reversibility in quantum chaotic systems. For this purpose we study a non-stationary dynamics of the chaotic quantum system. By analogy with classical chaos, we consider an influence of a small unavoidable error of the parameter of the system on the non-reversibility of the dynamics. It is shown in the Letter that due to the peculiarity of chaotic quantum systems, the statistical averaging over the small unavoidable error leads to the non-reversible transition from the pure state into the mixed one. The second part of the Letter is dedicated to the kinematic description of the chaotic quantum-mechanical system. Using the formalism of superoperators, a muster kinematic equation for chaotic quantum system was obtained from Liouville equation under a strict mathematical consideration
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.
A novel grid multiwing chaotic system with only non-hyperbolic equilibria
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.
Chaotic dynamics in nonlinear duopoly Stackelberg game with heterogeneous players
Xiao, Yue; Peng, Yu; Lu, Qian; Wu, Xue
2018-02-01
In this paper, a nonlinear duopoly Stackelberg game of competition on output is concerned. In consideration of the effects of difference between plan products and actual products, the two heterogeneous players always adopt suitable strategies which can improve their benefits most. In general, status of each firm is unequal. As the firms take strategies sequentially and produce simultaneously, complex behaviors are brought about. Numerical simulation presents period doubling bifurcation, maximal Lyapunov exponent and chaos. Moreover, an appropriate method of chaos controlling is applied and fractal dimension is analyzed as well.
Hybrid synchronization of two independent chaotic systems on ...
Indian Academy of Sciences (India)
Keywords. Hybrid synchronization; complex network; information source; chaotic system. ... encryption and decryption through synchronization. However, the ... Certainly, if the two systems are different, the security would be improved. How.
Cryptanalysis of a discrete-time synchronous chaotic encryption system
International Nuclear Information System (INIS)
Arroyo, David; Alvarez, Gonzalo; Li Shujun; Li Chengqing; Nunez, Juana
2008-01-01
Recently a chaotic cryptosystem based on discrete-time synchronization has been proposed. Some weaknesses of that new encryption system are addressed and exploited in order to successfully cryptanalyze the system
NUMERICAL ANALYSIS OF A CHAOTIC SYSTEM
Institute of Scientific and Technical Information of China (English)
任志坚
2001-01-01
This paper further proves that a single spiral strange attractor can be observed in an extremely simple autonomous electrical circuit by computer simulation. It is of third order and has only one nonlinear element: a three-segment piecewise linear resistor. The digital analyses show that the strange attractor has peculiar features compared with other third-order differential systems.
A stream cipher based on a spatiotemporal chaotic system
International Nuclear Information System (INIS)
Li Ping; Li Zhong; Halang, Wolfgang A.; Chen Guanrong
2007-01-01
A stream cipher based on a spatiotemporal chaotic system is proposed. A one-way coupled map lattice consisting of logistic maps is served as the spatiotemporal chaotic system. Multiple keystreams are generated from the coupled map lattice by using simple algebraic computations, and then are used to encrypt plaintext via bitwise XOR. These make the cipher rather simple and efficient. Numerical investigation shows that the cryptographic properties of the generated keystream are satisfactory. The cipher seems to have higher security, higher efficiency and lower computation expense than the stream cipher based on a spatiotemporal chaotic system proposed recently
Control of chaotic vibration in automotive wiper systems
International Nuclear Information System (INIS)
Wang Zheng; Chau, K.T.
2009-01-01
Chaotic vibration has been identified in the automotive wiper system at certain wiping speeds. This irregular vibration not only decreases the wiping efficiency, but also degrades the driving comfort. The purpose of this paper is to propose a new approach to stabilize the chaotic vibration in the wiper system. The key is to employ the extended time-delay feedback control in such a way that the applied voltage of the wiper motor is online adjusted according to its armature current feedback. Based on a practical wiper system, it is verified that the proposed approach can successfully stabilize the chaotic vibration, and provide a wide range of wiping speeds
An optical CDMA system based on chaotic sequences
Liu, Xiao-lei; En, De; Wang, Li-guo
2014-03-01
In this paper, a coherent asynchronous optical code division multiple access (OCDMA) system is proposed, whose encoder/decoder is an all-optical generator. This all-optical generator can generate analog and bipolar chaotic sequences satisfying the logistic maps. The formula of bit error rate (BER) is derived, and the relationship of BER and the number of simultaneous transmissions is analyzed. Due to the good property of correlation, this coherent OCDMA system based on these bipolar chaotic sequences can support a large number of simultaneous users, which shows that these chaotic sequences are suitable for asynchronous OCDMA system.
CHAOTIC DISINTEGRATION OF THE INNER SOLAR SYSTEM
Energy Technology Data Exchange (ETDEWEB)
Batygin, Konstantin [Division of Geological and Planetary Sciences, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125 (United States); Morbidelli, Alessandro [Department Lagrange, Observatoire de la Côte d' Azur, F-06304 Nice (France); Holman, Mathew J. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)
2015-02-01
On timescales that greatly exceed an orbital period, typical planetary orbits evolve in a stochastic yet stable fashion. On even longer timescales, however, planetary orbits can spontaneously transition from bounded to unbound chaotic states. Large-scale instabilities associated with such behavior appear to play a dominant role in shaping the architectures of planetary systems, including our own. Here we show how such transitions are possible, focusing on the specific case of the long-term evolution of Mercury. We develop a simple analytical model for Mercury's dynamics and elucidate the origins of its short-term stochastic behavior as well as of its sudden progression to unbounded chaos. Our model allows us to estimate the timescale on which this transition is likely to be triggered, i.e., the dynamical lifetime of the solar system as we know it. The formulated theory is consistent with the results of numerical simulations and is broadly applicable to extrasolar planetary systems dominated by secular interactions. These results constitute a significant advancement in our understanding of the processes responsible for sculpting of the dynamical structures of generic planetary systems.
An exponential observer for the generalized Rossler chaotic system
International Nuclear Information System (INIS)
Sun, Y.-J.
2009-01-01
In this paper, the generalized Rossler chaotic system is considered and the state observation problem of such a system is investigated. Based on the time-domain approach, a state observer for the generalized Rossler chaotic system is developed to guarantee the global exponential stability of the resulting error system. Moreover, the guaranteed exponential convergence rate can be arbitrarily pre-specified. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained result.
A simple observer of the generalized Chen chaotic systems
International Nuclear Information System (INIS)
Sun, Y.-J.
2009-01-01
In this paper, the generalized Chen chaotic system is considered and the state observation problem of such a system is investigated. Based on the time-domain approach, a simple observer for the generalized Chen chaotic system is proposed to guarantee the global exponential stability of the resulting error system. Furthermore, the guaranteed exponential convergence rate can be correctly estimated. Finally, a numerical example is provided to illustrate the use of the main result.
A simple observer design of the generalized Lorenz chaotic systems
International Nuclear Information System (INIS)
Sun, Y.-J.
2010-01-01
In this Letter, the generalized Lorenz chaotic system is considered and the state observation problem of such a system is investigated. Based on the time-domain approach, a simple observer for the generalized Lorenz chaotic system is developed to guarantee the global exponential stability of the resulting error system. Moreover, the guaranteed exponential convergence rate can be correctly estimated. Finally, a numerical example is given to show the effectiveness of the obtained result.
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)
Modified scaling function projective synchronization of chaotic systems
International Nuclear Information System (INIS)
Xu Yu-Hua; Zhou Wu-Neng; Fang Jian-An
2011-01-01
This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point, a periodic orbit, or even a chaotic attractor in the phase space. Based on LaSalle's invariance set principle, the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method. (general)
Chaos control of chaotic dynamical systems using backstepping design
International Nuclear Information System (INIS)
Yassen, M.T.
2006-01-01
This work presents chaos control of chaotic dynamical systems by using backstepping design method. This technique is applied to achieve chaos control for each of the dynamical systems Lorenz, Chen and Lue systems. Based on Lyapunov stability theory, control laws are derived. We used the same technique to enable stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory to be achieved in a systematic way. Numerical simulations are shown to verify the results
Mixed basin boundary structures of chaotic systems
International Nuclear Information System (INIS)
Rosa, E. Jr.; Ott, E.
1999-01-01
Motivated by recent numerical observations on a four-dimensional continuous-time dynamical system, we consider different types of basin boundary structures for chaotic systems. These general structures are essentially mixtures of the previously known types of basin boundaries where the character of the boundary assumes features of the previously known boundary types at different points arbitrarily finely interspersed in the boundary. For example, we discuss situations where an everywhere continuous boundary that is otherwise smooth and differentiable at almost every point has an embedded uncountable, zero Lebesgue measure set of points at which the boundary curve is nondifferentiable. Although the nondifferentiable set is only of zero Lebesgue measure, the curve close-quote s fractal dimension may (depending on parameters) still be greater than one. In addition, we discuss bifurcations from such a mixed boundary to a 'pure' boundary that is a fractal nowhere differentiable curve or surface and to a pure nonfractal boundary that is everywhere smooth. copyright 1999 The American Physical Society
Image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing
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.
Synchronization Between Two Different Switched Chaotic Systems By Switching Control
Directory of Open Access Journals (Sweden)
Du Li Ming
2016-01-01
Full Text Available This paper is concerned with the synchronization problem of two different switched chaotic systems, considering the general case that the master-slave switched chaotic systems have uncertainties. Two basic problems are considered: one is projective synchronization of switched chaotic systems under arbitrary switching; the other is projective synchronization of switched chaotic systems by design of switching when synchronization cannot achieved by using any subsystems alone. For the two problems, common Lyapunov function method and multiple Lyapunov function method are used respectively, an adaptive control scheme has been presented, some sufficient synchronization conditions are attainted, and the switching signal is designed. Finally, the numerical simulation is provide to show the effectiveness of our method.
Estimating parameters of chaotic systems synchronized by external driving signal
International Nuclear Information System (INIS)
Wu Xiaogang; Wang Zuxi
2007-01-01
Noise-induced synchronization (NIS) has evoked great research interests recently. Two uncoupled identical chaotic systems can achieve complete synchronization (CS) by feeding a common noise with appropriate intensity. Actually, NIS belongs to the category of external feedback control (EFC). The significance of applying EFC in secure communication lies in fact that the trajectory of chaotic systems is disturbed so strongly by external driving signal that phase space reconstruction attack fails. In this paper, however, we propose an approach that can accurately estimate the parameters of the chaotic systems synchronized by external driving signal through chaotic transmitted signal, driving signal and their derivatives. Numerical simulation indicates that this approach can estimate system parameters and external coupling strength under two driving modes in a very rapid manner, which implies that EFC is not superior to other methods in secure communication
Two novel synchronization criterions for a unified chaotic system
International Nuclear Information System (INIS)
Tao Chaohai; Xiong Hongxia; Hu Feng
2006-01-01
Two novel synchronization criterions are proposed in this paper. It includes drive-response synchronization and adaptive synchronization schemes. Moreover, these synchronization criterions can be applied to a large class of chaotic systems and are very useful for secure communication
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
A novel secret image sharing scheme based on chaotic system
Li, Li; Abd El-Latif, Ahmed A.; Wang, Chuanjun; Li, Qiong; Niu, Xiamu
2012-04-01
In this paper, we propose a new secret image sharing scheme based on chaotic system and Shamir's method. The new scheme protects the shadow images with confidentiality and loss-tolerance simultaneously. In the new scheme, we generate the key sequence based on chaotic system and then encrypt the original image during the sharing phase. Experimental results and analysis of the proposed scheme demonstrate a better performance than other schemes and confirm a high probability to resist brute force attack.
Synchronization of two chaotic systems: Dynamic compensator approach
International Nuclear Information System (INIS)
Chen, C.-K.; Lai, T.-W.; Yan, J.-J.; Liao, T.-L.
2009-01-01
This study is concerned with the identical synchronization problem for a class of chaotic systems. A dynamic compensator is proposed to achieve the synchronization between master and slave chaotic systems using only the accessible output variables. A sufficient condition is also proposed to ensure the global synchronization. Furthermore, the strictly positive real (SPR) restriction, which is normally required in most of the observer-based synchronization schemes, is released in our approach. Two numerical examples are included to illustrate the proposed scheme.
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)
Adaptive Control of the Chaotic System via Singular System Approach
Directory of Open Access Journals (Sweden)
Yudong Li
2014-01-01
Full Text Available This paper deals with the control problem of the chaotic system subject to disturbance. The sliding mode surface is designed by singular system approach, and sufficient condition for convergence is given. Then, the adaptive sliding mode controller is designed to make the state arrive at the sliding mode surface in finite time. Finally, Lorenz system is considered as an example to show the effectiveness of the proposed method.
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
Kemih, K.; Halimi, M.; Ghanes, M.; Zhang, G.
2011-12-01
In this paper, we study the design and implementation of analog secure communication systems via synchronized chaotic Chua's circuit with sliding mode observer. For this, we adopt an approach based on an inclusion of the message in the transmitter and in the receiver; we use a sliding mode observer with un-known input in order to recover the information. Finally, an analog electronic circuit with Multisim software is designed to physically realize the complete system (transmitter-receiver).
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.
Experimentally determined chaotic phase synchronization in a neuronal system
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...
Chaos control and duration time of a class of uncertain chaotic systems
International Nuclear Information System (INIS)
Bowong, Samuel; Moukam Kakmeni, F.M.
2003-01-01
This Letter presents a robust control scheme for a class of uncertain chaotic systems in the canonical form, with unknown nonlinearities. To cope with the uncertainties, we combine Lyapunov methodology with observer design. The proposed strategy comprises an exponential linearizing feedback and an uncertainty estimator. The developed control scheme allows chaos suppression. The advantage of this method over the existing results is that the control time is explicitly computed. Simulations studies are conducted to verify the effectiveness of the scheme
A New Chaotic System with Positive Topological Entropy
Directory of Open Access Journals (Sweden)
Zhonglin Wang
2015-08-01
Full Text Available This paper introduces a new simple system with a butterfly chaotic attractor. This system has rich and complex dynamics. With some typical parameters, its Lyapunov dimension is greater than other known three dimensional chaotic systems. It exhibits chaotic behavior over a large range of parameters, and the divergence of flow of this system is not a constant. The dynamics of this new system are analyzed via Lyapunov exponent spectrum, bifurcation diagrams, phase portraits and the Poincaré map. The compound structures of this new system are also analyzed. By means of topological horseshoe theory and numerical computation, the Poincaré map defined for the system is proved to be semi-conjugate to 3-shift map, and thus the system has positive topological entropy.
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
Modeling of Some Chaotic Systems with AnyLogic Software
Directory of Open Access Journals (Sweden)
Biljana Zlatanovska
2018-05-01
Full Text Available The chaotic systems are already known in the theory of chaos. In our paper will be analyzed the following chaotic systems: Rossler, Chua and Chen systems. All of them are systems of ordinary differential equations. By mathematical software Mathematica and MatLab, their graphical representation as continuous dynamical systems is already known. By computer simulations, via examples, the systems will be analyzed using AnyLogic software. We would like to present the way how ordinary differential equations are modeling with AnyLogic software, as one of the simplest software for use.
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)
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
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
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 Secure Communication Systems with an Adaptive State Observer
Directory of Open Access Journals (Sweden)
Wei-Der Chang
2015-01-01
Full Text Available This paper develops a new digital communication scheme based on using a unified chaotic system and an adaptive state observer. The proposed communication system basically consists of five important elements: signal modulation, chaotic encryption, adaptive state observer, chaotic decryption, and signal demodulation. A sequence of digital signals will be delivered from the transmitter to the receiver through a public channel. It is rather reasonable that if the number of signals delivered on the public channel is fewer, then the security of such communication system is more guaranteed. Therefore, in order to achieve this purpose, a state observer will be designed and its function is to estimate full system states only by using the system output signals. In this way, the signals delivered on the public channel can be reduced mostly. According to these estimated state signals, the original digital sequences are then retrieved completely. Finally, experiment results are provided to verify the applicability of the proposed communication system.
Estimating the state of large spatio-temporally chaotic systems
International Nuclear Information System (INIS)
Ott, E.; Hunt, B.R.; Szunyogh, I.; Zimin, A.V.; Kostelich, E.J.; Corazza, M.; Kalnay, E.; Patil, D.J.; Yorke, J.A.
2004-01-01
We consider the estimation of the state of a large spatio-temporally chaotic system from noisy observations and knowledge of a system model. Standard state estimation techniques using the Kalman filter approach are not computationally feasible for systems with very many effective degrees of freedom. We present and test a new technique (called a Local Ensemble Kalman Filter), generally applicable to large spatio-temporally chaotic systems for which correlations between system variables evaluated at different points become small at large separation between the points
Control of hyper-chaotic system
International Nuclear Information System (INIS)
Yin Xunhe; Feng Rupeng
2000-01-01
The approach based on the exact linearization via feedback is used for controlling Roessler hyper-chaos. A controller for hyper-chaos Roessler is designed by using the approach. The method is used to realize global stabilization and to control hyper-chaotic motion not only to any unstable equilibrium point but also to any desired periodic orbit. Simulation results presented here prove the feasibility of the method, and its robustness is analyzed numerically
A novel one equilibrium hyper-chaotic system generated upon Lü attractor
International Nuclear Information System (INIS)
Hong-Yan, Jia; Zeng-Qiang, Chen; Zhu-Zhi, Yuan
2010-01-01
By introducing an additional state feedback into a three-dimensional autonomous chaotic attractor Lü system, this paper presents a novel four-dimensional continuous autonomous hyper-chaotic system which has only one equilibrium. There are only 8 terms in all four equations of the new hyper-chaotic system, which may be less than any other four-dimensional continuous autonomous hyper-chaotic systems generated by three-dimensional (3D) continuous autonomous chaotic systems. The hyper-chaotic system undergoes Hopf bifurcation when parameter c varies, and becomes the 3D modified Lü system when parameter k varies. Although the hyper-chaotic system does not undergo Hopf bifurcation when parameter k varies, many dynamic behaviours such as periodic attractor, quasi periodic attractor, chaotic attractor and hyper-chaotic attractor can be observed. A circuit is also designed when parameter k varies and the results of the circuit experiment are in good agreement with those of simulation. (general)
A novel 3D autonomous system with different multilayer chaotic attractors
International Nuclear Information System (INIS)
Dong Gaogao; Du Ruijin; Tian Lixin; Jia Qiang
2009-01-01
This Letter proposes a novel three-dimensional autonomous system which has complex chaotic dynamics behaviors and gives analysis of novel system. More importantly, the novel system can generate three-layer chaotic attractor, four-layer chaotic attractor, five-layer chaotic attractor, multilayer chaotic attractor by choosing different parameters and initial condition. We analyze the new system by means of phase portraits, Lyapunov exponent spectrum, fractional dimension, bifurcation diagram and Poincare maps of the system. The three-dimensional autonomous system is totally different from the well-known systems in previous work. The new multilayer chaotic attractors are also worth causing attention.
Comparison between different synchronization methods of identical chaotic systems
International Nuclear Information System (INIS)
Haeri, Mohammad; Khademian, Behzad
2006-01-01
This paper studies and compares three nonadaptive (bidirectional, unidirectional, and sliding mode) and two adaptive (active control and backstepping) synchronization methods on the synchronizing of four pairs of identical chaotic systems (Chua's circuit, Roessler system, Lorenz system, and Lue system). Results from computer simulations are presented in order to illustrate the effectiveness of the methods and to compare them based on different criteria
Optimal Control for a Class of Chaotic Systems
Directory of Open Access Journals (Sweden)
Jianxiong Zhang
2012-01-01
Full Text Available This paper proposes the optimal control methods for a class of chaotic systems via state feedback. By converting the chaotic systems to the form of uncertain piecewise linear systems, we can obtain the optimal controller minimizing the upper bound on cost function by virtue of the robust optimal control method of piecewise linear systems, which is cast as an optimization problem under constraints of bilinear matrix inequalities (BMIs. In addition, the lower bound on cost function can be achieved by solving a semidefinite programming (SDP. Finally, numerical examples are given to illustrate the results.
Generalized projective synchronization of chaotic systems via adaptive learning control
International Nuclear Information System (INIS)
Yun-Ping, Sun; Jun-Min, Li; Hui-Lin, Wang; Jiang-An, Wang
2010-01-01
In this paper, a learning control approach is applied to the generalized projective synchronisation (GPS) of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov–Krasovskii functional stability theory, a differential-difference mixed parametric learning law and an adaptive learning control law are constructed to make the states of two different chaotic systems asymptotically synchronised. The scheme is successfully applied to the generalized projective synchronisation between the Lorenz system and Chen system. Moreover, numerical simulations results are used to verify the effectiveness of the proposed scheme. (general)
Importance sampling of rare events in chaotic systems
DEFF Research Database (Denmark)
Leitão, Jorge C.; Parente Lopes, João M.Viana; Altmann, Eduardo G.
