Function projective synchronization of different chaotic systems with uncertain parameters

2008 ◽  
Vol 372 (33) ◽  
pp. 5402-5410 ◽  
Author(s):  
Hongyue Du ◽  
Qingshuang Zeng ◽  
Changhong Wang
Keyword(s):  
Chaotic Systems ◽  
Projective Synchronization ◽  
Uncertain Parameters ◽  
Function Projective Synchronization ◽  
Different Chaotic Systems

THE HYBRID FUNCTION PROJECTIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS

2009 ◽  
Vol 20 (05) ◽  
pp. 789-797
Author(s):  
YONG-GUANG YU ◽  
HAN-XIONG LI ◽  
JUN-ZHI YU
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
Hybrid Function ◽  
Simulation Results ◽  
Different Chaotic Systems

This paper mainly investigated a hybrid function projective synchronization of two different chaotic systems. Based on the Lyapunov stability theory, an adaptive controller for the synchronization of two different chaotic systems is designed. This technique is applied to achieve the synchronization between Lorenz and Rössler chaotic systems, and the synchronization of hyperchaotic Rössler and Chen systems. The numerical simulation results illustrate the effectiveness and feasibility of the proposed scheme.

Generalized Hybrid Dislocated Function Projective Synchronization of Chaotic Systems with Time Delay

2014 ◽  
Vol 574 ◽  
pp. 672-678 ◽  
Author(s):  
Rui Li ◽  
Guang Jun Zhang ◽  
Tao Zhu ◽  
Xu Jing Wang ◽  
Jun Dong
Keyword(s):  
Time Delay ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Feedback Gain ◽  
Uncertain Parameters ◽  
Function Projective Synchronization ◽  
Feedback Control Method

In order to improve the security of secure communication, a novel generalized hybrid dislocated function projective synchronization (GHDFPS) was proposed and GHDFPS of time delay chaotic systems with uncertain parameters were researched in this paper. Due to time delay, the chaotic system can produce multiple positive Lyapunov exponential; this characteristic can enhance security in secure communications noticeably. Based on Lyapunove stability theory and modified hybrid feedback control method, the modified hybrid feedback controller and the parameter updating laws were designed for the GHDFPS between the two time delay chaotic systems with uncertain parameters. The feedback gain can be adjusted automatically according to the synchronization error values. Under the controller, generalized hybrid dislocated function projective synchronization of the two chaotic systems is achieved, and the uncertain parameters of response systems are identified. The chaotic item is added in the function scale factor. The chaotic item in the function scaling factor makes function scaling factor more complex and unpredictable. So this can enhance the features of indeterminism in secure communication. The time delay feedback Lorenz system as an example; by numerical simulations the effectiveness of the proposed method is demonstrated.

FUNCTION PROJECTIVE SYNCHRONIZATION OF THE CHAOTIC SYSTEMS WITH PARAMETERS UNKNOWN

2013 ◽  
Vol 27 (21) ◽  
pp. 1350110
Author(s):  
JIAKUN ZHAO ◽  
YING WU
Keyword(s):  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Parameter Update Law ◽  
Different Chaotic Systems ◽  
Hyperchaotic Systems ◽  
Adaptive Control Law

This work is concerned with the general methods for the function projective synchronization (FPS) of chaotic (or hyperchaotic) systems. The aim is to investigate the FPS of different chaotic (hyper-chaotic) systems with unknown parameters. The adaptive control law and the parameter update law are derived to make the states of two different chaotic systems asymptotically synchronized up to a desired scaling function by Lyapunov stability theory. The general approach for FPS of Chen hyperchaotic system and Lü system is provided. Numerical simulations are also presented to verify the effectiveness of the proposed scheme.

scholarly journals Adaptive Hybrid Function Projective Synchronization of Chaotic Systems with Time-Varying Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Jinsheng Xing
Keyword(s):  
Chaotic Systems ◽  
Projective Synchronization ◽  
Time Varying ◽  
Chen System ◽  
Varying Parameters ◽  
Function Projective Synchronization ◽  
Time Varying Parameters ◽  
Hybrid Function ◽  
Robust Adaptive ◽  
Different Chaotic Systems

The adaptive hybrid function projective synchronization (AHFPS) of different chaotic systems with unknown time-varying parameters is investigated. Based on the Lyapunov stability theory and adaptive bounding technique, the robust adaptive control law and the parameters update law are derived to make the states of two different chaotic systems asymptotically synchronized. In the control strategy, the parameters need not be known throughly if the time-varying parameters are bounded by the product of a known function oftand an unknown constant. In order to avoid the switching in the control signal, a modified robust adaptive synchronization approach with the leakage-like adaptation law is also proposed to guarantee the ultimately uni-formly boundedness (UUB) of synchronization errors. The schemes are successfully applied to the hybrid function projective synchronization between the Chen system and the Lorenz system and between hyperchaotic Chen system and generalized Lorenz system. Moreover, numerical simulation results are presented to verify the effectiveness of the proposed scheme.

scholarly journals Function Projective Synchronization of a Class of Chaotic Systems with Uncertain Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Junbiao Guan
Keyword(s):  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Control Law ◽  
Uncertain Parameters ◽  
Adaptive Scheme ◽  
Nonlinear Adaptive Control ◽  
Function Projective Synchronization ◽  
Parameter Update Law ◽  
Adaptive Control Law

This paper investigates the function projective synchronization of a class of chaotic systems with uncertain parameters. Based on Lyapunov stability theory, the nonlinear adaptive control law and the parameter update law are derived to make the state of two chaotic systems function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive scheme.

Synchronization Control of Chaotic Systems with Different Orders

2014 ◽  
Vol 721 ◽  
pp. 218-221
Author(s):  
Ya Fang Yang
Keyword(s):  
Numerical Simulations ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Order System ◽  
Synchronization Control ◽  
Uncertain Parameters ◽  
Chen System ◽  
Function Projective Synchronization ◽  
Full Synchronization ◽  
Identification Strategy

The mixed function projective synchronization is proposed in this paper, which includes the full synchronization and the anti-synchronization and so on. We design an effective controller and parameters identification strategy to study the synchronization phenomena between systems with different orders and uncertain parameters. The analytic results are complemented with numerical simulations for two chaotic systems which are the new integer-order system and the fractional-order Chen system, respectively. Several results show the effectiveness of the presented scheme.

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