Phase and anti-phase synchronization of two chaotic systems by using active control

Ho, Ming‐Chung; Hung, Ying; Chou, Chien-Ho

doi:10.1016/s0375-9601(02)00074-9

Cited by 172 publications

(72 citation statements)

References 17 publications

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“…It is widely used in many fields of physics, engineering and secure communications [2,29,31]. Currently, more works have been done in the study of chaos and hyperchaos synchronization and many different kinds of synchronizations have been discovered such as completed synchronization, generalized synchronization, phase synchronization, projective synchronization, lag synchronization and impulsive synchronization [5,9,10,12,16,25,36], of most important, chaotic synchronization can be described as hybrid [14,30], high-dimension [4,19], fractional order [34], coupled complex system [17,18,35], and neural network [6,7].…”

Section: Introductionmentioning

confidence: 99%

Scaling Synchronization of a 6D Hyperchaotic System

Osman¹,

Zhu²,

Yang³

2018

dtcse

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Abstract. This paper focuses on the scaling synchronization issue of a 6D hyperchaotic system with one or three equilibria which is obtained by controlling a 5D hyperchaotic system that is formed by adding a linear feedback controller and a nonlinear feedback controller to the Lorenz system. When the parameters are known in advance, applying the one-way linear coupling approach to synchronize the 6D hyperchaotic system up to a scaling factor. When the parameters are fully unknown, utilizing the adaptive method to synchronize the uncertain 6D hyperchaotic system up to a scaling factor. Finally, many numerical simulations have been carried out to verify the validation and efficiency of the proposed schemes.

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Section: Introductionmentioning

confidence: 99%

Scaling Synchronization of a 6D Hyperchaotic System

Osman¹,

Zhu²,

Yang³

2018

dtcse

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“…Until now, many kind of chaos control and synchronization schemes have developed by the researchers. Active method [1]- [3], adaptive method [4]- [6], phase method [7], backstepping method [8], [9], lag method [10], impulsive method [11], [12], linear feedback method [13], [14], nonlinear feedback control [15], [16], and projective method [17]- [20] are some of the investigated method during the last recent years. Among these investigated methods, chaos synchronization related to the projective method has considerably noticed during the last few decades due to its proportional feature, which the response chaotic system can be synchronized up to a typical aligned scaling factors.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems

Tirandaz¹,

Ahmadnia²,

Tavakoli³

2017

IJECE

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In this paper, the synchronization problem of T chaotic system and Lu chaotic system is studied. The parameter of the drive T chaotic system is considered unknown. An adaptive projective lag control method and also parameter estimation law are designed to achieve chaos synchronization problem between two chaotic systems. Then Lyapunov stability theorem is utilized to prove the validity of the proposed control method. After that, some numerical simulations are performed to assess the performance of the proposed method. The results show high accuracy of the proposed method in control and synchronization of chaotic systems. Keyword:Adaptive method Lyapunov stability theorem Chaos synchronization Projective lag method Copyright © 2017 Institute of Advanced Engineering and Science.All rights reserved. Corresponding Author:Hamed Tirandaz, Electrical and Computer Engineering Department, Hakim Sabzevari University, Sabzevar, Iran. Email: tirandaz@hsu.ac.ir INTRODUCTIONSensitivity to the initial values of the state variables is the main feature of any chaotic system, which causes exponentially different motion trajectories of the state variables with different initial conditions. The problem of chaos synchronization has received a lot of attention in the last three decades due to its potential applications in many different fields such as: physics, chemistry, electrical engineering, economics and secure communications. Until now, many kind of chaos control and synchronization schemes have developed by the researchers. [20] are some of the investigated method during the last recent years. Among these investigated methods, chaos synchronization related to the projective method has considerably noticed during the last few decades due to its proportional feature, which the response chaotic system can be synchronized up to a typical aligned scaling factors. So far many types of projective methods have been studied by the researchers. [30] are some of the projective related method for control and synchronization between two identical/non-identical chaotic systems. But, projective lag hybrid synchronization is rarely investigated by the researchers. So, this paper is devoted to the synchronization problem between T chaotic system and Lorenz chaotic system by designing an appropriate adaptive hybrid projective lag synchronization method.The rest reminder of this paper is constructed as follows: In Section 2, the structure of the T chaotic system and Lorenz chaotic system are described. Then, in Section 3, the problem of chaos synchronization of T chaotic system and Lorenz chaotic system is given. An adaptive projective lag control method is designed

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“…There are only a few papers on the combination projective synchronization [28,29]. On the other hand, the active control scheme [30][31][32] and backstepping design [33,34] have been widely recognized as two powerful design methods to control chaotic systems in recent years. The active control method is easier to manipulate so that it is used widely to control chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

Active backstepping control of combined projective synchronization among different nonlinear systems

et al. 2017

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In this article, the authors have studied combination projective synchronization using active backstepping method. The main contribution of this effort is realization of the projective synchronization between two drive systems and one response system. We relax some limitations of previous work, where only combination complete synchronization has been investigated. According to Lyapunov stability theory and active backstepping design method, the corresponding controllers are designed to observe combination projective synchronization among three different classical chaotic systems, i.e. the Lorenz system, R€ ossler system and Chen system. The numerical simulation examples verify the effectiveness of the theoretical analysis. Combination projective synchronization has stronger anti-attack ability and antitranslated ability than the normal projective synchronization scheme realized by one drive and one response system in secure communication.

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Phase and anti-phase synchronization of two chaotic systems by using active control

Cited by 172 publications

References 17 publications

Scaling Synchronization of a 6D Hyperchaotic System

Scaling Synchronization of a 6D Hyperchaotic System

Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems

Active backstepping control of combined projective synchronization among different nonlinear systems

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