2017-01-01
space of chaotic systems. As examples of our general framework we compute the distribution of finite-time Lyapunov exponents (in different chaotic maps) and the distribution of escape times (in transient-chaos problems). Our methods sample exponentially rare states in polynomial number of samples (in......Finding and sampling rare trajectories in dynamical systems is a difficult computational task underlying numerous problems and applications. In this paper we show how to construct Metropolis-Hastings Monte-Carlo methods that can efficiently sample rare trajectories in the (extremely rough) phase...... both low- and high-dimensional systems). An open-source software that implements our algorithms and reproduces our results can be found in reference [J. Leitao, A library to sample chaotic systems, 2017, https://github.com/jorgecarleitao/chaospp]....
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.
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 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.
H∞ synchronization of chaotic systems via dynamic feedback approach
International Nuclear Information System (INIS)
Lee, S.M.; Ji, D.H.; Park, Ju H.; Won, S.C.
2008-01-01
This Letter considers H ∞ synchronization of a general class of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an H ∞ norm constraint. A dynamic feedback control scheme is proposed for H ∞ synchronization in chaotic systems for the first time. Then, a criterion for existence of the controller is given in terms of LMIs. Finally, a numerical simulation is presented to show the effectiveness of the proposed chaos synchronization scheme
Shape synchronization control for three-dimensional chaotic systems
International Nuclear Information System (INIS)
Huang, Yuanyuan; Wang, Yinhe; Chen, Haoguang; Zhang, Siying
2016-01-01
This paper aims to the three-dimensional continuous chaotic system and shape of the chaotic attractor by utilizing the basic theory of plane curves in classical differential geometry, the continuous controller is synthesized for the master–slave synchronization in shape. This means that the slave system can possess the same shape of state trajectory with the master system via the continuous controller. The continuous controller is composed of three sub-controllers, which respectively correspond to the master–slave synchronization in shape for the three projective curves of the chaotic attractor onto the three coordinate planes. Moreover, the proposed shape synchronization technique as well as application of control scheme to secure communication is also demonstrated in this paper, where numerical simulation results show the proposed control method works well.
The control of an optical hyper-chaotic system
International Nuclear Information System (INIS)
Jiang Shumin; Tian Lixin; Wang Xuedi
2007-01-01
This paper discusses the problem of hyper-chaos control of an optical system. Based on Lyapunov stability theory, a non-autonomous feedback controller is designed. The proposed controller ensures that the hyper-chaotic system will be asymptotically stable. Numerical simulation of the original and the controlled system is provided to show the effectiveness of our method
Applications of Nonlinear Dynamics Model and Design of Complex Systems
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.
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.
Directory of Open Access Journals (Sweden)
Guangya Peng
2018-01-01
Full Text Available The four-wing memristive chaotic system used in synchronization is applied to secure communication which can increase the difficulty of deciphering effectively and enhance the security of information. In this paper, a novel four-wing memristive chaotic system with an active cubic flux-controlled memristor is proposed based on a Lorenz-like circuit. Dynamical behaviors of the memristive system are illustrated in terms of Lyapunov exponents, bifurcation diagrams, coexistence Poincaré maps, coexistence phase diagrams, and attraction basins. Besides, the modular equivalent circuit of four-wing memristive system is designed and the corresponding results are observed to verify its accuracy and rationality. A nonlinear synchronization controller with exponential function is devised to realize synchronization of the coexistence of multiple attractors, and the synchronization control scheme is applied to image encryption to improve secret key space. More interestingly, considering different influence of multistability on encryption, the appropriate key is achieved to enhance the antideciphering ability.
Design of output feedback controller for a unified chaotic system
International Nuclear Information System (INIS)
Li Wenlin; Chen Xiuqin; Shen Zhiping
2008-01-01
In this paper, the synchronization of a unified chaotic system is investigated by the use of output feedback controllers; a two-input single-output feedback controller and single-input single-output feedback controller are presented to synchronize the unified chaotic system when the states are not all measurable. Compared with the existing results, the controllers designed in this paper have some advantages such as small feedback gain, simple structure and less conservation. Finally, numerical simulations results are provided to demonstrate the validity and effectiveness of the proposed method
Directing orbits of chaotic systems by particle swarm optimization
International Nuclear Information System (INIS)
Liu Bo; Wang Ling; Jin Yihui; Tang Fang; Huang Dexian
2006-01-01
This paper applies a novel evolutionary computation algorithm named particle swarm optimization (PSO) to direct the orbits of discrete chaotic dynamical systems towards desired target region within a short time by adding only small bounded perturbations, which could be formulated as a multi-modal numerical optimization problem with high dimension. Moreover, the synchronization of chaotic systems is also studied, which can be dealt with as an online problem of directing orbits. Numerical simulations based on Henon Map demonstrate the effectiveness and efficiency of PSO, and the effects of some parameters are also investigated
Qualitative identification of chaotic systems behaviours
International Nuclear Information System (INIS)
Vicha, T.; Dohnal, M.
2008-01-01
There are only three qualitative values positive, negative and zero. This means that there is a maximal number of qualitatively distinguishable scenarios, prescribed by the number of variables and the highest qualitative derivative taken into consideration. There are several chaos related tasks, which can be solved with great difficulties on the numerical level if multidimensional problems are studied. One of them is the identification of all qualitatively different behaviours. To make sure that all distinctive qualitative scenarios are identified a qualitative interpretation of a classical quantitative phase portrait is used. The highest derivatives are usually the second derivatives as it is not possible to safely identify higher derivatives if tasks related to ecology or economics are studied. Two classical models are discussed - Damped oscillation (non chaotic) and Lorenz model (chaotic). There are 191 scenarios of the Lorenz model if only the second derivatives are considered. If the third derivatives are taken into consideration then the number of scenarios is 2619. Complete qualitative results are given in details
International Nuclear Information System (INIS)
Niu Yu-Jun; Wang Xing-Yuan; Nian Fu-Zhong; Wang Ming-Jun
2010-01-01
Based on the stability theory of the fractional order system, the dynamic behaviours of a new fractional order system are investigated theoretically. The lowest order we found to have chaos in the new three-dimensional system is 2.46, and the period routes to chaos in the new fractional order system are also found. The effectiveness of our analysis results is further verified by numerical simulations and positive largest Lyapunov exponent. Furthermore, a nonlinear feedback controller is designed to achieve the generalized projective synchronization of the fractional order chaotic system, and its validity is proved by Laplace transformation theory. (general)
Chaotic dynamic behavior analysis and control for a financial risk system
International Nuclear Information System (INIS)
Zhang Xiao-Dan; Zheng Yuan; Liu Xiang-Dong; Liu Cheng
2013-01-01
According to the risk management process of financial markets, a financial risk dynamic system is constructed in this paper. Through analyzing the basic dynamic properties, we obtain the conditions for stability and bifurcation of the system based on Hopf bifurcation theory of nonlinear dynamic systems. In order to make the system's chaos disappear, we select the feedback gain matrix to design a class of chaotic controller. Numerical simulations are performed to reveal the change process of financial market risk. It is shown that, when the parameter of risk transmission rate changes, the system gradually comes into chaos from the asymptotically stable state through bifurcation. The controller can then control the chaos effectively
Synchronizing the noise-perturbed Lue chaotic system
International Nuclear Information System (INIS)
Zhang Yan; Chen Shihua; Zhou Hong
2009-01-01
In this paper, synchronization between unidirectionally coupled Lue chaotic systems with noise perturbation is investigated theoretically and numerically. Sufficient conditions of synchronization between these noise-perturbed systems are established by means of the so-called sliding mode control method. Some numerical simulations are also included to visualize the effectiveness and the feasibility of the developed approach.
Collection of master-slave synchronized chaotic systems
Lerescu, AI; Constandache, N; Oancea, S; Grosu, [No Value
2004-01-01
In this work the open-plus-closed-loop (OPCL) method of synchronization is used in order to synchronize the systems from the Sprott's collection of the simplest chaotic systems. The method is general and we looked for the simplest coupling between master and slave. The main result is that for the
Jamming and chaotic dynamics in different granular systems
Maghsoodi, Homayoon; Luijten, Erik
Although common in nature and industry, the jamming transition has long eluded a concrete, mechanistic explanation. Recently, Banigan et al. (Nat. Phys. 9, 288-292, 2013) proposed a method for characterizing this transition in a granular system in terms of the system's chaotic properties, as quantified by the largest Lyapunov exponent. They demonstrated that in a two-dimensional shear cell the jamming transition coincides with the bulk density at which the system's largest Lyapunov exponent changes sign, indicating a transition between chaotic and non-chaotic regimes. To examine the applicability of this observation to realistic granular systems, we study a model that includes frictional forces within an expanded phase space. Furthermore, we test the generality of the relation between chaos and jamming by investigating the relationship between jamming and the chaotic properties of several other granular systems, notably sheared systems (Howell, D., Behringer R. P., Veje C., Phys. Rev. Lett. 82, 5241-5244, 1999) and systems with a free boundary. Finally, we quantify correlations between the largest Lyapunov vector and collective rearrangements of the system to demonstrate the predictive capabilities enabled by adopting this perspective of jamming.
Synchronization of spatiotemporal chaotic systems by feedback control
International Nuclear Information System (INIS)
Lai, Y.; Grebogi, C.
1994-01-01
We demonstrate that two identical spatiotemporal chaotic systems can be synchronized by (1) linking one or a few of their dynamical variables, and (2) applying a small feedback control to one of the systems. Numerical examples using the diffusively coupled logistic map lattice are given. The effect of noise and the limitation of the technique are discussed
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)
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.
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
Modified Levenberg-Marquardt Method for RÖSSLER Chaotic System Fuzzy Modeling Training
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.
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.
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.
Fully Digital Chaotic Differential Equation-based Systems And Methods
Radwan, Ahmed Gomaa Ahmed
2012-09-06
Various embodiments are provided for fully digital chaotic differential equation-based systems and methods. In one embodiment, among others, a digital circuit includes digital state registers and one or more digital logic modules configured to obtain a first value from two or more of the digital state registers; determine a second value based upon the obtained first values and a chaotic differential equation; and provide the second value to set a state of one of the plurality of digital state registers. In another embodiment, a digital circuit includes digital state registers, digital logic modules configured to obtain outputs from a subset of the digital shift registers and to provide the input based upon a chaotic differential equation for setting a state of at least one of the subset of digital shift registers, and a digital clock configured to provide a clock signal for operating the digital shift registers.
Fully Digital Chaotic Differential Equation-based Systems And Methods
Radwan, Ahmed Gomaa Ahmed; Zidan, Mohammed A.; Salama, Khaled N.
2012-01-01
Various embodiments are provided for fully digital chaotic differential equation-based systems and methods. In one embodiment, among others, a digital circuit includes digital state registers and one or more digital logic modules configured to obtain a first value from two or more of the digital state registers; determine a second value based upon the obtained first values and a chaotic differential equation; and provide the second value to set a state of one of the plurality of digital state registers. In another embodiment, a digital circuit includes digital state registers, digital logic modules configured to obtain outputs from a subset of the digital shift registers and to provide the input based upon a chaotic differential equation for setting a state of at least one of the subset of digital shift registers, and a digital clock configured to provide a clock signal for operating the digital shift registers.
Identification of chaotic systems with hidden variables (modified Bock's algorithm)
International Nuclear Information System (INIS)
Bezruchko, Boris P.; Smirnov, Dmitry A.; Sysoev, Ilya V.
2006-01-01
We address the problem of estimating parameters of chaotic dynamical systems from a time series in a situation when some of state variables are not observed and/or the data are very noisy. Using specially developed quantitative criteria, we compare performance of the original multiple shooting approach (Bock's algorithm) and its modified version. The latter is shown to be significantly superior for long chaotic time series. In particular, it allows to obtain accurate estimates for much worse starting guesses for the estimated parameters
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
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.
Chaotic Dynamics and Transport in Classical and Quantum Systems
International Nuclear Information System (INIS)
2003-01-01
The aim of this summer school is to provide a set of extended and pedagogical lectures, on the major present-day topics in dynamical systems and statistical mechanics including applications. Some articles are dedicated to chaotic transport in plasma turbulence and to quantum chaos. This document gathers the summaries of some presentations
Hybrid synchronization of two independent chaotic systems on ...
Indian Academy of Sciences (India)
The real network nodes are always interfered by other messages. So, how to realize the hybrid synchronization of two independent chaotic systems based on the complex network is very important. To solve this problem, two other problems should be considered. One is how the same network node of the complex network ...
Multiscality in the Dynamics of Coupled Chaotic Systems
DEFF Research Database (Denmark)
Pavlov, A.N.; Sosnovtseva, Olga; Ziganshin, A.R.
2002-01-01
We investigate the scaling features of complex motions in systems of two coupled chaotic oscillators by means of the wavelet-transform modulus maxima method and the detrended fluctuation analysis. We show that the transition from asynchronous to synchronous dynamics typically reduces the degree...
The adaptive synchronization of fractional-order Liu chaotic system ...
Indian Academy of Sciences (India)
In this paper, the chaos control and the synchronization of two fractional-order Liu chaotic systems with unknown parameters are studied. According to the Lyapunov stabilization theory and the adaptive control theorem, the adaptive control rule is obtained for the described error dynamic stabilization. Using the adaptive rule ...
Chaotic Dynamics and Transport in Classical and Quantum Systems
Energy Technology Data Exchange (ETDEWEB)
NONE
2003-07-01
The aim of this summer school is to provide a set of extended and pedagogical lectures, on the major present-day topics in dynamical systems and statistical mechanics including applications. Some articles are dedicated to chaotic transport in plasma turbulence and to quantum chaos. This document gathers the summaries of some presentations.
An Approach of Tracking Control for Chaotic Systems
Directory of Open Access Journals (Sweden)
Jin Xing
2016-01-01
Full Text Available Combining the ergodicity of chaos and the Jacobian matrix, we design a general tracking controller for continuous and discrete chaotic systems. The control scheme has the ability to track a bounded reference signal. We prove its globally asymptotic stability and extend it to generalized projective synchronization. Numerical simulations verify the effectiveness of the proposed scheme.
Synchronization of a unified chaotic system and the application in secure communication
International Nuclear Information System (INIS)
Lu Junan; Wu Xiaoqun; Lue Jinhu
2002-01-01
This Letter further investigates the synchronization of a unified chaotic system via different methods. Several sufficient theorems for the synchronization of the unified chaotic system are deduced. A scheme of secure communication based on the synchronization of the unified chaotic system is presented. Numerical simulation shows its feasibility
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.
Comparison between different synchronization methods of identical chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Haeri, Mohammad [Advanced Control System Laboratory, Electrical Engineering Department, Sharif University of Technology, Azadi Avenue, P.O. Box 11365-9363 Tehran (Iran, Islamic Republic of)]. E-mail: haeri@sina.sharif.edu; Khademian, Behzad [Advanced Control System Laboratory, Electrical Engineering Department, Sharif University of Technology, Azadi Avenue, P.O. Box 11365-9363 Tehran (Iran, Islamic Republic of)
2006-08-15
This paper studies and compares three nonadaptive (bidirectional, unidirectional, and sliding mode) and two adaptive (active control and backstepping) synchronization methods on the synchronizing of four pairs of identical chaotic systems (Chua's circuit, Roessler system, Lorenz system, and Lue system). Results from computer simulations are presented in order to illustrate the effectiveness of the methods and to compare them based on different criteria.
Lyapunov-Based Controller for a Class of Stochastic Chaotic Systems
Directory of Open Access Journals (Sweden)
Hossein Shokouhi-Nejad
2014-01-01
Full Text Available This study presents a general control law based on Lyapunov’s direct method for a group of well-known stochastic chaotic systems. Since real chaotic systems have undesired random-like behaviors which have also been deteriorated by environmental noise, chaotic systems are modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of Wiener process which eventually generates an Ito differential equation. Proposed controller not only can asymptotically stabilize these systems in mean-square sense against their undesired intrinsic properties, but also exhibits good transient response. Simulation results highlight effectiveness and feasibility of proposed controller in outperforming stochastic chaotic systems.
Exponential synchronization of the Genesio-Tesi chaotic system via a novel feedback control
International Nuclear Information System (INIS)
Park, Ju H
2007-01-01
A novel feedback control scheme is proposed for exponential synchronization of the Genesio-Tesi chaotic system. The feedback controller consists of two parts: a linear dynamic control law and a nonlinear control one. For exponential synchronization between the drive and response Genesio-Tesi systems, the Lyapunov stability analysis is used. Then an existence criterion for the stabilizing controller is presented in terms of linear matrix inequalities (LMIs). The LMIs can be solved easily by various convex optimization algorithms. Finally, a numerical simulation is illustrated to show the effectiveness of the proposed chaos synchronization scheme
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.)
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.)
Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation
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. ...
Balancing for nonlinear systems
Scherpen, J.M.A.
1993-01-01
We present a method of balancing for nonlinear systems which is an extension of balancing for linear systems in the sense that it is based on the input and output energy of a system. It is a local result, but gives 'broader' results than we obtain by just linearizing the system. Furthermore, the
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.
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.
Study on Unified Chaotic System-Based Wind Turbine Blade Fault Diagnostic System
Kuo, Ying-Che; Hsieh, Chin-Tsung; Yau, Her-Terng; Li, Yu-Chung
At present, vibration signals are processed and analyzed mostly in the frequency domain. The spectrum clearly shows the signal structure and the specific characteristic frequency band is analyzed, but the number of calculations required is huge, resulting in delays. Therefore, this study uses the characteristics of a nonlinear system to load the complete vibration signal to the unified chaotic system, applying the dynamic error to analyze the wind turbine vibration signal, and adopting extenics theory for artificial intelligent fault diagnosis of the analysis signal. Hence, a fault diagnostor has been developed for wind turbine rotating blades. This study simulates three wind turbine blade states, namely stress rupture, screw loosening and blade loss, and validates the methods. The experimental results prove that the unified chaotic system used in this paper has a significant effect on vibration signal analysis. Thus, the operating conditions of wind turbines can be quickly known from this fault diagnostic system, and the maintenance schedule can be arranged before the faults worsen, making the management and implementation of wind turbines smoother, so as to reduce many unnecessary costs.
Directory of Open Access Journals (Sweden)
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
Forward and adjoint sensitivity computation of chaotic dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Wang, Qiqi, E-mail: qiqi@mit.edu [Department of Aeronautics and Astronautics, MIT, 77 Mass Ave., Cambridge, MA 02139 (United States)
2013-02-15
This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged “statistical” quantities to infinitesimal perturbations of the system parameters. The algorithms are demonstrated on the Lorenz attractor. We show that sensitivity derivatives of statistical quantities can be accurately estimated using a single, short trajectory (over a time interval of 20) on the Lorenz attractor.
Guaranteed cost control of time-delay chaotic systems
International Nuclear Information System (INIS)
Park, Ju H.; Kwon, O.M.
2006-01-01
This article studies a guaranteed cost control problem for a class of time-delay chaotic systems. Attention is focused on the design of memory state feedback controllers such that the resulting closed-loop system is asymptotically stable and an adequate level of performance is also guaranteed. Using the Lyapunov method and LMI (linear matrix inequality) framework, two criteria for the existence of the controller are derived in terms of LMIs. A numerical example is given to illustrate the proposed method
Feedback control strategies for the Liu chaotic system
International Nuclear Information System (INIS)
Zhu Congxu; Chen Zhigang
2008-01-01
This Letter proposed three strategies of the dislocated feedback control, enhancing feedback control and speed feedback control of the Liu chaotic system to its unstable equilibrium points. It is found that the coefficients of enhancing feedback control and speed feedback control are smaller than those of ordinary feedback control, so, the complexity and cost of the system control are reduced. Theoretical analysis and numerical simulation are given, revealing the effectiveness of these strategies
Pitchfork bifurcation and circuit implementation of a novel Chen hyper-chaotic system
International Nuclear Information System (INIS)
Dong En-Zeng; Chen Zeng-Qiang; Chen Zai-Ping; Ni Jian-Yun
2012-01-01
In this paper, a novel four dimensional hyper-chaotic system is coined based on the Chen system, which contains two quadratic terms and five system parameters. The proposed system can generate a hyper-chaotic attractor in wide parameters regions. By using the center manifold theorem and the local bifurcation theory, a pitchfork bifurcation is demonstrated to arise at the zero equilibrium point. Numerical analysis demonstrates that the hyper-chaotic system can generate complex dynamical behaviors, e.g., a direct transition from quasi-periodic behavior to hyper-chaotic behavior. Finally, an electronic circuit is designed to implement the hyper-chaotic system, the experimental results are consist with the numerical simulations, which verifies the existence of the hyper-chaotic attractor. Due to the complex dynamic behaviors, this new hyper-chaotic system is useful in the secure communication. (general)
A Retrospection of Chaotic Phenomena in Electrical Systems
Directory of Open Access Journals (Sweden)
Umesh Kumar
1998-01-01
Full Text Available In the last decade new phenomena have been observed in all areas of non linear dynamics, principal among these being ‘Chaotic phenomena’. Chaos has been reported virtually from every scientific discipline. This paper summarizes a study of the chaotic phenomena in electrical systems and attempts to translate the mathematical ideas and techniques into language that engineers and applied scientists can use to study ‘Chaos’. Towards this end, the paper has summarized the study of chaos in several examples like Chua’s circuit family; Folded Torus circuit; non-autonomous circuits; switched capacitor circuits and hyper-chaos circuits. As observed in power systems, control systems and digital filters, chaos has been exhibited and shown on examples.
