Generalized synchronization of continuous chaotic system

Wang, Yan‐Wu; Guan, Zhi‐Hong

doi:10.1016/j.chaos.2004.12.038

Cited by 162 publications

(90 citation statements)

References 19 publications

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“…From the error equations (17), it is clear that one part of the two hyperchaotic systems is completely synchronized (first and third states), while the other part is completely antisynchronized (second and fourth states) so that complete synchronization (CS) and antisynchronization (AS) coexist in the synchronization process of the two hyperchaotic systems (15) and (16).…”

Section: Theoretical Resultsmentioning

confidence: 99%

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Hybrid Chaos Synchronization of Hyperchaotic LIU And Hyperchaotic CHEN Systems by Active Nonlinear Control

Vaidyanathan¹

2011

IJCSEIT

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Section: Theoretical Resultsmentioning

confidence: 99%

“…For the numerical simulations, the fourth order Runge-Kutta method is used to solve the two systems of differential equations (15) and (16) …”

Section: Numerical Resultsmentioning

confidence: 99%

Hybrid Chaos Synchronization of Hyperchaotic LIU And Hyperchaotic CHEN Systems by Active Nonlinear Control

Vaidyanathan¹

2011

IJCSEIT

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“…Up to now, many types of controling methods are revealed and investigated for control and synchronization of chaotic systems. Active method [2,3,4,5,6], adaptive method [7,8,9], linear feedback method [10,11], nonlinear feedback method [12,14,15], sliding mode method [16,17,18], impulsive method [19], phase method [20], generalized method [21], robust synchronization [13] and projective method [22,23,24] are some of the introduced methods by the researchers. Among these methods, synchronization with some types of projective methods are extensively investigated in the last decades, since the faster synchronization due to its synchronization scaling factors, which master and slave chaotic systems would be synchronized up to a proportional rate.…”

Section: Introductionmentioning

confidence: 99%

Modified Projective Synchronization of Chaotic Systems with Noise Disturbance, an Active Nonlinear Control Method

Tirandaz

Ahmadnia

Tavakoli

2017

IJECE

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The synchronization problem of chaotic systems using active modified projective nonlinear control method is rarely addressed. Thus the concentration of this study is to derive a modified projective controller to synchronize the two chaotic systems. Since, the parameter of the master and follower systems are considered known, so active methods are employed instead of adaptive methods. The validity of the proposed controller is studied by means of the Lyapunov stability theorem. Furthermore, some numerical simulations are shown to verify the validity of the theoretical discussions. The results demonstrate the effectiveness of the proposed method in both speed and accuracy points of views.Copyright c 2017 Institute of Advanced Engineering and Science.All rights reserved. Corresponding Author:Hamed Tirandaz Hakim Sabzevari University Electrical and Computer Engineering Faculty, Hakim Sabzevari University, Sabzevar, Iran. Phone +98051-4401288 Email: tirandaz@hsu.ac.ir INTRODUCTIONMaster-slave synchronization of chaotic systems is strikely nonlinear, since the aperiodic and nonregular behavior of chaotic systems and their sensitivity to the initial conditions. Chaotic behavior may appear in many physical systems. So, chaos synchronization subject has received a great deal of attention in the last to decades, due to its potential applications in physics, chemistry, electrical engineering, secure communication and so on [1]. Up to now, many types of controling methods are revealed and investigated for control and synchronization of chaotic systems. Active method [2,3,4,5,6], adaptive method [7,8,9] [22,23,24] are some of the introduced methods by the researchers. Among these methods, synchronization with some types of projective methods are extensively investigated in the last decades, since the faster synchronization due to its synchronization scaling factors, which master and slave chaotic systems would be synchronized up to a proportional rate. Projective lag method [25], modified projective synchronization (MPS) [26,27,28], function projective synchronization (FPS) [29], modified function projective synchronization [30,28], generalized function projective synchronization [31,32] and modified projective lag synchronization [33,34] are some generalized schemes of projective method, which utilize some type of scaling factors.When the parameters of a chaotic system are known beforehand, active related methods are preferably chosen than adaptive methods. Active synchronization problem of two chaotic systems with known parameters are vastly investigated by the researchers. For example, in [5,3,35], the active controlling method is studied for synchronization of two typical chaotic systems. And also, in [2], an active method for controling the behavior of a unified chaotic system is presented. Chaos synchronization of complex Chen and Lu chaotic systems are addressed in citeMahmoud, with designing an active control method. Furthermore, in [36] active

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“…So far, many types of chaos synchronization method have been presented such as complete synchronization [1], phase synchronization [13], generalized synchronization [14], anti-synchronization [15,16], projective synchronization [17], generalized projective synchronization [18,19], etc.…”

Section: A Introductionmentioning

confidence: 99%

Anti-synchronization in different new chaotic systems via active nonlinear control

Khan¹,

Prasad²

2013

Archives of Control Sciences

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In this paper, we discuss anti-synchronization between two identical new chaotic systems and anti-synchronization between another two identical new chaotic systems by active nonlinear control. The sufficient conditions for achieving the anti-synchronization of two new chaotic systems are derived based on Lyapunov stability theory. Numerical simulations are provided for illustration and verification of the proposed method.Key words: anti-synchronization, new chaotic system, active nonlinear control A. IntroductionIn 1990 Chaos synchronization is a phenomenon that may occur when two or more chaotic oscillators are coupled or when a chaotic oscillator drives another chaotic oscillator. In most of the chaos anti-synchronization approaches, the master -slave or driveresponse is used. A particular chaotic system is called the master or drive system and another chaotic system is called slave or response system. Then idea of chaos antisynchronization is used for the output of the master system to control the slave system so that output of the slave system follow the output of the master system asymptotically. There are different types of method for chaos anti-synchronization of the chaotic nonlinear systems, such as OGY [6]

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Generalized synchronization of continuous chaotic system

Cited by 162 publications

References 19 publications

Hybrid Chaos Synchronization of Hyperchaotic LIU And Hyperchaotic CHEN Systems by Active Nonlinear Control

Hybrid Chaos Synchronization of Hyperchaotic LIU And Hyperchaotic CHEN Systems by Active Nonlinear Control

Modified Projective Synchronization of Chaotic Systems with Noise Disturbance, an Active Nonlinear Control Method

Anti-synchronization in different new chaotic systems via active nonlinear control

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