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
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
Stochastic Resonance in a System of Coupled Chaotic Oscillators
International Nuclear Information System (INIS)
Krawiecki, A.
1999-01-01
Noise-free stochastic resonance is investigated numerically in a system of two coupled chaotic Roessler oscillators. Periodic signal is applied either additively or multiplicatively to the coupling term. When the coupling constant is varied the oscillators lose synchronization via attractor bubbling or on-off intermittency. Properly chosen signals are analyzed which reflect the sequence of synchronized (laminar) phases and non-synchronized bursts in the time evolution of the oscillators. Maximum of the signal-to-noise ratio as a function of the coupling constant is observed. Dependence of the signal-to-noise ratio on the frequency of the periodic signal and parameter mismatch between the oscillators is investigated. Possible applications of stochastic resonance in the recovery of signals in secure communication systems based on chaotic synchronization are briefly discussed. (author)
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)
Chaotic Music Generation System Using Music Conductor Gesture
Chen, Shuai; Maeda, Yoichiro; Takahashi, Yasutake
2013-01-01
In the research of interactive music generation, we propose a music generation method, that the computer generates the music, under the recognition of human music conductor's gestures.In this research, the generated music is tuned by the recognized gestures for the parameters of the network of chaotic elements in real time. The music conductor's hand motions are detected by Microsoft Kinect in this system. Music theories are embedded in the algorithm, as a result, the generated music will be ...
Synchronization of complex chaotic systems in series expansion form
International Nuclear Information System (INIS)
Ge Zhengming; Yang Chenghsiung
2007-01-01
This paper studies the synchronization of complex chaotic systems in series expansion form by Lyapunov asymptotical stability theorem. A sufficient condition is given for the asymptotical stability of an error dynamics, and is applied to guiding the design of the secure communication. Finally, numerical results are studied for the Quantum-CNN oscillators synchronizing with unidirectional/bidirectional linear coupling to show the effectiveness of the proposed synchronization strategy
Oscillations in nonlinear systems
Hale, Jack K
2015-01-01
By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Pa
Gross-Pitaevski map as a chaotic dynamical system.
Guarneri, Italo
2017-03-01
The Gross-Pitaevski map is a discrete time, split-operator version of the Gross-Pitaevski dynamics in the circle, for which exponential instability has been recently reported. Here it is studied as a classical dynamical system in its own right. A systematic analysis of Lyapunov exponents exposes strongly chaotic behavior. Exponential growth of energy is then shown to be a direct consequence of rotational invariance and for stationary solutions the full spectrum of Lyapunov exponents is analytically computed. The present analysis includes the "resonant" case, when the free rotation period is commensurate to 2π, and the map has countably many constants of the motion. Except for lowest-order resonances, this case exhibits an integrable-chaotic transition.
Robust synchronization of chaotic systems via adaptive sliding mode control
International Nuclear Information System (INIS)
Yan, J.-J.; Hung, M.-L.; Chiang, T.-Y.; Yang, Y.-S.
2006-01-01
This Letter investigates the synchronization problem for a general class of chaotic systems. Using the sliding mode control technique, an adaptive control law is established to guarantee synchronization of the master and slave systems even when unknown parameters and external disturbances are present. In contrast to the previous works, the structure of slave system is simple and need not be identical to the master system. Furthermore, a novel proportional-integral (PI) switching surface is proposed to simplify the task of assigning the performance of the closed-loop error system in sliding mode. An illustrative example of Chua's circuit is given to demonstrate the effectiveness of the proposed synchronization scheme
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 ...
Energy Technology Data Exchange (ETDEWEB)
Liu, Xiaojun [State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi' an Jiaotong University, Xi' an 710049 (China); School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001 (China); Hong, Ling, E-mail: hongling@mail.xjtu.edu.cn; Jiang, Jun [State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi' an Jiaotong University, Xi' an 710049 (China)
2016-08-15
Global bifurcations include sudden changes in chaotic sets due to crises. There are three types of crises defined by Grebogi et al. [Physica D 7, 181 (1983)]: boundary crisis, interior crisis, and metamorphosis. In this paper, by means of the extended generalized cell mapping (EGCM), boundary and interior crises of a fractional-order Duffing system are studied as one of the system parameters or the fractional derivative order is varied. It is found that a crisis can be generally defined as a collision between a chaotic basic set and a basic set, either periodic or chaotic, to cause a sudden discontinuous change in chaotic sets. Here chaotic sets involve three different kinds: a chaotic attractor, a chaotic saddle on a fractal basin boundary, and a chaotic saddle in the interior of a basin and disjoint from the attractor. A boundary crisis results from the collision of a periodic (or chaotic) attractor with a chaotic (or regular) saddle in the fractal (or smooth) boundary. In such a case, the attractor, together with its basin of attraction, is suddenly destroyed as the control parameter passes through a critical value, leaving behind a chaotic saddle in the place of the original attractor and saddle after the crisis. An interior crisis happens when an unstable chaotic set in the basin of attraction collides with a periodic attractor, which causes the appearance of a new chaotic attractor, while the original attractor and the unstable chaotic set are converted to the part of the chaotic attractor after the crisis. These results further demonstrate that the EGCM is a powerful tool to reveal the mechanism of crises in fractional-order systems.
Projective synchronization of chaotic systems with bidirectional ...
Indian Academy of Sciences (India)
2Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road,. Kolkata 700 009, India. ∗ ... versal phenomenon in a variety of natural and engineering systems [4]. Over the past two decades ..... Now, following the rule for the construction of master–slave system, we obtain the master system as. ˙x1 = x2 + ...
A Simple Hybrid Synchronization for a Class of Chaotic Financial Systems
Directory of Open Access Journals (Sweden)
Jiming Zheng
2017-01-01
Full Text Available It is an important to achieve the hybrid synchronization of the chaotic financial system. Chaos synchronization is equivalent to the error system which is asymptotically stable. The hybrid synchronization for a class of finance chaotic systems is discussed. First, a simple single variable controller is obtained to synchronize two identical chaotic financial systems with different initial conditions. Second, a novel algorithm is proposed to determine the variables of the master system that should antisynchronize with corresponding variables of the slave system and use this algorithm to determine the corresponding variables in the chaotic financial systems. The hybrid synchronization of the chaotic financial systems is realized by a simple controller. At the same time, different controllers can implement the chaotic financial system hybrid synchronization. In comparison with the existing results, the obtained controllers in this paper are simpler than those of the existing results. Finally, numerical simulations show the effectiveness of the proposed results.
Transient Dynamics of Electric Power Systems: Direct Stability Assessment and Chaotic Motions
Chu, Chia-Chi
A power system is continuously experiencing disturbances. Analyzing, predicting, and controlling transient dynamics, which describe transient behaviors of the power system following disturbances, is a major concern in the planning and operation of a power utility. Important conclusions and decisions are made based on the result of system transient behaviors. As today's power network becomes highly interconnected and much more complex, it has become essential to enhance the fundamental understanding of transient dynamics, and to develop fast and reliable computational algorithms. In this thesis, we emphasize mathematical rigor rather than physical insight. Nonlinear dynamical system theory is applied to study two fundamental topics: direct stability assessment and chaotic motions. Conventionally, power system stability is determined by calculating the time-domain transient behaviors for a given disturbance. In contrast, direct methods identify whether or not the system will remain stable once the disturbance is removed by comparing the corresponding energy value of the post-fault system to a calculated threshold value. Direct methods not only avoid the time-consuming numerical integration of the time domain approach, but also provide a quantitative measure of the degree of system stability. We present a general framework for the theoretical foundations of direct methods. Canonical representations of network-reduction models as well as network-preserving models are proposed to facilitate the analysis and the construction of energy functions of various power system models. An advanced and practical method, called the boundary of stability region based controlling unstable equilibrium point method (BCU method), of computing the controlling unstable equilibrium point is proposed along with its theoretical foundation. Numerical solution algorithms capable of supporting on-line applications of direct methods are provided. Further possible improvements and enhancements are
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.)
The role of model dynamics in ensemble Kalman filter performance for chaotic systems
Ng, G.-H.C.; McLaughlin, D.; Entekhabi, D.; Ahanin, A.
2011-01-01
The ensemble Kalman filter (EnKF) is susceptible to losing track of observations, or 'diverging', when applied to large chaotic systems such as atmospheric and ocean models. Past studies have demonstrated the adverse impact of sampling error during the filter's update step. We examine how system dynamics affect EnKF performance, and whether the absence of certain dynamic features in the ensemble may lead to divergence. The EnKF is applied to a simple chaotic model, and ensembles are checked against singular vectors of the tangent linear model, corresponding to short-term growth and Lyapunov vectors, corresponding to long-term growth. Results show that the ensemble strongly aligns itself with the subspace spanned by unstable Lyapunov vectors. Furthermore, the filter avoids divergence only if the full linearized long-term unstable subspace is spanned. However, short-term dynamics also become important as non-linearity in the system increases. Non-linear movement prevents errors in the long-term stable subspace from decaying indefinitely. If these errors then undergo linear intermittent growth, a small ensemble may fail to properly represent all important modes, causing filter divergence. A combination of long and short-term growth dynamics are thus critical to EnKF performance. These findings can help in developing practical robust filters based on model dynamics. ?? 2011 The Authors Tellus A ?? 2011 John Wiley & Sons A/S.
Directory of Open Access Journals (Sweden)
Roman Senkerik
2014-01-01
Full Text Available Evolutionary technique differential evolution (DE is used for the evolutionary tuning of controller parameters for the stabilization of set of different chaotic systems. The novelty of the approach is that the selected controlled discrete dissipative chaotic system is used also as the chaotic pseudorandom number generator to drive the mutation and crossover process in the DE. The idea was to utilize the hidden chaotic dynamics in pseudorandom sequences given by chaotic map to help differential evolution algorithm search for the best controller settings for the very same chaotic system. The optimizations were performed for three different chaotic systems, two types of case studies and developed cost functions.
Chaotic Behavior of a Generalized Sprott E Differential System
Oliveira, Regilene; Valls, Claudia
A chaotic system with only one equilibrium, a stable node-focus, was introduced by Wang and Chen [2012]. This system was found by adding a nonzero constant b to the Sprott E system [Sprott, 1994]. The coexistence of three types of attractors in this autonomous system was also considered by Braga and Mello [2013]. Adding a second parameter to the Sprott E differential system, we get the autonomous system ẋ = ayz + b,ẏ = x2 - y,ż = 1 - 4x, where a,b ∈ ℝ are parameters and a≠0. In this paper, we consider theoretically some global dynamical aspects of this system called here the generalized Sprott E differential system. This polynomial differential system is relevant because it is the first polynomial differential system in ℝ3 with two parameters exhibiting, besides the point attractor and chaotic attractor, coexisting stable limit cycles, demonstrating that this system is truly complicated and interesting. More precisely, we show that for b sufficiently small this system can exhibit two limit cycles emerging from the classical Hopf bifurcation at the equilibrium point p = (1/4, 1/16, 0). We also give a complete description of its dynamics on the Poincaré sphere at infinity by using the Poincaré compactification of a polynomial vector field in ℝ3, and we show that it has no first integrals in the class of Darboux functions.
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
GCS of a class of chaotic dynamic systems
International Nuclear Information System (INIS)
Park, Ju H.
2005-01-01
This article studies a guaranteed cost synchronization (GCS) problem for a class of chaotic systems. Attention is focused on the design of state feedback controllers such that the resulting closed-loop error system is asymptotically stable and an adequate level of performance is also guaranteed. Using the Lyapunov method and LMI (linear matrix inequality) technique, two criteria for the existence of the controller for GCS are derived in terms of LMIs. To show the effectiveness of the proposed method, GCS problem of Genesio system verified by a numerical example
A New Feigenbaum-Like Chaotic 3D System
Directory of Open Access Journals (Sweden)
Huitao Zhao
2014-01-01
Full Text Available Based on Sprott N system, a new three-dimensional autonomous system is reported. It is demonstrated to be chaotic in the sense of having positive largest Lyapunov exponent and fractional dimension. To further understand the complex dynamics of the system, some basic properties such as Lyapunov exponents, bifurcation diagram, Poincaré mapping, and period-doubling route to chaos are analyzed with careful numerical simulations. The obtained results also show that the period-doubling sequence of bifurcations leads to a Feigenbaum-like strange attractor.
Chaotic diffusion in the Solar System
Laskar, Jacques
2008-01-01
A statistical analysis is performed over more than 1001 different integrations of the secular equations of the Solar system over 5 Gyr. With this secular system, the probability of the eccentricity of Mercury to reach 0.6 in 5 Gyr is about 1 to 2 %. In order to compare with (Ito and Tanikawa, 2002), we have performed the same analysis without general relativity, and obtained even more orbits of large eccentricity for Mercury. We have performed as well a direct integration of the planetary orb...
Chaotic renormalization group approach to disordered systems
International Nuclear Information System (INIS)
Oliveira, P.M.C. de; Continentino, M.A.; Makler, S.S.; Anda, E.V.
1984-01-01
We study the eletronic properties of the disordered linear chain using a technique previously developed by some of the authors for an ordered chain. The equations of motion for the one electron Green function are obtained and the configuration average is done according to the GK scheme. The dynamical problem is transformed, using a renormalization group procedure, into a bidimensional map. The properties of this map are investigated and related to the localization properties of the eletronic system. (Author) [pt
Robust synchronization of unified chaotic systems via sliding mode control
International Nuclear Information System (INIS)
Yan Junjuh; Yang Yisung; Chiang Tsungying; Chen Chingyuan
2007-01-01
This paper investigates the chaos synchronization problem for a class of uncertain master-slave unified chaotic systems. Based on the sliding mode control technique, a robust control scheme is established which guarantees the occurrence of a sliding motion of error states even when the parameter uncertainty and external perturbation are present. Furthermore, a novel proportional-integral (PI) switching surface is introduced for determining the synchronization performance of systems in the sliding mode motion. Simulation results are proposed to demonstrate the effectiveness of the method
On entanglement spreading in chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Mezei, Márk [Princeton Center for Theoretical Science, Princeton University,Princeton, NJ 08544 (United States); Stanford, Douglas [Institute for Advanced Study,Princeton, NJ 08540 (United States)
2017-05-11
We discuss the time dependence of subsystem entropies in interacting quantum systems. As a model for the time dependence, we suggest that the entropy is as large as possible given two constraints: one follows from the existence of an emergent light cone, and the other is a conjecture associated to the “entanglement velocity” v{sub E}. We compare this model to new holographic and spin chain computations, and to an operator growth picture. Finally, we introduce a second way of computing the emergent light cone speed in holographic theories that provides a boundary dynamics explanation for a special case of entanglement wedge subregion duality in AdS/CFT.
International Nuclear Information System (INIS)
Alvarez, Gonzalo; Hernandez, Luis; Munoz, Jaime; Montoya, Fausto; Li Shujun
2005-01-01
This Letter analyzes the security weakness of a recently proposed communication method based on chaotic modulation and masking using synchronization of two chaotic systems with different orders. It is shown that its application to secure communication is unsafe, because it can be broken in two different ways, by high-pass filtering and by reduced order system synchronization, without knowing neither the system parameter values nor the system key
Applications of modularized circuit designs in a new hyper-chaotic system circuit implementation
International Nuclear Information System (INIS)
Wang Rui; Sun Hui; Wang Jie-Zhi; Wang Lu; Wang Yan-Chao
2015-01-01
Modularized circuit designs for chaotic systems are introduced in this paper. Especially, a typical improved modularized design strategy is proposed and applied to a new hyper-chaotic system circuit implementation. In this paper, the detailed design procedures are described. Multisim simulations and physical experiments are conducted, and the simulation results are compared with Matlab simulation results for different system parameter pairs. These results are consistent with each other and they verify the existence of the hyper-chaotic attractor for this new hyper-chaotic system. (paper)
Synchronization and an application of a novel fractional order King Cobra chaotic system
Energy Technology Data Exchange (ETDEWEB)
Muthukumar, P., E-mail: muthukumardgl@gmail.com; Balasubramaniam, P., E-mail: balugru@gmail.com [Department of Mathematics, Gandhigram Rural Institute‐Deemed University, Gandhigram 624 302, Tamilnadu (India); Ratnavelu, K., E-mail: kuru052001@gmail.com [Faculty of Science, Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur (Malaysia)
2014-09-01
In this paper, we design a new three dimensional King Cobra face shaped fractional order chaotic system. The multi-scale synchronization scheme of two fractional order chaotic systems is described. The necessary conditions for the multi-scale synchronization of two identical fractional order King Cobra chaotic systems are derived through feedback control. A new cryptosystem is proposed for an image encryption and decryption by using synchronized fractional order King Cobra chaotic systems with the supports of multiple cryptographic assumptions. The security of the proposed cryptosystem is analyzed by the well known algebraic attacks. Numerical simulations are given to show the effectiveness of the proposed theoretical results.
Optimizing Markovian modeling of chaotic systems with recurrent neural networks
International Nuclear Information System (INIS)
Cechin, Adelmo L.; Pechmann, Denise R.; Oliveira, Luiz P.L. de
2008-01-01
In this paper, we propose a methodology for optimizing the modeling of an one-dimensional chaotic time series with a Markov Chain. The model is extracted from a recurrent neural network trained for the attractor reconstructed from the data set. Each state of the obtained Markov Chain is a region of the reconstructed state space where the dynamics is approximated by a specific piecewise linear map, obtained from the network. The Markov Chain represents the dynamics of the time series in its statistical essence. An application to a time series resulted from Lorenz system is included
The n-level spectral correlations for chaotic systems
International Nuclear Information System (INIS)
Nagao, Taro; Mueller, Sebastian
2009-01-01
We study the n-level spectral correlation functions of classically chaotic quantum systems without time-reversal symmetry. According to Bohigas, Giannoni and Schmit's universality conjecture, it is expected that the correlation functions are in agreement with the prediction of the circular unitary ensemble (CUE) of random matrices. A semiclassical resummation formalism allows us to express the correlation functions as sums over pseudo-orbits. Using an extended version of the diagonal approximation on the pseudo-orbit sums, we derive the n-level correlation functions identical to the n x n determinantal correlation functions of the CUE.
Correlation function behavior in quantum systems which are classically chaotic
International Nuclear Information System (INIS)
Berman, G.P.; Kolovsky, A.R.
1983-01-01
The time behavior of a phase correlation function for dynamical quantum systems which are classically chaotic is considered. It is shown that under certain conditions there are three time regions of the quantum correlations behavior; the region of classical stochasticity (exponential decay of quantum correlations); the region of the correlations decay with a power law; the region of the constant level of the quantum correlations. The boundaries of these time regions are presented. The estimation of a remaining level of the quantum correlations is given. (orig.)
H∞ Balancing for Nonlinear Systems
Scherpen, Jacquelien M.A.
1996-01-01
In previously obtained balancing methods for nonlinear systems a past and a future energy function are used to bring the nonlinear system in balanced form. By considering a different pair of past and future energy functions that are related to the H∞ control problem for nonlinear systems we define
Consistency properties of chaotic systems driven by time-delayed feedback
Jüngling, T.; Soriano, M. C.; Oliver, N.; Porte, X.; Fischer, I.
2018-04-01
Consistency refers to the property of an externally driven dynamical system to respond in similar ways to similar inputs. In a delay system, the delayed feedback can be considered as an external drive to the undelayed subsystem. We analyze the degree of consistency in a generic chaotic system with delayed feedback by means of the auxiliary system approach. In this scheme an identical copy of the nonlinear node is driven by exactly the same signal as the original, allowing us to verify complete consistency via complete synchronization. In the past, the phenomenon of synchronization in delay-coupled chaotic systems has been widely studied using correlation functions. Here, we analytically derive relationships between characteristic signatures of the correlation functions in such systems and unequivocally relate them to the degree of consistency. The analytical framework is illustrated and supported by numerical calculations of the logistic map with delayed feedback for different replica configurations. We further apply the formalism to time series from an experiment based on a semiconductor laser with a double fiber-optical feedback loop. The experiment constitutes a high-quality replica scheme for studying consistency of the delay-driven laser and confirms the general theoretical results.
A novel four-wing non-equilibrium chaotic system and its circuit ...
Indian Academy of Sciences (India)
Abstract. In this paper, we construct a novel, 4D smooth autonomous system. Compared to the existing chaotic systems, the most attractive point is that this system does not display any equilib- ria, but can still exhibit four-wing chaotic attractors. The proposed system is investigated through numerical simulations and ...
Chaotic Excitation and Tidal Damping in the GJ 876 System
Puranam, Abhijit; Batygin, Konstantin
2018-04-01
The M-dwarf GJ 876 is the closest known star to harbor a multi-planetary system. With three outer planets locked in a chaotic Laplace-type resonance and an appreciably eccentric short-period super-Earth, this system represents a unique exposition of extrasolar planetary dynamics. A key question that concerns the long-term evolution of this system, and the fate of close-in planets in general, is how the significant eccentricity of the inner-most planet is maintained against tidal circularization on timescales comparable to the age of the universe. Here, we employ stochastic secular perturbation theory and N-body simulations to show that the orbit of the inner-most planet is shaped by a delicate balance between extrinsic chaotic forcing and tidal dissipation. As such, the planet’s orbital eccentricity represents an indirect measure of its tidal quality factor. Based on the system’s present-day architecture, we estimate that the extrasolar super-Earth GJ 876 d has a tidal Q ∼ 104–105, a value characteristic of solar system gas giants.
A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling Chaos
Directory of Open Access Journals (Sweden)
Shiyun Shen
2017-01-01
Full Text Available One 3D fractional-order chaotic system with only one locally asymptotically stable equilibrium is reported. To verify the chaoticity, the maximum Lyapunov exponent (MAXLE with respect to the fractional-order and chaotic attractors are obtained by numerical calculation for this system. Furthermore, by linear scalar controller consisting of a single state variable, one control scheme for stabilization of the 3D fractional-order chaotic system is suggested. The numerical simulations show the feasibility of the control scheme.
Adaptive control of discrete-time chaotic systems: a fuzzy control approach
International Nuclear Information System (INIS)
Feng Gang; Chen Guanrong
2005-01-01
This paper discusses adaptive control of a class of discrete-time chaotic systems from a fuzzy control approach. Using the T-S model of discrete-time chaotic systems, an adaptive control algorithm is developed based on some conventional adaptive control techniques. The resulting adaptively controlled chaotic system is shown to be globally stable, and its robustness is discussed. A simulation example of the chaotic Henon map control is finally presented, to illustrate an application and the performance of the proposed control algorithm
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
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)
A novel double-convection chaotic attractor, its adaptive control and circuit simulation
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.
Data transmission system with encryption by chaotic sequences
Directory of Open Access Journals (Sweden)
Politans’kyy R. L.
2014-06-01
Full Text Available Protection of transferable information in the telecommunication systems is possible by its imposition of coding sequence on a plaintext. Encryption of pseudorandom sequences can be performed by using generation algorithms which are implemented on the basis of the phenomenon of dynamical chaos, which is sensitive to changes in the initial conditions. One of the major problems encountered in the construction of secure communication systems is to provide synchronization between the receiving and transmitting parties of communication systems. Improvement of methods of hidden data transfer based on the systems with chaotic synchronization is the important task of research in the field of information and telecommunication systems based on chaos. This article shows an implementation of a data transmission system, encrypted by sequences, generated on the basis of one-dimensional discrete chaotic maps with ensuring synchronization of the transmitting and receiving sides of the system. In this system realization of synchronization is offered by a transmission through certain time domains of current value of xn generated by a logistic reflection. Xn transmission period depends on computer speed and distance between subscribers of the system. Its value is determined by transmitting a test message before the session. Infallible reception of test message indicates the optimal choice of a transmission period of the current value of xn. Selection period is done at the program level. For the construction of communication network modern software was used, in particular programming language Delphi 7.0. The work of the system is shown on the example of information transmission between the users of the system. The system operates in real time full duplex mode at any hardware implementation of Internet access. It is enough for the users of the system to specify IP address only.
Controlling a Chaotic System through Control Parameter Self-Modulation
International Nuclear Information System (INIS)
Pastor, I.
1994-01-01
A method for obtaining active control of a chaotic system based on the modulation of a control parameter by adding to it a small perturbation proportional to one output signal is proposed. From a theoretical point of view, chaos can be stabilized in the framework of this method because small modifications of the vector field controlling the dynamics are allowed, and thus some of the previously existing unstable periodic trajectories can be made stable. The method is much inspired on recent treatments of some related problems, and it is compared with them. One of its most attractive features is that it should be very easy to implement it on real experiments. The method is tested on a system of ordinary differential equations modelling the coupling of two self-oscillating electronic circuits (van der Pol oscillators). Some brief comments are made on the possibility that it could be applied to complex spatio-temporal systems where multiple chaotic structures can coexist for some values of the control parameters
Controlling a Chaotic System through Control Parameter Self-Modulation
International Nuclear Information System (INIS)
Pastor, I.
1994-01-01
A method for obtaining active control of a chaotic system based on the modulation of a control parameter by adding to it a small perturbation proportional to one output signal is proposed. From a theoretical point of view, chaos can be stabilized in the framework of this method because small modifications of the vector field controlling the dynamics are allowed, and thus some of the previously oxi sting unstable periodic trajectories can be made stable. The method is much inspired on recent treatments of some related problems, and i t is compared with them. One of its most attractive features is that is should be very easy to implement it on real experiments. The method is tested on a system of ordinary differential equations model ling the coupling of two se If - oscillating electronic circuits (van der Pol oscillators). Some brief comments are made on the no possibility that it could be applied to complex spatio-temporal systems where multiple chaotic structures can coexist for some values of the control parameters. (Author) 28 refs
Controlling a Chaotic System through Control Parameter Self-Modulation
Energy Technology Data Exchange (ETDEWEB)
Pastor, I
1994-07-01
A method for obtaining active control of a chaotic system based on the modulation of a control parameter by adding to it a small perturbation proportional to one output signal is proposed. From a theoretical point of view, chaos can be stabilized in the framework of this method because small modifications of the vector field controlling the dynamics are allowed, and thus some of the previously oxi sting unstable periodic trajectories can be made stable. The method is much inspired on recent treatments of some related problems, and i t is compared with them. One of its most attractive features is that is should be very easy to implement it on real experiments. The method is tested on a system of ordinary differential equations model ling the coupling of two se If - oscillating electronic circuits (van der Pol oscillators). Some brief comments are made on the no possibility that it could be applied to complex spatio-temporal systems where multiple chaotic structures can coexist for some values of the control parameters. (Author) 28 refs.
Deterministic nonlinear systems a short course
Anishchenko, Vadim S; Strelkova, Galina I
2014-01-01
This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems. This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.
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.
Chaotic dynamics in the (47171) Lempo triple system
Correia, Alexandre C. M.
2018-05-01
We investigate the dynamics of the (47171) Lempo triple system, also known by 1999 TC36. We derive a full 3D N-body model that takes into account the orbital and spin evolution of all bodies, which are assumed triaxial ellipsoids. We show that, for reasonable values of the shapes and rotational periods, the present best fitted orbital solution for the Lempo system is chaotic and unstable in short time-scales. The formation mechanism of this system is unknown, but the orbits can be stabilised when tidal dissipation is taken into account. The dynamics of the Lempo system is very rich, but depends on many parameters that are presently unknown. A better understanding of this systems thus requires more observations, which also need to be fitted with a complete model like the one presented here.
A unified approach for impulsive lag synchronization of chaotic systems with time delay
International Nuclear Information System (INIS)
Li Chuandong; Liao Xiaofeng; Zhang Rong
2005-01-01
In this paper, we propose a unified approach for impulsive lag-synchronization of a class of chaotic systems with time delay by employing the stability theory of impulsive delayed differential equations. Three well-known delayed chaotic systems are presented to illustrate our results. Also, the estimates of the stable regions for these systems are given, respectively
An Anti-Cheating Visual Cryptography Scheme Based on Chaotic Encryption System
Han, Yanyan; Xu, Zhuolin; Ge, Xiaonan; He, Wencai
By chaotic encryption system and introducing the trusted third party (TTP), in this paper, an anti-cheating visual cryptography scheme (VCS) is proposed. The scheme solved the problem of dishonest participants and improved the security of chaotic encryption system. Simulation results and analysis show that the recovery image is acceptable, the system can detect the cheating in participants effectively and with high security.
Pattern formations in chaotic spatio-temporal systems
Indian Academy of Sciences (India)
5Beijing–Hong Kong–Singapore Joint Center of Nonlinear and Complex Systems, ... For theoretical studies most previous work has focused on pattern .... Lyapunov exponents from arbitrary initial conditions, and the plots look rather.
Stochastic perturbations in open chaotic systems: random versus noisy maps.
Bódai, Tamás; Altmann, Eduardo G; Endler, Antonio
2013-04-01
We investigate the effects of random perturbations on fully chaotic open systems. Perturbations can be applied to each trajectory independently (white noise) or simultaneously to all trajectories (random map). We compare these two scenarios by generalizing the theory of open chaotic systems and introducing a time-dependent conditionally-map-invariant measure. For the same perturbation strength we show that the escape rate of the random map is always larger than that of the noisy map. In random maps we show that the escape rate κ and dimensions D of the relevant fractal sets often depend nonmonotonically on the intensity of the random perturbation. We discuss the accuracy (bias) and precision (variance) of finite-size estimators of κ and D, and show that the improvement of the precision of the estimations with the number of trajectories N is extremely slow ([proportionality]1/lnN). We also argue that the finite-size D estimators are typically biased. General theoretical results are combined with analytical calculations and numerical simulations in area-preserving baker maps.
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.
International Nuclear Information System (INIS)
Wang, Cong; Zhang, Hong-li; Fan, Wen-hui
2017-01-01
In this paper, we propose a new method to improve the safety of secure communication. This method uses the generalized dislocated lag projective synchronization and function projective synchronization to form a new generalized dislocated lag function projective synchronization. Moreover, this paper takes the examples of fractional order Chen system and Lü system with uncertain parameters as illustration. As the parameters of the two systems are uncertain, the nonlinear controller and parameter update algorithms are designed based on the fractional stability theory and adaptive control method. Moreover, this synchronization form and method of control are applied to secure communication via chaotic masking modulation. Many information signals can be recovered and validated. Finally, simulations are used to show the validity and feasibility of the proposed scheme.
Hybrid information privacy system: integration of chaotic neural network and RSA coding
Hsu, Ming-Kai; Willey, Jeff; Lee, Ting N.; Szu, Harold H.
2005-03-01
Electronic mails are adopted worldwide; most are easily hacked by hackers. In this paper, we purposed a free, fast and convenient hybrid privacy system to protect email communication. The privacy system is implemented by combining private security RSA algorithm with specific chaos neural network encryption process. The receiver can decrypt received email as long as it can reproduce the specified chaos neural network series, so called spatial-temporal keys. The chaotic typing and initial seed value of chaos neural network series, encrypted by the RSA algorithm, can reproduce spatial-temporal keys. The encrypted chaotic typing and initial seed value are hidden in watermark mixed nonlinearly with message media, wrapped with convolution error correction codes for wireless 3rd generation cellular phones. The message media can be an arbitrary image. The pattern noise has to be considered during transmission and it could affect/change the spatial-temporal keys. Since any change/modification on chaotic typing or initial seed value of chaos neural network series is not acceptable, the RSA codec system must be robust and fault-tolerant via wireless channel. The robust and fault-tolerant properties of chaos neural networks (CNN) were proved by a field theory of Associative Memory by Szu in 1997. The 1-D chaos generating nodes from the logistic map having arbitrarily negative slope a = p/q generating the N-shaped sigmoid was given first by Szu in 1992. In this paper, we simulated the robust and fault-tolerance properties of CNN under additive noise and pattern noise. We also implement a private version of RSA coding and chaos encryption process on messages.
FRF decoupling of nonlinear systems
Kalaycıoğlu, Taner; Özgüven, H. Nevzat
2018-03-01
Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.
Chaotic Behaviour Investigation of a Front Opposed-Hemispherical Spiral-Grooved Air Bearing System
Directory of Open Access Journals (Sweden)
Cheng-Chi Wang
2017-01-01
Full Text Available In recent years, spiral-grooved air bearing systems have attracted much attention and are especially useful in precision instruments and machines with spindles that rotate at high speed. Load support can be multidirectional and this type of bearing can also be very rigid. Studies show that some of the design problems encountered are dynamic and include critical speed, nonlinearity, gas film pressure, unbalanced rotors, and even poor design, all of which can result in the generation of chaotic aperiodic motion and instability under certain conditions. Such irregular motion on a large scale can cause severe damage to a machine or instrument. Therefore, understanding the conditions under which aperiodic behaviour and vibration arise is crucial for prevention. In this study, numerical analysis, including the Finite Difference and Differential Transformation Methods, is used to study these effects in detail in a front opposed-hemispherical spiral-grooved air bearing system. It was found that different rotor masses and bearing number could cause undesirable behaviour including periodic, subperiodic, quasi-periodic, and chaotic motion. The results obtained in this study can be used as a basis for future bearing system design and the prevention of instability.
International Nuclear Information System (INIS)
Goh, S.M.; Noorani, M.S.M.; Hashim, I.
2009-01-01
This is a case study of solving the Genesio system by using the classical variational iteration method (VIM) and a newly modified version called the multistage VIM (MVIM). VIM is an analytical technique that grants us a continuous representation of the approximate solution, which allows better information of the solution over the time interval. Unlike its counterpart, numerical techniques, such as the Runge-Kutta method, provide solutions only at two ends of the time interval (with condition that the selected time interval is adequately small for convergence). Furthermore, it offers approximate solutions in a discretized form, making it complicated in achieving a continuous representation. The explicit solutions through VIM and MVIM are compared with the numerical analysis of the fourth-order Runge-Kutta method (RK4). VIM had been successfully applied to linear and nonlinear systems of non-chaotic in nature and this had been testified by numerous scientists lately. Our intention is to determine whether VIM is also a feasible method in solving a chaotic system like Genesio. At the same time, MVIM will be applied to gauge its accuracy compared to VIM and RK4. Since, for most situations, the validity domain of the solutions is often an issue, we will consider a reasonably large time frame in our work.
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.
Huynh, B. H.; Tjahjowidodo, T.; Zhong, Z.-W.; Wang, Y.; Srikanth, N.
2018-01-01
Vortex induced vibration based energy harvesting systems have gained interests in these recent years due to its potential as a low water current energy source. However, the effectiveness of the system is limited only at a certain water current due to the resonance principle that governs the concept. In order to extend the working range, a bistable spring to support the structure is introduced on the system. The improvement on the performance is essentially dependent on the bistable gap as one of the main parameters of the nonlinear spring. A sufficiently large bistable gap will result in a significant performance improvement. Unfortunately, a large bistable gap might also increase a chance of chaotic responses, which in turn will result in diminutive harvested power. To mitigate the problem, an appropriate control structure is required to stabilize the chaotic vibrations of a VIV energy converter with the bistable supporting structure. Based on the nature of the double-well potential energy in a bistable spring, the ideal control structure will attempt to drive the responses to inter-well periodic vibrations in order to maximize the harvested power. In this paper, the OGY control algorithm is designed and implemented to the system. The control strategy is selected since it requires only a small perturbation in a structural parameter to execute the control effort, thus, minimum power is needed to drive the control input. Facilitated by a wake oscillator model, the bistable VIV system is modelled as a 4-dimensional autonomous continuous-time dynamical system. To implement the controller strategy, the system is discretized at a period estimated from the subspace hyperplane intersecting to the chaotic trajectory, whereas the fixed points that correspond to the desired periodic orbits are estimated by the recurrence method. Simultaneously, the Jacobian and sensitivity matrices are estimated by the least square regression method. Based on the defined fixed point and the
International Nuclear Information System (INIS)
Chien, T.-I; Hung, Y.-C.; Liao, T.-L.
2006-01-01
This paper presents a novel non-correlator-based digital communication system with the application of interleaved chaotic differential peaks keying (I-CDPK) modulation technique. The proposed communication system consists of four major modules: I-CDPK modulator (ICM), frequency modulation (FM) transmitter, FM receiver and I-CDPK demodulator (ICDM). In the ICM module, there are four components: a chaotic circuit to generate the chaotic signals, A/D converter, D/A converter and a digital processing mechanism to control all signal flows and performs I-CDPK modulation corresponding to the input digital bits. For interleaving every input digital bit set, every state of the chaotic system is used to represent one portion of it, but only a scalar state variable (i.e. the system output) is sent to the ICDM's chaotic circuit through both FM transmitter and FM receiver. An observer-based chaotic synchronization scheme is designed to synchronize the chaotic circuits of the ICM and ICDM. Meanwhile, the bit detector in ICDM is devoted to recover the transmitted input digital bits. Some numerical simulations of an illustrative communication system are given to demonstrate its theoretical effectiveness. Furthermore, the performance of bit error rate of the proposed system is analyzed and compared with those of the correlator-based communication systems adopting coherent binary phase shift keying (BPSK) and coherent differential chaotic shift keying (DCSK) schemes
Observer based on sliding mode variable structure for synchronization of chaotic systems
International Nuclear Information System (INIS)
Yin Xunhe; Shan Xiuming; Ren Yong
2003-01-01
In the paper an approach, based on the state observer of sliding mode variable structure, is used for synchronizing chaotic systems. It does not require either the computation of the Lyapunov exponents, or the initial conditions belonging to the same basin of attraction as the existed approaches based on the state observer for synchronizing chaotic systems. The approach is more robust against noise and parameter mismatch than the existed approaches based on the state observer for synchronizing chaotic systems, because the former uses variable structure control, which is strong robust with respect to noise and parameter mismatch in the error dynamics, the later uses an appropriate choice of the feedback gain. Two well-known chaotic systems, a chaotic Roessler system and a hyperchaotic Roessler system are considered as illustrative examples to demonstrate the effectiveness of the used approach by numerical simulations
Constructing a one-way hash function based on the unified chaotic system
International Nuclear Information System (INIS)
Long Min; Peng Fei; Chen Guanrong
2008-01-01
A new one-way hash function based on the unified chaotic system is constructed. With different values of a key parameter, the unified chaotic system represents different chaotic systems, based on which the one-way hash function algorithm is constructed with three round operations and an initial vector on an input message. In each round operation, the parameters are processed by three different chaotic systems generated from the unified chaotic system. Feed-forwards are used at the end of each round operation and at the end of each element of the message processing. Meanwhile, in each round operation, parameter-exchanging operations are implemented. Then, the hash value of length 160 bits is obtained from the last six parameters. Simulation and analysis both demonstrate that the algorithm has great flexibility, satisfactory hash performance, weak collision property, and high security. (general)
Robust chaotic control of Lorenz system by backstepping design
International Nuclear Information System (INIS)
Peng, C.-C.; Chen, C.-L.
2008-01-01
This work presents a robust chaotic control strategy for the Lorenz chaos via backstepping design. Backstepping technique is a systematic tool of control law design to provide Lyapunov stability. The concept of extended system is used such that a continuous sliding mode control (SMC) effort is generated using backstepping scheme. In the proposed control algorithm, an adaptation law is applied to estimate the system parameter and the SMC offers the robustness to model uncertainties and external disturbances so that the asymptotical convergence of tracking error can be achieved. Regarding the SMC, an equivalent control algorithm is chosen based on the selection of Lyapunov stability criterion during backstepping approach. The converging rate of error state is relative to the corresponding dynamics of sliding surface. Numerical simulations demonstrate its advantages to a regulation problem and an orbit tracking problem of the Lorenz chaos
Lifetime of chaotic attractors in a multidimensional laser system
International Nuclear Information System (INIS)
Pando L, C.L.; Cerdeira, H.A.
1995-01-01
We study the lifetimes of chaotic attractors at crises in a multidimensional laser system. This system describes the CO 2 laser with modulated losses and is known as the four-level model. The critical exponents which are related to the lifetimes of the attractors are estimated in terms of the corresponding eigenvalues and the measured characteristic lifetime in the model. The critical exponents in this model and those of its center manifold version are in good agreement. We conjecture that generically in the four-level model the critical exponents are close to 1/2 at crises. In addition, we compare predictions of a simpler and popular model known as the two-level model with those of the above mentioned models. (author). 21 refs, 2 figs, 3 tabs
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
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.
International Nuclear Information System (INIS)
Jiang Chuanwen; Bompard, Etorre
2005-01-01
This paper proposes a short term hydroelectric plant dispatch model based on the rule of maximizing the benefit. For the optimal dispatch model, which is a large scale nonlinear planning problem with multi-constraints and multi-variables, this paper proposes a novel self-adaptive chaotic particle swarm optimization algorithm to solve the short term generation scheduling of a hydro-system better in a deregulated environment. Since chaotic mapping enjoys certainty, ergodicity and the stochastic property, the proposed approach introduces chaos mapping and an adaptive scaling term into the particle swarm optimization algorithm, which increases its convergence rate and resulting precision. The new method has been examined and tested on a practical hydro-system. The results are promising and show the effectiveness and robustness of the proposed approach in comparison with the traditional particle swarm optimization algorithm
Mallory, Kristina; van Gorder, Robert A.
We study chaotic behavior of solutions to the bilinear system of Lorenz type developed by Celikovsky and Vanecek [1994] through an application of competitive modes. This bilinear system of Lorenz type is one possible canonical form holding the Lorenz equation as a special case. Using a competitive modes analysis, which is a completely analytical method allowing one to identify parameter regimes for which chaos may occur, we are able to demonstrate a number of parameter regimes which admit a variety of distinct chaotic behaviors. Indeed, we are able to draw some interesting conclusions which relate the behavior of the mode frequencies arising from writing the state variables for the Celikovsky-Vanecek model as coupled oscillators, and the types of emergent chaotic behaviors observed. The competitive modes analysis is particularly useful if all but one of the model parameters are fixed, and the remaining free parameter is used to modify the chaos observed, in a manner analogous to a bifurcation parameter. Through a thorough application of the method, we are able to identify several parameter regimes which give new dynamics (such as specific forms of chaos) which were not observed or studied previously in the Celikovsky-Vanecek model. Therefore, the results demonstrate the advantage of the competitive modes approach for detecting new parameter regimes leading to chaos in third-order dynamical systems.
International Nuclear Information System (INIS)
Xu Yuhua; Zhou Wuneng; Fang Jianan
2009-01-01
This paper introduces a modified Lue chaotic system, and some basic dynamical properties are studied. Based on these properties, we present hybrid dislocated control method for stabilizing chaos to unstable equilibrium and limit cycle. In addition, based on the Lyapunov stability theorem, general hybrid projective dislocated synchronization (GHPDS) is proposed, which includes complete dislocated synchronization, dislocated anti-synchronization and projective dislocated synchronization as its special item. The drive and response systems discussed in this paper can be strictly different dynamical systems (including different dimensional systems). As examples, the modified Lue chaotic system, Chen chaotic system and hyperchaotic Chen system are discussed. Numerical simulations are given to show the effectiveness of these methods.
Energy Technology Data Exchange (ETDEWEB)
Xu Yuhua [College of Information Science and Technology, Donghua University, Shanghai 201620 (China) and Department of Maths, Yunyang Teacher' s College, Hubei 442000 (China)], E-mail: yuhuaxu2004@163.com; Zhou Wuneng [College of Information Science and Technology, Donghua University, Shanghai 201620 (China)], E-mail: wnzhou@163.com; Fang Jianan [College of Information Science and Technology, Donghua University, Shanghai 201620 (China)
2009-11-15
This paper introduces a modified Lue chaotic system, and some basic dynamical properties are studied. Based on these properties, we present hybrid dislocated control method for stabilizing chaos to unstable equilibrium and limit cycle. In addition, based on the Lyapunov stability theorem, general hybrid projective dislocated synchronization (GHPDS) is proposed, which includes complete dislocated synchronization, dislocated anti-synchronization and projective dislocated synchronization as its special item. The drive and response systems discussed in this paper can be strictly different dynamical systems (including different dimensional systems). As examples, the modified Lue chaotic system, Chen chaotic system and hyperchaotic Chen system are discussed. Numerical simulations are given to show the effectiveness of these methods.
Balancing for Unstable Nonlinear Systems
Scherpen, J.M.A.
1993-01-01
A previously obtained method of balancing for stable nonlinear systems is extended to unstable nonlinear systems. The similarity invariants obtained by the concept of LQG balancing for an unstable linear system can also be obtained by considering a past and future energy function of the system. By
Finite-time synchronization of a class of autonomous chaotic systems
Indian Academy of Sciences (India)
Some criteria for achieving the finite-time synchronization of a class of autonomous chaotic systems are derived by the finite-time stability theory and Gerschgorin disc theorem. Numerical simulations are shown to illustrate the effectiveness of the proposed method. Keywords. Finite-time synchronization; autonomous chaotic ...
System for Information Encryption Implementing Several Chaotic Orbits
Directory of Open Access Journals (Sweden)
Jiménez-Rodríguez Maricela
2015-07-01
Full Text Available This article proposes a symmetric encryption algorithm that takes, as input value, the original information of length L, that when encoded, generates the ciphertext of greater length LM. A chaotic discrete system (logistic map is implemented to generate 3 different orbits: the first is used for applying a diffusion technique in order to mix the original data, the second orbit is combined with the mixed information and increases the length of L to LM, and with the third orbit, the confusion technique is implemented. The encryption algorithm was applied to encode an image which is then totally recovered by the keys used to encrypt and his respective, decrypt algorithm. The algorithm can encode any information, just dividing into 8 bits, it can cover the requirements for high level security, it uses 7 keys to encrypt and provides good encryption speed
International Nuclear Information System (INIS)
Hu Manfeng; Xu Zhenyuan; Zhang Rong; Hu Aihua
2007-01-01
This Letter further investigates the full state hybrid projective synchronization (FSHPS) of chaotic and hyper-chaotic systems with fully unknown parameters. Based on the Lyapunov stability theory, a unified adaptive controller and parameters update law can be designed for achieving the FSHPS of chaotic and/or hyper-chaotic systems with the same and different order. Especially, for two chaotic systems with different order, reduced order MFSHPS (an acronym for modified full state hybrid projective synchronization) and increased order MFSHPS are first studied in this Letter. Five groups numerical simulations are provided to verify the effectiveness of the proposed scheme. In addition, the proposed FSHPS scheme is quite robust against the effect of noise
Adaptive observer based synchronization of a class of uncertain chaotic systems
International Nuclear Information System (INIS)
Bowong, S.; Yamapi, R.
2005-05-01
This study addresses the adaptive synchronization of a class of uncertain chaotic systems in the drive-response framework. For a class of uncertain chaotic systems with unknown parameters and external disturbances, a robust adaptive observer based response system is constructed to synchronize the uncertain chaotic system. Lyapunov stability theory and Barbalat lemma ensure the global synchronization between the drive and response systems even if Lipschitz constants on function matrices and bounds on uncertainties are unknown. Numerical simulation of the Genesio-Tesi system verifies the effectiveness of the proposed method. (author)
Analysis of transition between chaos and hyper-chaos of an improved hyper-chaotic system
International Nuclear Information System (INIS)
Qiao-Lun, Gu; Tie-Gang, Gao
2009-01-01
An improved hyper-chaotic system based on the hyper-chaos generated from Chen's system is presented, and some basic dynamical properties of the system are investigated by means of Lyapunov exponent spectrum, bifurcation diagrams and characteristic equation roots. Simulations show that the new improved system evolves into hyper-chaotic, chaotic, various quasi-periodic or periodic orbits when one parameter of the system is fixed to be a certain value while the other one is variable. Some computer simulations and bifurcation analyses are given to testify the findings. (general)
Generalized Combination Complex Synchronization for Fractional-Order Chaotic Complex Systems
Directory of Open Access Journals (Sweden)
Cuimei Jiang
2015-07-01
Full Text Available Based on two fractional-order chaotic complex drive systems and one fractional-order chaotic complex response system with different dimensions, we propose generalized combination complex synchronization. In this new synchronization scheme, there are two complex scaling matrices that are non-square matrices. On the basis of the stability theory of fractional-order linear systems, we design a general controller via active control. Additionally, by virtue of two complex scaling matrices, generalized combination complex synchronization between fractional-order chaotic complex systems and real systems is investigated. Finally, three typical examples are given to demonstrate the effectiveness and feasibility of the schemes.
Fractional order fuzzy control of hybrid power system with renewable generation using chaotic PSO.
Pan, Indranil; Das, Saptarshi
2016-05-01
This paper investigates the operation of a hybrid power system through a novel fuzzy control scheme. The hybrid power system employs various autonomous generation systems like wind turbine, solar photovoltaic, diesel engine, fuel-cell, aqua electrolyzer etc. Other energy storage devices like the battery, flywheel and ultra-capacitor are also present in the network. A novel fractional order (FO) fuzzy control scheme is employed and its parameters are tuned with a particle swarm optimization (PSO) algorithm augmented with two chaotic maps for achieving an improved performance. This FO fuzzy controller shows better performance over the classical PID, and the integer order fuzzy PID controller in both linear and nonlinear operating regimes. The FO fuzzy controller also shows stronger robustness properties against system parameter variation and rate constraint nonlinearity, than that with the other controller structures. The robustness is a highly desirable property in such a scenario since many components of the hybrid power system may be switched on/off or may run at lower/higher power output, at different time instants. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
Empirically characteristic analysis of chaotic PID controlling particle swarm optimization.
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.
Parametric Control on Fractional-Order Response for Lü Chaotic System
Moaddy, K; Radwan, A G; Salama, Khaled N.; Momani, S; Hashim, I
2013-01-01
This paper discusses the influence of the fractional order parameter on conventional chaotic systems. These fractional-order parameters increase the system degree of freedom allowing it to enter new domains and thus it can be used as a control for such dynamical systems. This paper investigates the behaviour of the equally-fractional-order Lü chaotic system when changing the fractional-order parameter and determines the fractional-order ranges for chaotic behaviour. Five different parameter values and six fractional-order cases are discussed through this paper. Unlike the conventional parameters, as the fractional-order increases the system response begins with stability, passing by chaotic behaviour then reaches periodic response. As the system parameter α increases, a shift in the fractional order is required to maintain chaotic response.Therefore, the range of chaotic response can be expanded or minimized by controlling the fractional-order parameter. The non-standard finite difference method is used to solve the fractional-order Lü chaotic system numerically to validate these responses.
Parametric Control on Fractional-Order Response for Lü Chaotic System
Moaddy, K
2013-04-10
This paper discusses the influence of the fractional order parameter on conventional chaotic systems. These fractional-order parameters increase the system degree of freedom allowing it to enter new domains and thus it can be used as a control for such dynamical systems. This paper investigates the behaviour of the equally-fractional-order Lü chaotic system when changing the fractional-order parameter and determines the fractional-order ranges for chaotic behaviour. Five different parameter values and six fractional-order cases are discussed through this paper. Unlike the conventional parameters, as the fractional-order increases the system response begins with stability, passing by chaotic behaviour then reaches periodic response. As the system parameter α increases, a shift in the fractional order is required to maintain chaotic response.Therefore, the range of chaotic response can be expanded or minimized by controlling the fractional-order parameter. The non-standard finite difference method is used to solve the fractional-order Lü chaotic system numerically to validate these responses.
Adaptive control of chaotic systems with stochastic time varying unknown parameters
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, Azadi Avenue, 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, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: aalasti@sharif.edu
2008-10-15
In this paper based on the Lyapunov stability theorem, an adaptive control scheme is proposed for stabilizing the unstable periodic orbits (UPO) of chaotic systems. It is assumed that the chaotic system has some linearly dependent unknown parameters which are stochastically time varying. The stochastic parameters are modeled through the Weiner process derivative. To demonstrate the effectiveness of the proposed technique it has been applied to the Lorenz, Chen and Rossler dynamical systems, as some case studies. Simulation results indicate that the proposed adaptive controller has a high performance in stabilizing the UPO of chaotic systems in noisy environment.
Parameter and state estimation of experimental chaotic systems using synchronization
Quinn, John C.; Bryant, Paul H.; Creveling, Daniel R.; Klein, Sallee R.; Abarbanel, Henry D. I.
2009-07-01
We examine the use of synchronization as a mechanism for extracting parameter and state information from experimental systems. We focus on important aspects of this problem that have received little attention previously and we explore them using experiments and simulations with the chaotic Colpitts oscillator as an example system. We explore the impact of model imperfection on the ability to extract valid information from an experimental system. We compare two optimization methods: an initial value method and a constrained method. Each of these involves coupling the model equations to the experimental data in order to regularize the chaotic motions on the synchronization manifold. We explore both time-dependent and time-independent coupling and discuss the use of periodic impulse coupling. We also examine both optimized and fixed (or manually adjusted) coupling. For the case of an optimized time-dependent coupling function u(t) we find a robust structure which includes sharp peaks and intervals where it is zero. This structure shows a strong correlation with the location in phase space and appears to depend on noise, imperfections of the model, and the Lyapunov direction vectors. For time-independent coupling we find the counterintuitive result that often the optimal rms error in fitting the model to the data initially increases with coupling strength. Comparison of this result with that obtained using simulated data may provide one measure of model imperfection. The constrained method with time-dependent coupling appears to have benefits in synchronizing long data sets with minimal impact, while the initial value method with time-independent coupling tends to be substantially faster, more flexible, and easier to use. We also describe a method of coupling which is useful for sparse experimental data sets. Our use of the Colpitts oscillator allows us to explore in detail the case of a system with one positive Lyapunov exponent. The methods we explored are easily
Synchronization of the unified chaotic systems using a sliding mode controller
International Nuclear Information System (INIS)
Zribi, Mohamed; Smaoui, Nejib; Salim, Haitham
2009-01-01
The unified chaotic system incorporates the behaviors of the Lorenz, the Chen and the Lue chaotic systems. This paper deals with the synchronization of two identical unified chaotic systems where the slave system is assumed to have a single input. A sliding mode controller is proposed to synchronize the two systems. The asymptotic convergence to zero of the errors between the states of the master and the slave systems is shown. Simulations results are presented to illustrate the proposed controller; they indicate that the designed controller is able to synchronize the unified chaotic systems. Also, simulation results show that the proposed control scheme is robust to random bounded disturbances acting on the master system. Moreover, the proposed scheme is applied to the secure communications field, where simulation results indicate that the proposed scheme is effective.
Chaos Q-S synchronization between Rossler system and the new unified chaotic system
International Nuclear Information System (INIS)
Yan Zhenya
2005-01-01
In this Letter, we investigate the Q-S synchronization between two different chaotic systems: the Rossler system and the new unified Lorenz-Chen-Lu system based on the backstepping design method and Lyapunov stability theory. Moreover numerical simulations are used to verify the effectiveness of the proposed controller
Modelling of long-wave chaotic radar system for anti-stealth applications
Al-Suhail, Ghaida A.; Tahir, Fadhil Rahma; Abd, Mariam Hussien; Pham, Viet-Thanh; Fortuna, Luigi
2018-04-01
Although the Very Low-Frequency (VLF) waveforms have limited practical applications in acoustics (sonar) and secure military communications with radars and submarines; to this end; this paper presents a new and simple analytical model of VLF monostatic direct chaotic radar system. The model hypothetically depends on the two identical coupled time-delayed feedback chaotic systems which can generate and recover a long-wave chaotic signal. To resist the influence of positive Lyapunov exponents of the time-delay chaotic systems, the complete replacement of Pecaro and Carroll (PC) synchronization is employed. It can faithfully recover the chaotic signal from the back-scattered (echo) signal from the target over a noisy channel. The system performance is characterized in terms of the time series of synchronization in addition to the peak of the cross-correlation. Simulation results are conducted for substantial sensitivities of the chaotic signal to the system parameters and initial conditions. As a result, it is found that an effective and robust chaotic radar (CRADAR) model can be obtained when the signal-to-noise ratio (SNR) highly degrades to 0 dB, but with clear peak in correlation performance for detecting the target. Then, the model can be considered as a state of the art towards counter stealth technology and might be developed for other acoustic secure applications.
Robust networked H∞ synchronization of nonidentical chaotic Lur'e systems
International Nuclear Information System (INIS)
Yang De-Dong
2014-01-01
We mainly investigate the robust networked H ∞ synchronization problem of nonidentical chaotic Lur'e systems. In the design of the synchronization scheme, some network characteristics, such as nonuniform sampling, transmission-induced delays, and data packet dropouts, are considered. The parameters of master—slave chaotic Lur'e systems often allow differences. The sufficient condition in terms of linear matrix inequality (LMI) is obtained to guarantee the dissipative synchronization of nonidentical chaotic Lur'e systems in network environments. A numerical example is given to illustrate the validity of the proposed method. (general)
Directory of Open Access Journals (Sweden)
Cheng-Hsiung Yang
2013-01-01
Full Text Available A new symplectic chaos synchronization of chaotic systems with uncertain chaotic parameters is studied. The traditional chaos synchronizations are special cases of the symplectic chaos synchronization. A sufficient condition is given for the asymptotical stability of the null solution of error dynamics and a parameter difference. The symplectic chaos synchronization with uncertain chaotic parameters may be applied to the design of secure communication systems. Finally, numerical results are studied for symplectic chaos synchronized from two identical Lorenz-Stenflo systems in three different cases.
Development of adaptive control applied to chaotic systems
Rhode, Martin Andreas
1997-12-01
Continuous-time derivative control and adaptive map-based recursive feedback control techniques are used to control chaos in a variety of systems and in situations that are of practical interest. The theoretical part of the research includes the review of fundamental concept of control theory in the context of its applications to deterministic chaotic systems, the development of a new adaptive algorithm to identify the linear system properties necessary for control, and the extension of the recursive proportional feedback control technique, RPF, to high dimensional systems. Chaos control was applied to models of a thermal pulsed combustor, electro-chemical dissolution and the hyperchaotic Rossler system. Important implications for combustion engineering were suggested by successful control of the model of the thermal pulsed combustor. The system was automatically tracked while maintaining control into regions of parameter and state space where no stable attractors exist. In a simulation of the electrochemical dissolution system, application of derivative control to stabilize a steady state, and adaptive RPF to stabilize a period one orbit, was demonstrated. The high dimensional adaptive control algorithm was applied in a simulation using the Rossler hyperchaotic system, where a period-two orbit with two unstable directions was stabilized and tracked over a wide range of a system parameter. In the experimental part, the electrochemical system was studied in parameter space, by scanning the applied potential and the frequency of the rotating copper disk. The automated control algorithm is demonstrated to be effective when applied to stabilize a period-one orbit in the experiment. We show the necessity of small random perturbations applied to the system in order to both learn the dynamics and control the system at the same time. The simultaneous learning and control capability is shown to be an important part of the active feedback control.
Estimating model parameters in nonautonomous chaotic systems using synchronization
International Nuclear Information System (INIS)
Yang, Xiaoli; Xu, Wei; Sun, Zhongkui
2007-01-01
In this Letter, a technique is addressed for estimating unknown model parameters of multivariate, in particular, nonautonomous chaotic systems from time series of state variables. This technique uses an adaptive strategy for tracking unknown parameters in addition to a linear feedback coupling for synchronizing systems, and then some general conditions, by means of the periodic version of the LaSalle invariance principle for differential equations, are analytically derived to ensure precise evaluation of unknown parameters and identical synchronization between the concerned experimental system and its corresponding receiver one. Exemplifies are presented by employing a parametrically excited 4D new oscillator and an additionally excited Ueda oscillator. The results of computer simulations reveal that the technique not only can quickly track the desired parameter values but also can rapidly respond to changes in operating parameters. In addition, the technique can be favorably robust against the effect of noise when the experimental system is corrupted by bounded disturbance and the normalized absolute error of parameter estimation grows almost linearly with the cutoff value of noise strength in simulation
Why do Reservoir Computing Networks Predict Chaotic Systems so Well?
Lu, Zhixin; Pathak, Jaideep; Girvan, Michelle; Hunt, Brian; Ott, Edward
Recently a new type of artificial neural network, which is called a reservoir computing network (RCN), has been employed to predict the evolution of chaotic dynamical systems from measured data and without a priori knowledge of the governing equations of the system. The quality of these predictions has been found to be spectacularly good. Here, we present a dynamical-system-based theory for how RCN works. Basically a RCN is thought of as consisting of three parts, a randomly chosen input layer, a randomly chosen recurrent network (the reservoir), and an output layer. The advantage of the RCN framework is that training is done only on the linear output layer, making it computationally feasible for the reservoir dimensionality to be large. In this presentation, we address the underlying dynamical mechanisms of RCN function by employing the concepts of generalized synchronization and conditional Lyapunov exponents. Using this framework, we propose conditions on reservoir dynamics necessary for good prediction performance. By looking at the RCN from this dynamical systems point of view, we gain a deeper understanding of its surprising computational power, as well as insights on how to design a RCN. Supported by Army Research Office Grant Number W911NF1210101.
Multimedia Security Application of a Ten-Term Chaotic System without Equilibrium
Directory of Open Access Journals (Sweden)
Xiong Wang
2017-01-01
Full Text Available A system without equilibrium has been proposed in this work. Although there is an absence of equilibrium points, the system displays chaos, which has been confirmed by phase portraits and Lyapunov exponents. The system is realized on an electronic card, which exhibits chaotic signals. Furthermore, chaotic property of the system is applied in multimedia security such as image encryption and sound steganography.
Stabilizing periodic orbits of chaotic systems using fuzzy control of Poincare map
International Nuclear Information System (INIS)
Bonakdar, Mohammad; Samadi, Mostafa; Salarieh, Hassan; Alasty, Aria
2008-01-01
In this paper a fuzzy control algorithm is used to stabilize the fixed points of a chaotic system. No knowledge of the dynamic equations of the system is needed in this approach and the whole system is considered as a black box. Two main approaches have been investigated: fuzzy clustering and table look up methods. As illustrative examples these methods have been applied to Bonhoeffer van der Pol oscillator and the Henon chaotic system and the convergence toward fixed points is observed
Stabilizing periodic orbits of chaotic systems using fuzzy control of Poincare map
Energy Technology Data Exchange (ETDEWEB)
Bonakdar, Mohammad; Samadi, Mostafa [Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, 1458889694 Tehran (Iran, Islamic Republic of); Salarieh, Hassan [Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, 1458889694 Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, 1458889694 Tehran (Iran, Islamic Republic of)
2008-05-15
In this paper a fuzzy control algorithm is used to stabilize the fixed points of a chaotic system. No knowledge of the dynamic equations of the system is needed in this approach and the whole system is considered as a black box. Two main approaches have been investigated: fuzzy clustering and table look up methods. As illustrative examples these methods have been applied to Bonhoeffer van der Pol oscillator and the Henon chaotic system and the convergence toward fixed points is observed.
Lag synchronization of chaotic systems with time-delayed linear ...
Indian Academy of Sciences (India)
delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differen- tial equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic ...
Analytical-Algebraic Approach to Solving Chaotic System
Czech Academy of Sciences Publication Activity Database
Beran, Zdeněk; Čelikovský, Sergej
2016-01-01
Roč. 26, č. 3 (2016), č. článku 1650051. ISSN 0218-1274 R&D Projects: GA ČR GA13-20433S Institutional support: RVO:67985556 Keywords : Laplace transform * Laplace-Adomian decomposition * Adomian polynomials * nonlinear systems * chaos Subject RIV: BC - Control Systems Theory Impact factor: 1.329, year: 2016 http://library.utia.cas.cz/separaty/2016/TR/beran-0458430.pdf
A controllability approach to the control of a class of chaotic systems
International Nuclear Information System (INIS)
Bowong, Samuel; Moukam Kakmeni, F.M.; Tchawoua, Clement; Abdus Salam International Centre for Theoretical Physics, Trieste
2003-10-01
In this paper the exponential control problem for a class of chaotic systems with affine dependence on the control is addressed and solved by the controllability approach. It is shown that the controllability approach in conjunction with Lyapunov Direct Method yields a promising way of controlling chaotic dynamics. The proposed strategy is an input-output control scheme which comprises a state estimator and an exponential linearizing feedback. The proposed output feedback controller allows chaos suppression and can be applied to a large class of chaotic systems. Explicit expression of the control time is given. Computer simulations confirm the feasibility of the proposed approach. (author)
International Nuclear Information System (INIS)
Krysko, A.V.; Awrejcewicz, J.; Papkova, I.V.; Krysko, V.A.
2012-01-01
In second part of the paper both classical and novel scenarios of transition from regular to chaotic dynamics of dissipative continuous mechanical systems are studied. A detailed analysis allowed us to detect the already known classical scenarios of transition from periodic to chaotic dynamics, and in particular the Feigenbaum scenario. The Feigenbaum constant was computed for all continuous mechanical objects studied in the first part of the paper. In addition, we illustrate and discuss different and novel scenarios of transition of the analysed systems from regular to chaotic dynamics, and we show that the type of scenario depends essentially on excitation parameters.
International Nuclear Information System (INIS)
Santos Coelho, Leandro dos
2009-01-01
Despite the popularity, the tuning aspect of proportional-integral-derivative (PID) controllers is a challenge for researchers and plant operators. Various controllers tuning methodologies have been proposed in the literature such as auto-tuning, self-tuning, pattern recognition, artificial intelligence, and optimization methods. Chaotic optimization algorithms as an emergent method of global optimization have attracted much attention in engineering applications. Chaotic optimization algorithms, which have the features of easy implementation, short execution time and robust mechanisms of escaping from local optimum, is a promising tool for engineering applications. In this paper, a tuning method for determining the parameters of PID control for an automatic regulator voltage (AVR) system using a chaotic optimization approach based on Lozi map is proposed. Since chaotic mapping enjoys certainty, ergodicity and the stochastic property, the proposed chaotic optimization introduces chaos mapping using Lozi map chaotic sequences which increases its convergence rate and resulting precision. Simulation results are promising and show the effectiveness of the proposed approach. Numerical simulations based on proposed PID control of an AVR system for nominal system parameters and step reference voltage input demonstrate the good performance of chaotic optimization.
Finite-Time Synchronization of Chaotic Systems with Different Dimension and Secure Communication
Directory of Open Access Journals (Sweden)
Shouquan Pang
2016-01-01
Full Text Available Finite-time synchronization of chaotic systems with different dimension and secure communication is investigated. It is rigorously proven that global finite-time synchronization can be achieved between three-dimension Lorenz chaotic system and four-dimension Lorenz hyperchaotic system which have certain parameters or uncertain parameters. The electronic circuits of finite-time synchronization using Multisim 12 are designed to verify our conclusion. And the application to the secure communications is also analyzed and discussed.
Directory of Open Access Journals (Sweden)
Y. Saiki
2007-09-01
Full Text Available An infinite number of unstable periodic orbits (UPOs are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chaotic systems have been proposed. In this article the damped Newton-Raphson-Mees algorithm is reviewed, and some important techniques and remarks concerning the practical numerical computations are exemplified by employing the Lorenz system.
Directory of Open Access Journals (Sweden)
Ping Zhou
2012-01-01
Full Text Available The unstable equilibrium points of the fractional-order Lorenz chaotic system can be controlled via fractional-order derivative, and chaos synchronization for the fractional-order Lorenz chaotic system can be achieved via fractional-order derivative. The control and synchronization technique, based on stability theory of fractional-order systems, is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed method.
Adaptive fuzzy observer based synchronization design and secure communications of chaotic systems
International Nuclear Information System (INIS)
Hyun, Chang-Ho; Kim, Jae-Hun; Kim, Euntai; Park, Mignon
2006-01-01
This paper proposes a synchronization design scheme based on an alternative indirect adaptive fuzzy observer and its application to secure communication of chaotic systems. It is assumed that their states are unmeasurable and their parameters are unknown. Chaotic systems and the structure of the fuzzy observer are represented by the Takagi-Sugeno fuzzy model. Using Lyapunov stability theory, an adaptive law is derived to estimate the unknown parameters and the stability of the proposed system is guaranteed. Through this process, the asymptotic synchronization of chaotic systems is achieved. The proposed observer is applied to secure communications of chaotic systems and some numerical simulation results show the validity of theoretical derivations and the performance of the proposed observer
Is Cygus X-1 a chaotic dynamical system?
International Nuclear Information System (INIS)
Unno, Wasaburo; Yoneyama, Tadaoki; Urata, Kenji; Masaki, Isao; Kondo, Masa-aki; Inoue, Hajime.
1990-01-01
X-ray data of Cyg X-1 observed by the Tenma satellite were analyzed to determine whether Cyg X-1 is a chaotic dynamical system of low dimension. Since Poisson noise disturbs the determination of the attractor dimension of the system, comparative studies were carried out for the Cyg X-1 data relative to artificial data of purely stochastic Poisson noise and to a Lorenz attractor plus noise. The attractor dimension was searched using trajectories of time series data in phase space, the dimension of which was varied up to 21. The relation between the attractor dimension and the phase-space dimension for the Cyg X-1 data starts to deviate from that of noise data from a phase-space dimension of about 7, showing the presence of an attractor with a dimension of about 7 or less. Though three positive Lyapunov exponents were calculated, they are too small (∼10 -2 ) to prove with certainty that the Cyg X-1 attractor should be a strange attractor. (author)
Delayed feedback control of fractional-order chaotic systems
International Nuclear Information System (INIS)
Gjurchinovski, A; Urumov, V; Sandev, T
2010-01-01
We study the possibility to stabilize unstable steady states and unstable periodic orbits in chaotic fractional-order dynamical systems by the time-delayed feedback method. By performing a linear stability analysis, we establish the parameter ranges for successful stabilization of unstable equilibria in the plane parameterized by the feedback gain and the time delay. An insight into the control mechanism is gained by analyzing the characteristic equation of the controlled system, showing that the control scheme fails to control unstable equilibria having an odd number of positive real eigenvalues. We demonstrate that the method can also stabilize unstable periodic orbits for a suitable choice of the feedback gain, providing that the time delay is chosen to coincide with the period of the target orbit. In addition, it is shown numerically that delayed feedback control with a sinusoidally modulated time delay significantly enlarges the stability region of steady states in comparison to the classical time-delayed feedback scheme with a constant delay.
On the synchronization of a class of chaotic systems based on backstepping method
International Nuclear Information System (INIS)
Wang Bo; Wen Guangjun
2007-01-01
This Letter focuses on the synchronization problem of a class of chaotic systems. A synchronization method is presented based on Lyapunov method and backstepping method. Finally some typical numerical examples are given to show the effectiveness of the theoretical results
Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale
International Nuclear Information System (INIS)
Maslennikov, Oleg V.; Nekorkin, Vladimir I.
2016-01-01
In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.
Synchronization in Complex Networks of Nonlinear Dynamical Systems
Wu, Chai Wah
2007-01-01
This book brings together two emerging research areas: synchronization in coupled nonlinear systems and complex networks, and study conditions under which a complex network of dynamical systems synchronizes. While there are many texts that study synchronization in chaotic systems or properties of complex networks, there are few texts that consider the intersection of these two very active and interdisciplinary research areas. The main theme of this book is that synchronization conditions can be related to graph theoretical properties of the underlying coupling topology. The book introduces ide
Qiu, Junchao; Zhang, Lin; Li, Diyang; Liu, Xingcheng
2016-06-01
Chaotic sequences can be applied to realize multiple user access and improve the system security for a visible light communication (VLC) system. However, since the map patterns of chaotic sequences are usually well known, eavesdroppers can possibly derive the key parameters of chaotic sequences and subsequently retrieve the information. We design an advanced encryption standard (AES) interleaving aided multiple user access scheme to enhance the security of a chaotic code division multiple access-based visible light communication (C-CDMA-VLC) system. We propose to spread the information with chaotic sequences, and then the spread information is interleaved by an AES algorithm and transmitted over VLC channels. Since the computation complexity of performing inverse operations to deinterleave the information is high, the eavesdroppers in a high speed VLC system cannot retrieve the information in real time; thus, the system security will be enhanced. Moreover, we build a mathematical model for the AES-aided VLC system and derive the theoretical information leakage to analyze the system security. The simulations are performed over VLC channels, and the results demonstrate the effectiveness and high security of our presented AES interleaving aided chaotic CDMA-VLC system.
Investigation of a Unified Chaotic System and Its Synchronization by Simulations
International Nuclear Information System (INIS)
Qing-Chu, Wu; Xin-Chu, Fu; Small, Michael
2010-01-01
We investigate a unified chaotic system and its synchronization including feedback synchronization and adaptive synchronization by numerical simulations. We propose a new dynamical quantity denoted by K, which connects adaptive synchronization and feedback synchronization, to analyze synchronization schemes. We find that K can estimate the smallest coupling strength for a unified chaotic system whether it is complete feedback or one-sided feedback. Based on the previous work, we also give a new dynamical method to compute the leading Lyapunov exponent. (general)
Synchronization of Different Fractional Order Time-Delay Chaotic Systems Using Active Control
Directory of Open Access Journals (Sweden)
Jianeng Tang
2014-01-01
Full Text Available Chaos synchronization of different fractional order time-delay chaotic systems is considered. Based on the Laplace transform theory, the conditions for achieving synchronization of different fractional order time-delay chaotic systems are analyzed by use of active control technique. Then numerical simulations are provided to verify the effectiveness and feasibility of the developed method. At last, effects of the fraction order and the time delay on synchronization are further researched.
International Nuclear Information System (INIS)
Chen, H.-H.; Chen, C.-S.; Lee, C.-I
2009-01-01
This paper investigates the synchronization of unidirectional and bidirectional coupled unified chaotic systems. A balanced coupling coefficient control method is presented for global asymptotic synchronization using the Lyapunov stability theorem and a minimum scheme with no constraints/constraints. By using the result of the above analysis, the balanced coupling coefficients are then designed to achieve the chaos synchronization of linearly coupled unified chaotic systems. The feasibility and effectiveness of the proposed chaos synchronization scheme are verified via numerical simulations.
Function Projective Synchronization in Discrete-Time Chaotic System with Uncertain Parameters
International Nuclear Information System (INIS)
Chen Yong; Li Xin
2009-01-01
The function projective synchronization of discrete-time chaotic systems is presented. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate function projective synchronization (FPS) of discrete-time chaotic systems with uncertain parameters. With the aid of symbolic-numeric computation, we use the proposed scheme to illustrate FPS between two identical 3D Henon-like maps with uncertain parameters. Numeric simulations are used to verify the effectiveness of our scheme. (general)
Exact Recovery of Chaotic Systems from Highly Corrupted Data
2016-08-01
dimension to reconstruct a state space which preserves the topological properties of the original system. In [CM87, RS92], the authors use the singular...in high dimensional nonlinear functional spaces [Spr94, SL00, LCC04]. In this work, we bring together connections between compressed sensing, splitting... compact , connected attractor Λ and the flow admits a unique so-called “physical" measure µ with supp(µ) = Λ. An invariant probability measure µ for a flow
Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems
International Nuclear Information System (INIS)
Yau, H.-T.; Chen, C.-L.
2006-01-01
This paper proposes a chattering-free fuzzy sliding-mode control (FSMC) strategy for uncertain chaotic systems. A fuzzy logic control is used to replace the discontinuous sign function of the reaching law in traditional sliding-mode control (SMC), and hence a control input without chattering is obtained in the chaotic systems with uncertainties. Base on the Lyapunov stability theory, we address the design schemes of integration fuzzy sliding-mode control, where the reaching law is proposed by a set of linguistic rules and the control input is chattering free. The Genesio chaotic system is used to test the proposed control strategy and the simulation results show the FSMC not only can control the uncertain chaotic behaviors to a desired state without oscillator very fast, but also the switching function is smooth without chattering. This result implies that this strategy is feasible and effective for chaos control
A one-time pad color image cryptosystem based on SHA-3 and multiple chaotic systems
Wang, Xingyuan; Wang, Siwei; Zhang, Yingqian; Luo, Chao
2018-04-01
A novel image encryption algorithm is proposed that combines the SHA-3 hash function and two chaotic systems: the hyper-chaotic Lorenz and Chen systems. First, 384 bit keystream hash values are obtained by applying SHA-3 to plaintext. The sensitivity of the SHA-3 algorithm and chaotic systems ensures the effect of a one-time pad. Second, the color image is expanded into three-dimensional space. During permutation, it undergoes plane-plane displacements in the x, y and z dimensions. During diffusion, we use the adjacent pixel dataset and corresponding chaotic value to encrypt each pixel. Finally, the structure of alternating between permutation and diffusion is applied to enhance the level of security. Furthermore, we design techniques to improve the algorithm's encryption speed. Our experimental simulations show that the proposed cryptosystem achieves excellent encryption performance and can resist brute-force, statistical, and chosen-plaintext attacks.
International Nuclear Information System (INIS)
Ghasemi, Mojtaba; Ghavidel, Sahand; Aghaei, Jamshid; Gitizadeh, Mohsen; Falah, Hasan
2014-01-01
Highlights: • Chaotic invasive weed optimization techniques based on chaos. • Nonlinear environmental OPF problem considering non-smooth fuel cost curves. • A comparative study of CIWO techniques for environmental OPF problem. - Abstract: This paper presents efficient chaotic invasive weed optimization (CIWO) techniques based on chaos for solving optimal power flow (OPF) problems with non-smooth generator fuel cost functions (non-smooth OPF) with the minimum pollution level (environmental OPF) in electric power systems. OPF problem is used for developing corrective strategies and to perform least cost dispatches. However, cost based OPF problem solutions usually result in unattractive system gaze emission issue (environmental OPF). In the present paper, the OPF problem is formulated by considering the emission issue. The total emission can be expressed as a non-linear function of power generation, as a multi-objective optimization problem, where optimal control settings for simultaneous minimization of fuel cost and gaze emission issue are obtained. The IEEE 30-bus test power system is presented to illustrate the application of the environmental OPF problem using CIWO techniques. Our experimental results suggest that CIWO techniques hold immense promise to appear as efficient and powerful algorithm for optimization in the power systems
Chaotic structure of oil prices
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.
Improving performance of DS-CDMA systems using chaotic complex Bernoulli spreading codes
Farzan Sabahi, Mohammad; Dehghanfard, Ali
2014-12-01
The most important goal of spreading spectrum communication system is to protect communication signals against interference and exploitation of information by unintended listeners. In fact, low probability of detection and low probability of intercept are two important parameters to increase the performance of the system. In Direct Sequence Code Division Multiple Access (DS-CDMA) systems, these properties are achieved by multiplying the data information in spreading sequences. Chaotic sequences, with their particular properties, have numerous applications in constructing spreading codes. Using one-dimensional Bernoulli chaotic sequence as spreading code is proposed in literature previously. The main feature of this sequence is its negative auto-correlation at lag of 1, which with proper design, leads to increase in efficiency of the communication system based on these codes. On the other hand, employing the complex chaotic sequences as spreading sequence also has been discussed in several papers. In this paper, use of two-dimensional Bernoulli chaotic sequences is proposed as spreading codes. The performance of a multi-user synchronous and asynchronous DS-CDMA system will be evaluated by applying these sequences under Additive White Gaussian Noise (AWGN) and fading channel. Simulation results indicate improvement of the performance in comparison with conventional spreading codes like Gold codes as well as similar complex chaotic spreading sequences. Similar to one-dimensional Bernoulli chaotic sequences, the proposed sequences also have negative auto-correlation. Besides, construction of complex sequences with lower average cross-correlation is possible with the proposed method.
New Chaotic Dynamical System with a Conic-Shaped Equilibrium Located on the Plane Structure
Directory of Open Access Journals (Sweden)
Jiri Petrzela
2017-09-01
Full Text Available This paper presents a new autonomous deterministic dynamical system with equilibrium degenerated into a plane-oriented hyperbolic geometrical structure. It is demonstrated via numerical analysis and laboratory experiments that the discovered system has both a structurally stable strange attractor and experimentally measurable chaotic behavior. It is shown that the evolution of complex dynamics can be associated with a single parameter of a mathematical model and, due to one-to-one correspondence, to a single circuit parameter. Two-dimensional high resolution plots of the largest Lyapunov exponent and basins of attraction expressed in terms of final state energy are calculated and put into the context of the discovered third-order mathematical model and real chaotic oscillator. Both voltage- and current-mode analog chaotic oscillators are presented and verified by visualization of the typical chaotic attractor in a different fashion.
The non-linear paradigm: The climate system as an egg box''
International Nuclear Information System (INIS)
Iversen, Trond
2000-01-01
The article is the last of three dealing with the problems of climatic forecasting. It presents various ways of applying models and points out that regarding the climate system as non-linear and chaotic may be useful for interpreting observations and models. Some applications of the paradigm are presented. The emphasis is on climatic changes due to energy and human activities
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
1993-01-01
The inverse operator method (IOM) for solutions of nonlinear dynamical systems (NDS) is briefly described and realized by the Mathematics-Mechanization (MM) in computers. For the first time IOM and MM are successfully applied to study the chaotic behaviors of Lorentz equation
Inverse chaos synchronization in linearly and nonlinearly coupled systems with multiple time-delays
International Nuclear Information System (INIS)
Shahverdiev, E.M.; Hashimov, R.H.; Nuriev, R.A.; Hashimova, L.H.; Huseynova, E.M.; Shore, K.A.
2005-04-01
We report on inverse chaos synchronization between two unidirectionally linearly and nonlinearly coupled chaotic systems with multiple time-delays and find the existence and stability conditions for different synchronization regimes. We also study the effect of parameter mismatches on synchonization regimes. The method is tested on the famous Ikeda model. Numerical simulations fully support the analytical approach. (author)
Nonlinear signal processing using neural networks: Prediction and system modelling
Energy Technology Data Exchange (ETDEWEB)
Lapedes, A.; Farber, R.
1987-06-01
The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing. We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks. The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing. Simulations are presented that document the additional performance achieved by using nonlinear neural networks. First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method. Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics. Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function. It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series. Furthermore, the neural net seems to be extremely parsimonious in its requirements for data points from the time series. We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps. 24 refs., 13 figs.
Hyperchaos and chaotic hierarchy in low-dimensional chemical systems
Baier, Gerold; Sahle, Sven
1994-06-01
Chemical reaction chains with feedback of one of the products on the source of the chain are considered. A strategy is presented in terms of ordinary differential equations which creates one, two, and three positive Lyapunov exponents as the finite dimension of the system is increased. In particular, a nonlinear inhibition loop in a chemical reaction sequence controls the type of chaos. The bifurcation scenarios are studied and chaos and hyperchaos are found for broad regions of bifurcation parameter. Some implications for the occurrence of higher chaos in real systems are discussed.
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
A simple time-delayed method to control chaotic systems
International Nuclear Information System (INIS)
Chen Maoyin; Zhou Donghua; Shang Yun
2004-01-01
Based on the adaptive iterative learning strategy, a simple time-delayed controller is proposed to stabilize unstable periodic orbits (UPOs) embedded in chaotic attractors. This controller includes two parts: one is a linear feedback part; the other is an adaptive iterative learning estimation part. Theoretical analysis and numerical simulation show the effectiveness of this controller
Studies of nonlinear and chaotic phenomena in solid state systems
Energy Technology Data Exchange (ETDEWEB)
Bryant, P.H.
1987-09-01
This thesis contains three sections discussing different areas. Spin wave interactions in iron garnets are described in section one. Mathematical analysis of a magnetic oscillator is presented in section two. In the final section, the source of noise in Josephson Junctions is investigated. The three sections are indexed separately. (JDH)
Studies of nonlinear and chaotic phenomena in solid state systems
International Nuclear Information System (INIS)
Bryant, P.H.
1987-09-01
This thesis contains three sections discussing different areas. Spin wave interactions in iron garnets are described in section one. Mathematical analysis of a magnetic oscillator is presented in section two. In the final section, the source of noise in Josephson Junctions is investigated. The three sections are indexed separately
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 ...
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
Extreme multistability in a memristor-based multi-scroll hyper-chaotic system
Energy Technology Data Exchange (ETDEWEB)
Yuan, Fang, E-mail: yf210yf@163.com; Wang, Guangyi, E-mail: wanggyi@163.com [Institute of Modern Circuits and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018 (China); Wang, Xiaowei [Department of Automation, Shanghai University, Shanghai 200072 (China)
2016-07-15
In this paper, a new memristor-based multi-scroll hyper-chaotic system is designed. The proposed memristor-based system possesses multiple complex dynamic behaviors compared with other chaotic systems. Various coexisting attractors and hidden coexisting attractors are observed in this system, which means extreme multistability arises. Besides, by adjusting parameters of the system, this chaotic system can perform single-scroll attractors, double-scroll attractors, and four-scroll attractors. Basic dynamic characteristics of the system are investigated, including equilibrium points and stability, bifurcation diagrams, Lyapunov exponents, and so on. In addition, the presented system is also realized by an analog circuit to confirm the correction of the numerical simulations.
Extreme multistability in a memristor-based multi-scroll hyper-chaotic system.
Yuan, Fang; Wang, Guangyi; Wang, Xiaowei
2016-07-01
In this paper, a new memristor-based multi-scroll hyper-chaotic system is designed. The proposed memristor-based system possesses multiple complex dynamic behaviors compared with other chaotic systems. Various coexisting attractors and hidden coexisting attractors are observed in this system, which means extreme multistability arises. Besides, by adjusting parameters of the system, this chaotic system can perform single-scroll attractors, double-scroll attractors, and four-scroll attractors. Basic dynamic characteristics of the system are investigated, including equilibrium points and stability, bifurcation diagrams, Lyapunov exponents, and so on. In addition, the presented system is also realized by an analog circuit to confirm the correction of the numerical simulations.
A universal approach to the study of nonlinear systems
Hwa, Rudolph C.
2004-07-01
A large variety of nonlinear systems have been treated by a common approach that emphasizes the fluctuation of spatial patterns. By using the same method of analysis it is possible to discuss the chaotic behaviors of quark jets and logistic map in the same language. Critical behaviors of quark-hadron phase transition in heavy-ion collisions and of photon production at the threshold of lasing can also be described by a common scaling behavior. The universal approach also makes possible an insight into the recently discovered phenomenon of wind reversal in cryogenic turbulence as a manifestation of self-organized criticality.
International Nuclear Information System (INIS)
Wu Xiangjun; Lu Hongtao
2011-01-01
Highlights: → Adaptive generalized function projective lag synchronization (AGFPLS) is proposed. → Two uncertain chaos systems are lag synchronized up to a scaling function matrix. → The synchronization speed is sensitively influenced by the control gains. → The AGFPLS scheme is robust against noise perturbation. - Abstract: In this paper, a novel projective synchronization scheme called adaptive generalized function projective lag synchronization (AGFPLS) is proposed. In the AGFPLS method, the states of two different chaotic systems with fully uncertain parameters are asymptotically lag synchronized up to a desired scaling function matrix. By means of the Lyapunov stability theory, an adaptive controller with corresponding parameter update rule is designed for achieving AGFPLS between two diverse chaotic systems and estimating the unknown parameters. This technique is employed to realize AGFPLS between uncertain Lue chaotic system and uncertain Liu chaotic system, and between Chen hyperchaotic system and Lorenz hyperchaotic system with fully uncertain parameters, respectively. Furthermore, AGFPLS between two different uncertain chaotic systems can still be achieved effectively with the existence of noise perturbation. The corresponding numerical simulations are performed to demonstrate the validity and robustness of the presented synchronization method.
Robust function projective synchronization of a class of uncertain chaotic systems
International Nuclear Information System (INIS)
Shen Liqun; Liu Wanyu; Ma Jianwei
2009-01-01
In this paper, the function projective synchronization problem of chaotic systems is investigated, where parameter mismatch exists between the drive system and the response system. Based on Lyapunov stability theory, a novel robust function projective synchronization scheme is proposed. And the parameter mismatch problem is also solved. Simulation results of Lorenz system and Chen system verify the effectiveness of the proposed control scheme.
Nonlinear robust hierarchical control for nonlinear uncertain systems
Directory of Open Access Journals (Sweden)
Leonessa Alexander
1999-01-01
Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.
Soliton dynamics in periodic system with different nonlinear media
International Nuclear Information System (INIS)
Zabolotskij, A.A.
2001-01-01
To analyze pulse dynamics in the optical system consisting of periodic sequence of nonlinear media one uses a composition model covering a model of resonance interaction of light ultrashort pulse with energy transition of medium with regard to pumping of the upper level and quasi-integrable model describing propagation of light field in another medium with cubic nonlinearity and dispersion. One additionally takes account of losses and other types of interaction in the from of perturbation members. On the basis of the method of scattering back problem and perturbation theory one developed a simple method to study peculiarities of soliton evolution in such periodic system. Due to its application one managed to describe different modes of soliton evolution in such a system including chaotic dynamics [ru
Directory of Open Access Journals (Sweden)
Hua Wang
2016-01-01
Full Text Available This paper proposes a new fractional-order approach for synchronization of a class of fractional-order chaotic systems in the presence of model uncertainties and external disturbances. A simple but practical method to synchronize many familiar fractional-order chaotic systems has been put forward. A new theorem is proposed for a class of cascade fractional-order systems and it is applied in chaos synchronization. Combined with the fact that the states of the fractional chaotic systems are bounded, many coupled items can be taken as zero items. Then, the whole system can be simplified greatly and a simpler controller can be derived. Finally, the validity of the presented scheme is illustrated by numerical simulations of the fractional-order unified system.
Parameter estimation for chaotic systems with a Drift Particle Swarm Optimization method
International Nuclear Information System (INIS)
Sun Jun; Zhao Ji; Wu Xiaojun; Fang Wei; Cai Yujie; Xu Wenbo
2010-01-01
Inspired by the motion of electrons in metal conductors in an electric field, we propose a variant of Particle Swarm Optimization (PSO), called Drift Particle Swarm Optimization (DPSO) algorithm, and apply it in estimating the unknown parameters of chaotic dynamic systems. The principle and procedure of DPSO are presented, and the algorithm is used to identify Lorenz system and Chen system. The experiment results show that for the given parameter configurations, DPSO can identify the parameters of the systems accurately and effectively, and it may be a promising tool for chaotic system identification as well as other numerical optimization problems in physics.
Ndoye, Ibrahima
2014-12-01
In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown parameters are also adapted to their values. Sufficient conditions for the stability of the adaptive observer error dynamics are derived in terms of linear matrix inequalities. Simulation results for chaotic Lorenz systems with unknown parameters in the presence of external perturbations are given to illustrate the effectiveness of our proposed approach. © 2014 IEEE.
Synchronizing strict-feedback and general strict-feedback chaotic systems via a single controller
International Nuclear Information System (INIS)
Chen Shihua; Wang Feng; Wang Changping
2004-01-01
We present a systematic design procedure to synchronize a class of chaotic systems in a so-called strict-feedback form based on back-stepping procedure. This approach needs only a single controller to realize synchronization no matter how many dimensions the chaotic system contains. Furthermore, we point out that the method does not work for general strict-feedback chaotic systems, for instance, Lorenz system. Therefore, we propose three kinds of synchronization schemes for Lorenz system using the Lyapunov function method. All the three schemes avoid including divergence factor as in Ref. [Chaos, Solitons and Fractals 16 (2003) 37]. Especially in the last two schemes, we need only one state variable in controller, which has important significance in chaos synchronization used for communication purposes. Finally numerical simulations are provided to show the effectiveness and feasibility of the developed methods
Nonlinear transport of dynamic system phase space
International Nuclear Information System (INIS)
Xie Xi; Xia Jiawen
1993-01-01
The inverse transform of any order solution of the differential equation of general nonlinear dynamic systems is derived, realizing theoretically the nonlinear transport for the phase space of nonlinear dynamic systems. The result is applicable to general nonlinear dynamic systems, with the transport of accelerator beam phase space as a typical example
A Novel Type of Chaotic Attractor for Quadratic Systems Without Equilibriums
Dantsev, Danylo
In this paper, a new chaotic dynamic system without equilibriums is presented. A conducted research of the qualitative properties of the discovered system reveals a noncompliance between the bifurcation behavior of the system and the Feigenbaum-Sharkovskii-Magnitsky theory. Additional research of known systems confirms the discrepancy.
Synchronization of Harb-Zohdy Chaotic System via Back-Stepping Design
Directory of Open Access Journals (Sweden)
M. R. Shamsyeh Zahedi∗
2015-12-01
Full Text Available This paper is concerned with the problem of synchronization of the Harb-Zohdy chaotic system using the back-stepping. Based on the stability theory, the control for the synchronization of chaotic systems Harb-Zohdy is considered without unknown parameters. Next, an adaptive back-stepping control law is derived to generate an error signal between the drive and response systems Harb-Zohdy with an uncertain parameter asymptotically synchronized. Finally, this method is extended to synchronize the system with two unknown parameters. Note that the method presented here needs only one controller to realize the synchronization. Numerical simulations indicate the effectiveness of the proposed chaos synchronization scheme
Chaotic incommensurate fractional order Rössler system: active control and synchronization
Directory of Open Access Journals (Sweden)
Baleanu Dumitru
2011-01-01
Full Text Available Abstract In this article, we present an active control methodology for controlling the chaotic behavior of a fractional order version of Rössler system. The main feature of the designed controller is its simplicity for practical implementation. Although in controlling such complex system several inputs are used in general to actuate the states, in the proposed design, all states of the system are controlled via one input. Active synchronization of two chaotic fractional order Rössler systems is also investigated via a feedback linearization method. In both control and synchronization, numerical simulations show the efficiency of the proposed methods.
An image encryption scheme based on three-dimensional Brownian motion and chaotic system
International Nuclear Information System (INIS)
Chai Xiu-Li; Yuan Ke; Gan Zhi-Hua; Lu Yang; Chen Yi-Ran
2017-01-01
At present, many chaos-based image encryption algorithms have proved to be unsafe, few encryption schemes permute the plain images as three-dimensional (3D) bit matrices, and thus bits cannot move to any position, the movement range of bits are limited, and based on them, in this paper we present a novel image encryption algorithm based on 3D Brownian motion and chaotic systems. The architecture of confusion and diffusion is adopted. Firstly, the plain image is converted into a 3D bit matrix and split into sub blocks. Secondly, block confusion based on 3D Brownian motion (BCB3DBM) is proposed to permute the position of the bits within the sub blocks, and the direction of particle movement is generated by logistic-tent system (LTS). Furthermore, block confusion based on position sequence group (BCBPSG) is introduced, a four-order memristive chaotic system is utilized to give random chaotic sequences, and the chaotic sequences are sorted and a position sequence group is chosen based on the plain image, then the sub blocks are confused. The proposed confusion strategy can change the positions of the bits and modify their weights, and effectively improve the statistical performance of the algorithm. Finally, a pixel level confusion is employed to enhance the encryption effect. The initial values and parameters of chaotic systems are produced by the SHA 256 hash function of the plain image. Simulation results and security analyses illustrate that our algorithm has excellent encryption performance in terms of security and speed. (paper)
International Nuclear Information System (INIS)
Shi-Jian, Cang; Zeng-Qiang, Chen; Wen-Juan, Wu
2009-01-01
This paper presents a non-autonomous hyper-chaotic system, which is formed by adding a periodic driving signal to a four-dimensional chaotic model extended from the Lorenz system. The resulting non-autonomous hyper-chaotic system can display any dynamic behaviour among the periodic orbits, intermittency, chaos and hyper-chaos by controlling the frequency of the periodic signal. The phenomenon has been well demonstrated by numerical simulations, bifurcation analysis and electronic circuit realization. Moreover, the system is concrete evidence for the presence of Pomeau–Manneville Type-I intermittency and crisis-induced intermittency. The emergence of a different type of intermittency is similarly subjected to the frequency of periodic forcing. By statistical analysis, power scaling laws consisting in different intermittency are obtained for the lifetime in the laminar state between burst states
Multifractal chaotic attractors in a system of delay-differential equations modeling road traffic.
Safonov, Leonid A.; Tomer, Elad; Strygin, Vadim V.; Ashkenazy, Yosef; Havlin, Shlomo
2002-12-01
We study a system of delay-differential equations modeling single-lane road traffic. The cars move in a closed circuit and the system's variables are each car's velocity and the distance to the car ahead. For low and high values of traffic density the system has a stable equilibrium solution, corresponding to the uniform flow. Gradually decreasing the density from high to intermediate values we observe a sequence of supercritical Hopf bifurcations forming multistable limit cycles, corresponding to flow regimes with periodically moving traffic jams. Using an asymptotic technique we find approximately small limit cycles born at Hopf bifurcations and numerically preform their global continuations with decreasing density. For sufficiently large delay the system passes to chaos following the Ruelle-Takens-Newhouse scenario (limit cycles-two-tori-three-tori-chaotic attractors). We find that chaotic and nonchaotic attractors coexist for the same parameter values and that chaotic attractors have a broad multifractal spectrum. (c) 2002 American Institute of Physics.
International Nuclear Information System (INIS)
Yang Dong-Sheng; Liu Zhen-Wei; Liu Zhao-Bing; Zhao Yan
2012-01-01
The networked synchronization problem of a class of master-slave chaotic systems with time-varying communication topologies is investigated in this paper. Based on algebraic graph theory and matrix theory, a simple linear state feedback controller is designed to synchronize the master chaotic system and the slave chaotic systems with a time-varying communication topology connection. The exponential stability of the closed-loop networked synchronization error system is guaranteed by applying Lyapunov stability theory. The derived novel criteria are in the form of linear matrix inequalities (LMIs), which are easy to examine and tremendously reduce the computation burden from the feedback matrices. This paper provides an alternative networked secure communication scheme which can be extended conveniently. An illustrative example is given to demonstrate the effectiveness of the proposed networked synchronization method. (general)
Intermittently chaotic oscillations for a differential-delay equation with Gaussian nonlinearity
Hamilton, Ian
1992-01-01
For a differential-delay equation the time dependence of the variable is a function of the variable at a previous time. We consider a differential-delay equation with Gaussian nonlinearity that displays intermittent chaos. Although not the first example of a differential-delay equation that displays such behavior, for this example the intermittency is classified as type III, and the origin of the intermittent chaos may be qualitatively understood from the limiting forms of the equation for large and small variable magnitudes.
International Nuclear Information System (INIS)
Ding Qing
2007-01-01
We prove that the integrable-nonintegrable discrete nonlinear Schroedinger equation (AL-DNLS) introduced by Cai, Bishop and Gronbech-Jensen (Phys. Rev. Lett. 72 591(1994)) is the discrete gauge equivalent to an integrable-nonintegrable discrete Heisenberg model from the geometric point of view. Then we study whether the transmission and bifurcation properties of the AL-DNLS equation are preserved under the action of discrete gauge transformations. Our results reveal that the transmission property of the AL-DNLS equation is completely preserved and the bifurcation property is conditionally preserved to those of the integrable-nonintegrable discrete Heisenberg model
Directory of Open Access Journals (Sweden)
Chunyan Han
2015-01-01
Full Text Available Based on the heteroclinic Shil’nikov theorem and switching control, a kind of multipiecewise linear chaotic system is constructed in this paper. Firstly, two fundamental linear systems are constructed via linearization of a chaotic system at its two equilibrium points. Secondly, a two-piecewise linear chaotic system which satisfies the Shil’nikov theorem is generated by constructing heteroclinic loop between equilibrium points of the two fundamental systems by switching control. Finally, another multipiecewise linear chaotic system that also satisfies the Shil’nikov theorem is obtained via alternate translation of the two fundamental linear systems and heteroclinic loop construction of adjacent equilibria for the multipiecewise linear system. Some basic dynamical characteristics, including divergence, Lyapunov exponents, and bifurcation diagrams of the constructed systems, are analyzed. Meanwhile, computer simulation and circuit design are used for the proposed chaotic systems, and they are demonstrated to be effective for the method of chaos anticontrol.
Yu, Yue; Zhang, Zhengdi; Han, Xiujing
2018-03-01
In this work, we aim to demonstrate the novel routes to periodic and chaotic bursting, i.e., the different bursting dynamics via delayed pitchfork bifurcations around stable attractors, in the classical controlled Lü system. First, by computing the corresponding characteristic polynomial, we determine where some critical values about bifurcation behaviors appear in the Lü system. Moreover, the transition mechanism among different stable attractors has been introduced including homoclinic-type connections or chaotic attractors. Secondly, taking advantage of the above analytical results, we carry out a study of the mechanism for bursting dynamics in the Lü system with slowly periodic variation of certain control parameter. A distinct delayed supercritical pitchfork bifurcation behavior can be discussed when the control item passes through bifurcation points periodically. This delayed dynamical behavior may terminate at different parameter areas, which leads to different spiking modes around different stable attractors (equilibriums, limit cycles, or chaotic attractors). In particular, the chaotic attractor may appear by Shilnikov connections or chaos boundary crisis, which leads to the occurrence of impressive chaotic bursting oscillations. Our findings enrich the study of bursting dynamics and deepen the understanding of some similar sorts of delayed bursting phenomena. Finally, some numerical simulations are included to illustrate the validity of our study.
Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems
Agarwal, S.; Wettlaufer, J. S.
2014-12-01
We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.
Control uncertain Genesio-Tesi chaotic system: Adaptive sliding mode approach
International Nuclear Information System (INIS)
Dadras, Sara; Momeni, Hamid Reza
2009-01-01
An adaptive sliding mode control (ASMC) technique is introduced in this paper for a chaotic dynamical system (Genesio-Tesi system). Using the sliding mode control technique, a sliding surface is determined and the control law is established. An adaptive sliding mode control law is derived to make the states of the Genesio-Tesi system asymptotically track and regulate the desired state. The designed control scheme can control the uncertain chaotic behaviors to a desired state without oscillating very fast and guarantee the property of asymptotical stability. An illustrative simulation result is given to demonstrate the effectiveness of the proposed adaptive sliding mode control design.
Adaptive robust PID controller design based on a sliding mode for uncertain chaotic systems
International Nuclear Information System (INIS)
Chang Weider; Yan Junjuh
2005-01-01
A robust adaptive PID controller design motivated from the sliding mode control is proposed for a class of uncertain chaotic systems in this paper. Three PID control gains, K p , K i , and K d , are adjustable parameters and will be updated online with an adequate adaptation mechanism to minimize a previously designed sliding condition. By introducing a supervisory controller, the stability of the closed-loop PID control system under with the plant uncertainty and external disturbance can be guaranteed. Finally, a well-known Duffing-Holmes chaotic system is used as an illustrative to show the effectiveness of the proposed robust adaptive PID controller
Feedback control and adaptive control of the energy resource chaotic system
International Nuclear Information System (INIS)
Sun Mei; Tian Lixin; Jiang Shumin; Xu Jun
2007-01-01
In this paper, the problem of control for the energy resource chaotic system is considered. Two different method of control, feedback control (include linear feedback control, non-autonomous feedback control) and adaptive control methods are used to suppress chaos to unstable equilibrium or unstable periodic orbits. The Routh-Hurwitz criteria and Lyapunov direct method are used to study the conditions of the asymptotic stability of the steady states of the controlled system. The designed adaptive controller is robust with respect to certain class of disturbances in the energy resource chaotic system. Numerical simulations are presented to show these results
A novel hybrid color image encryption algorithm using two complex chaotic systems
Wang, Leyuan; Song, Hongjun; Liu, Ping
2016-02-01
Based on complex Chen and complex Lorenz systems, a novel color image encryption algorithm is proposed. The larger chaotic ranges and more complex behaviors of complex chaotic systems, which compared with real chaotic systems could additionally enhance the security and enlarge key space of color image encryption. The encryption algorithm is comprised of three step processes. In the permutation process, the pixels of plain image are scrambled via two-dimensional and one-dimensional permutation processes among RGB channels individually. In the diffusion process, the exclusive-or (XOR for short) operation is employed to conceal pixels information. Finally, the mixing RGB channels are used to achieve a multilevel encryption. The security analysis and experimental simulations demonstrate that the proposed algorithm is large enough to resist the brute-force attack and has excellent encryption performance.
Security scheme in IMDD-OFDM-PON system with the chaotic pilot interval and scrambling
Chen, Qianghua; Bi, Meihua; Fu, Xiaosong; Lu, Yang; Zeng, Ran; Yang, Guowei; Yang, Xuelin; Xiao, Shilin
2018-01-01
In this paper, a random chaotic pilot interval and permutations scheme without any requirement of redundant sideband information is firstly proposed for the physical layer security-enhanced intensity modulation direct detection orthogonal frequency division multiplexing passive optical network (IMDD-OFDM-PON) system. With the help of the position feature of inserting the pilot, a simple logistic chaos map is used to generate the random pilot interval and scramble the chaotic subcarrier allocation of each column pilot data for improving the physical layer confidentiality. Due to the dynamic chaotic permutations of pilot data, the enhanced key space of ∼103303 is achieved in OFDM-PON. Moreover, the transmission experiment of 10-Gb/s 16-QAM encrypted OFDM data is successfully demonstrated over 20-km single-mode fiber, which indicates that the proposed scheme not only improves the system security, but also can achieve the same performance as in the common IMDD-OFDM-PON system without encryption scheme.
Amplification through chaotic synchronization in spatially extended beam-plasma systems
Moskalenko, Olga I.; Frolov, Nikita S.; Koronovskii, Alexey A.; Hramov, Alexander E.
2017-12-01
In this paper, we have studied the relationship between chaotic synchronization and microwave signal amplification in coupled beam-plasma systems. We have considered a 1D particle-in-cell numerical model of unidirectionally coupled beam-plasma oscillatory media being in the regime of electron pattern formation. We have shown the significant gain of microwave oscillation power in coupled beam-plasma media being in the different regimes of generation. The discovered effect has a close connection with the chaotic synchronization phenomenon, so we have observed that amplification appears after the onset of the complete time scale synchronization regime in the analyzed coupled spatially extended systems. We have also provided the numerical study of physical processes in the chain of beam-plasma systems leading to the chaotic synchronization and the amplification of microwave oscillations power, respectively.
A simple method of chaos control for a class of chaotic discrete-time systems
International Nuclear Information System (INIS)
Jiang Guoping; Zheng Weixing
2005-01-01
In this paper, a simple method is proposed for chaos control for a class of discrete-time chaotic systems. The proposed method is built upon the state feedback control and the characteristic of ergodicity of chaos. The feedback gain matrix of the controller is designed using a simple criterion, so that control parameters can be selected via the pole placement technique of linear control theory. The new controller has a feature that it only uses the state variable for control and does not require the target equilibrium point in the feedback path. Moreover, the proposed control method cannot only overcome the so-called 'odd eigenvalues number limitation' of delayed feedback control, but also control the chaotic systems to the specified equilibrium points. The effectiveness of the proposed method is demonstrated by a two-dimensional discrete-time chaotic system
Directory of Open Access Journals (Sweden)
Yu Huang
Full Text Available Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm.
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.
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.
Tlelo-Cuautle, Esteban; de la Fraga, Luis Gerardo
2016-01-01
This book offers readers a clear guide to implementing engineering applications with FPGAs, from the mathematical description to the hardware synthesis, including discussion of VHDL programming and co-simulation issues. Coverage includes FPGA realizations such as: chaos generators that are described from their mathematical models; artificial neural networks (ANNs) to predict chaotic time series, for which a discussion of different ANN topologies is included, with different learning techniques and activation functions; random number generators (RNGs) that are realized using different chaos generators, and discussions of their maximum Lyapunov exponent values and entropies. Finally, optimized chaotic oscillators are synchronized and realized to implement a secure communication system that processes black and white and grey-scale images. In each application, readers will find VHDL programming guidelines and computer arithmetic issues, along with co-simulation examples with Active-HDL and Simulink. Readers will b...
Dynamics of quantum-classical differences for chaotic systems
International Nuclear Information System (INIS)
Ballentine, L.E.
2002-01-01
The differences between quantum and classical dynamics can be studied through the moments and correlations of the position and momentum variables in corresponding quantum and classical statistical states. In chaotic states the quantum-classical differences grow exponentially with an exponent that exceeds the classical Lyapunov exponent. It is shown analytically that the quantum-classical differences scale as (ℎ/2π) 2 , and that the exponent for the growth of these differences is independent of (ℎ/2π). The quantum-classical difference exponent is studied for two quartic potential models, and the results are compared with previous work on the Henon-Heiles model
Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion
Directory of Open Access Journals (Sweden)
Jun Wang
2013-01-01
Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.
Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks.
Vlachas, Pantelis R; Byeon, Wonmin; Wan, Zhong Y; Sapsis, Themistoklis P; Koumoutsakos, Petros
2018-05-01
We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPs in short-term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks.
Nonlinear dynamics in biological systems
Carballido-Landeira, Jorge
2016-01-01
This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...
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.
Nonlinear forecasting of stream flows using a chaotic approach and artificial neural networks
Directory of Open Access Journals (Sweden)
Hakan Tongal
2013-07-01
Full Text Available This paper evaluates the forecasting performance of two nonlinear models, k-nearest neighbor (kNN and feed-forward neural networks (FFNN, using stream flow data of the Kızılırmak River, the longest river in Turkey. For the kNN model, the required parameters are delay time, number of nearest neigh- bors and embedding dimension. The optimal delay time was obtained with the mutual information function; the number of nearest neighbors was obtained with the optimization process that minimi- zes RMSE as a function of the neighbor number and the embedding dimension was obtained with the correlation dimension method. The correlation dimension of the Kızılırmak River was d = 2.702, which was used in forming the input structure of the FFNN. The nearest integer above the correlation dimension (i.e., 3 provided the minimal number of required variables to characterize the system, and the maximum number of required variables was obtained with the nearest integer above the value 2d + 1 (Takens, 1981 (i.e., 7. Two FFNN models were developed that incorporate 3 and 7 lagged discharge values and the predicted performance compared to that of the kNN model. The results showed that the kNN model was superior to the FFNN model in stream flow forecasting. However, as a result from the kNN model structure, the model failed in the prediction of peak values. Additionally, it was found that the correlation dimension (if it existed could successfully be used in time series where the determina- tion of the input structure is difficult because of high inter-dependency, as in stream flow time series. Resumen Este trabajo evalúa el desempeño de pronóstico de dos modelos no lineares, de método de clasificación no paramétrico kNN y de redes neuronales con alimentación avanzada (FNNN, usando datos de flujo del río Kizilirmak, el mayor de Turquía. Para el modelo kNN, los parámetros requeridos son tiempo de retraso, número de vecindarios cercanos y dimensión de
Synchronization in node of complex networks consist of complex chaotic system
Energy Technology Data Exchange (ETDEWEB)
Wei, Qiang, E-mail: qiangweibeihua@163.com [Beihua University computer and technology College, BeiHua University, Jilin, 132021, Jilin (China); Digital Images Processing Institute of Beihua University, BeiHua University, Jilin, 132011, Jilin (China); Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024 (China); Xie, Cheng-jun [Beihua University computer and technology College, BeiHua University, Jilin, 132021, Jilin (China); Digital Images Processing Institute of Beihua University, BeiHua University, Jilin, 132011, Jilin (China); Liu, Hong-jun [School of Information Engineering, Weifang Vocational College, Weifang, 261041 (China); Li, Yan-hui [The Library, Weifang Vocational College, Weifang, 261041 (China)
2014-07-15
A new synchronization method is investigated for node of complex networks consists of complex chaotic system. When complex networks realize synchronization, different component of complex state variable synchronize up to different scaling complex function by a designed complex feedback controller. This paper change synchronization scaling function from real field to complex field for synchronization in node of complex networks with complex chaotic system. Synchronization in constant delay and time-varying coupling delay complex networks are investigated, respectively. Numerical simulations are provided to show the effectiveness of the proposed method.
Parameter identification of Rossler's chaotic system by an evolutionary algorithm
Energy Technology Data Exchange (ETDEWEB)
Chang, W.-D. [Department of Computer and Communication, Shu-Te University, Kaohsiung 824, Taiwan (China)]. E-mail: wdchang@mail.stu.edu.tw
2006-09-15
In this paper, a differential evolution (DE) algorithm is applied to parameter identification of Rossler's chaotic system. The differential evolution has been shown to possess a powerful searching capability for finding the solutions for a given optimization problem, and it allows for parameter solution to appear directly in the form of floating point without further numerical coding or decoding. Three unknown parameters of Rossler's Chaotic system are optimally estimated by using the DE algorithm. Finally, a numerical example is given to verify the effectiveness of the proposed method.
Finite-time synchronization of Lorenz chaotic systems: theory and circuits
International Nuclear Information System (INIS)
Louodop, Patrick; Fotsin, Hilaire; Kountchou, Michaux; Bowong, Samuel
2013-01-01
This paper addresses the problem of finite-time master–slave synchronization of Lorenz chaotic systems from a control theoretic point of view. We propose a family of feedback couplings which accomplish the synchronization of Lorenz chaotic systems based on Lyapunov stability theory. These feedback couplings are based on non-periodic functions. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at established time. An advantage is that some of the proposed feedback couplings are simple and easy to implement. Both mathematical investigations and numerical simulations followed by a Pspice experiment are presented to show the feasibility of the proposed method. (paper)
Cryptanalysis of the public key encryption based on multiple chaotic systems
International Nuclear Information System (INIS)
Zhang Linhua
2008-01-01
Recently, Ranjan proposed a novel public key encryption technique based on multiple chaotic systems [Phys Lett 2005;95]. Unfortunately, Wang soon gave a successful attack on its special case based on Parseval's theorem [Wang K, Pei W, Zhou L, et al. Security of public key encryption technique based on multiple chaotic system. Phys Lett A, in press]. In this letter, we give an improved example which can avoid the attack and point out that Wang cannot find the essential drawback of the technique. However, further experimental result shows Ruanjan's encryption technique is inefficient, and detailed theoretic analysis shows that the complexity to break the cryptosystem is overestimated
Bogomolov, Sergey A.; Slepnev, Andrei V.; Strelkova, Galina I.; Schöll, Eckehard; Anishchenko, Vadim S.
2017-02-01
We explore the bifurcation transition from coherence to incoherence in ensembles of nonlocally coupled chaotic systems. It is firstly shown that two types of chimera states, namely, amplitude and phase, can be found in a network of coupled logistic maps, while only amplitude chimera states can be observed in a ring of continuous-time chaotic systems. We reveal a bifurcation mechanism by analyzing the evolution of space-time profiles and the coupling function with varying coupling coefficient and formulate the necessary and sufficient conditions for realizing the chimera states in the ensembles.
Analysis of the time structure of synchronization in multidimensional chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Makarenko, A. V., E-mail: avm.science@mail.ru [Constructive Cybernetics Research Group (Russian Federation)
2015-05-15
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete.
Analysis of the time structure of synchronization in multidimensional chaotic systems
International Nuclear Information System (INIS)
Makarenko, A. V.
2015-01-01
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete
The brief time-reversibility of the local Lyapunov exponents for a small chaotic Hamiltonian system
International Nuclear Information System (INIS)
Waldner, Franz; Hoover, William G.; Hoover, Carol G.
2014-01-01
Highlights: •We consider the local Lyapunov spectrum for a four-dimensional Hamilton system. •Its stable periodic motion can be reversed for long times. •In the chaotic motion, time reversal occurs only for a short time. •Perturbations will change this short unstable case into a different stable case. •These observations might relate chaos to the Second Law of Thermodynamics. - Abstract: We consider the local (instantaneous) Lyapunov spectrum for a four-dimensional Hamiltonian system. Its stable periodic motion can be reversed for long times. Its unstable chaotic motion, with two symmetric pairs of exponents, cannot. In the latter case reversal occurs for more than a thousand fourth-order Runge–Kutta time steps, followed by a transition to a new set of paired Lyapunov exponents, unrelated to those seen in the forward time direction. The relation of the observed chaotic dynamics to the Second Law of Thermodynamics is discussed
Controlling effect of geometrically defined local structural changes on chaotic Hamiltonian systems.
Ben Zion, Yossi; Horwitz, Lawrence
2010-04-01
An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model through an inverse map in the tangent space. The second covariant derivative of the geodesic deviation in this space generates a dynamical curvature, resulting in (energy-dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We show here that this criterion can be constructively used to modify locally the potential of a chaotic Hamiltonian model in such a way that stable motion is achieved. Since our criterion for instability is local in coordinate space, these results provide a minimal method for achieving control of a chaotic system.
Frequency response functions for nonlinear convergent systems
Pavlov, A.V.; Wouw, van de N.; Nijmeijer, H.
2007-01-01
Convergent systems constitute a practically important class of nonlinear systems that extends the class of asymptotically stable linear time-invariant systems. In this note, we extend frequency response functions defined for linear systems to nonlinear convergent systems. Such nonlinear frequency
Introduction to nonlinear science
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...
Anti-synchronization of two new different chaotic systems via active ...
African Journals Online (AJOL)
This paper investigates the anti-synchronization of chaos between two new different chaotic systems by using active control. Numerical simulations are used to show the robustness of the active control scheme in anti-synchronizing the two different coupled systems. JONAMP Vol. 11 2007: pp. 15-20 ...
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.
Cornick, Matthew; Hunt, Brian; Ott, Edward; Kurtuldu, Huseyin; Schatz, Michael F
2009-03-01
Data assimilation refers to the process of estimating a system's state from a time series of measurements (which may be noisy or incomplete) in conjunction with a model for the system's time evolution. Here we demonstrate the applicability of a recently developed data assimilation method, the local ensemble transform Kalman filter, to nonlinear, high-dimensional, spatiotemporally chaotic flows in Rayleigh-Bénard convection experiments. Using this technique we are able to extract the full temperature and velocity fields from a time series of shadowgraph measurements. In addition, we describe extensions of the algorithm for estimating model parameters. Our results suggest the potential usefulness of our data assimilation technique to a broad class of experimental situations exhibiting spatiotemporal chaos.
Gac, J. M.; Żebrowski, J. J.
A chaotic transition occurs when a continuous change of one of the parameters of the system causes a discontinuous change in the properties of the chaotic attractor of the system. Such phenomena are present in many dynamical systems, in which a chaotic behavior occurs. The best known of these transitions are: the period-doubling bifurcation cascade, intermittency and crises. The effect of dichotomous Markov noise (DMN) on the properties of systems with chaotic transitions is discussed. DMN is a very simple two-valued stochastic process, with constant transition rates between the two states. In spite of its simplicity, this kind of noise is a very powerful tool to describe various phenomena present in many physical, chemical or biological systems. Many interesting phenomena induced by DMN are known. However, there is no research on the effect of this kind of noise on intermittency or crises. We present the change of the mean laminar phase length and of laminar phase length distribution caused by DMN modulating the parameters of a system with intermittency and the modification of the mean life time on the pre-crisis attractor in the case of a boundary crisis. The results obtained analytically are compared with numerical simulations for several simple dynamical systems.
Wada basins and chaotic invariant sets in the H non-Heiles system
Aguirre, J E; Sanjun, M A F
2001-01-01
The H non-Heiles Hamiltonian is investigated in the context of chaotic scattering, in the range of energies where escaping from the scattering region is possible. Special attention is paid to the analysis of the different nature of the orbits, and the invariant sets, such as the stable and unstable manifolds and the chaotic saddle. Furthermore, a discussion on the average decay time associated to the typical chaotic transients, which are present in this problem is presented. The main goal of this paper is to show, by using various computational methods, that the corresponding exit basins of this open Hamiltonian are not only fractal, but they also verify the more restrictive property of Wada. We argue that this property is verified by typical open Hamiltonian systems with three or more escapes.
Chaos suppression based on adaptive observer for a P-class of chaotic systems
International Nuclear Information System (INIS)
Rodriguez, Angel; Leon, Jesus de; Femat, Ricardo
2007-01-01
A feedback approach is presented to suppress chaos in a P-class of chaotic system. The approach is based on an adaptive observer; which provides estimated values of both the unmeasured states and the uncertain model parameters. A continuous-time feedback law is taken as suppressing force. The feedback law attains chaos suppression as the observer provides estimated values close to the actual state/parameter values along time. The proposed scheme is robust in the sense that suppression is achieved despite only some states are measured and uncertainties in parameters are compensated. Results are corroborated experimentally by implementation in chaotic circuits
A new type of chaotic synchronization with application to communication systems
International Nuclear Information System (INIS)
Kharel, Rupak; Busawon, Krishna
2011-01-01
In this paper, we propose a new methodology to synchronize a class of chaotic systems starting from different initial conditions under some given conditions. The method we propose is not based on the unidirectional synchronization method like the one proposed by Pecora-Caroll. The proposed method is unique in the sense that the chaotic oscillators to be synchronized have no direct connection between them; that is, there is no signal being sent from one to the other. Simulation result is presented to show the synchronization performance.
Chaos suppression based on adaptive observer for a P-class of chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Rodriguez, Angel [Universidad Autonoma de Nuevo Leon, Facultad de Ingenieria Mecanica y Electrica, Av. Pedro de Alba s/n Cd. Universitaria, CP 66450 San Nicolas de los Garza, NL (Mexico); Leon, Jesus de [Universidad Autonoma de Nuevo Leon, Facultad de Ingenieria Mecanica y Electrica, Av. Pedro de Alba s/n Cd. Universitaria, CP 66450 San Nicolas de los Garza, NL (Mexico); Femat, Ricardo [Division de Matematicas Aplicadas y Sistemas Computacionales, IPICyT, Camino a la Presa San Jose 2055 Col. Lomas 4a. Secc. CP 78216 San Luis Potosi, SLP (Mexico)]. E-mail: rfemat@ipicyt.edu.mx
2007-05-15
A feedback approach is presented to suppress chaos in a P-class of chaotic system. The approach is based on an adaptive observer; which provides estimated values of both the unmeasured states and the uncertain model parameters. A continuous-time feedback law is taken as suppressing force. The feedback law attains chaos suppression as the observer provides estimated values close to the actual state/parameter values along time. The proposed scheme is robust in the sense that suppression is achieved despite only some states are measured and uncertainties in parameters are compensated. Results are corroborated experimentally by implementation in chaotic circuits.