Generalized Projective Synchronization for a Class of Continuous Chaotic Systems

2011 ◽  
Vol 50-51 ◽  
pp. 258-261
Author(s):  
Ya Fei Zhou ◽  
Dong Zhang
Keyword(s):  
Numerical Simulation ◽  
Chaotic Systems ◽  
Mathematical Proof ◽  
Construction Method ◽  
Projective Synchronization ◽  
Response System ◽  
Simulation Results ◽  
Generalized Projective Synchronization

In this paper, a generalized projective synchronization (GPS) scheme for a class of continuous chaotic systems is investigated by using only one sate variable and its time derivatives. The construction method of response system is proposed. The mathematical proof of the GPS scheme is provided. The synchronization technique is simple and theoretically rigorous. Finally, the corresponding numerical simulation results demonstrate the effectiveness of the proposed schemes.

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.

scholarly journals Projective Synchronization of Chaotic Systems Via Backstepping Design

2013 ◽  
Vol 18 (3) ◽  
pp. 965-973 ◽  
Author(s):  
A. Tarai ◽  
M.A. Khan
Keyword(s):  
Numerical Simulation ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Discrete Dynamical Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Backstepping Design ◽  
Simulation Results ◽  
Duffing Map

Abstract Chaos synchronization of discrete dynamical systems is investigated. An algorithm is proposed for projective synchronization of chaotic 2D Duffing map and chaotic Tinkerbell map. The control law was derived from the Lyapunov stability theory. Numerical simulation results are presented to verify the effectiveness of the proposed algorithm

FUNCTION PROJECTIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS VIA NONLINEAR ADAPTIVE–IMPULSIVE CONTROL

2011 ◽  
Vol 22 (11) ◽  
pp. 1281-1291 ◽  
Author(s):  
RANCHAO WU ◽  
DONGXU CAO
Keyword(s):  
Numerical Simulation ◽  
Dynamical Systems ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
Simulation Results ◽  
Invariant Principle

In this paper, function projective synchronization of chaotic systems is investigated through nonlinear adaptive–impulsive control. To achieve synchronization, suitable nonlinear continuous and impulsive controllers are designed, according to invariant principle of impulsive dynamical systems. Sufficient conditions are given to ensure the synchronization. Numerical simulation results show the effectiveness of the proposed scheme.

Generalized Projective Synchronization for Fractional-Order Chaotic Systems with Different Fractional Order

2011 ◽  
Vol 474-476 ◽  
pp. 2106-2109 ◽  
Author(s):  
Ping Zhou ◽  
Rui Ding
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Chen System ◽  
Response System ◽  
Generalized Projective Synchronization

In this paper, we propose a generalized projective synchronization with different scaling factor for fractional-order chaotic systems with different fractional order. A method of constructing response system is given. The generalized projective synchronization conditions are obtained theoretically. Finally, the fractional-order Chen system is used to demonstrate the effectiveness of the proposed schemes.

SYNCHRONIZATION OF CHAOTIC SYSTEMS WITH PARAMETRIC UNCERTAINTIES USING SLIDING OBSERVERS

2004 ◽  
Vol 14 (07) ◽  
pp. 2467-2475 ◽  
Author(s):  
MOEZ FEKI
Keyword(s):  
Numerical Simulation ◽  
Finite Time ◽  
Chaotic Systems ◽  
Parametric Uncertainties ◽  
Response Type ◽  
Unknown Parameters ◽  
Response System ◽  
Parameter Variations ◽  
Transmitted Signal ◽  
Simulation Results

This paper is concerned with synchronization of chaotic systems. We consider a drive-response type of synchronization via a scalar transmitted signal. Given some structural conditions of chaotic systems, a sliding observer-based response system is constructed to synchronize with the drive system within a finite time. Moreover, if the observer gain is judiciously chosen, robustness with respect to bounded parameter variations is guaranteed. To improve furthermore the performance of the response system, unknown parameters are adaptively estimated in conjunction with the sliding observer. To demonstrate the efficiency of the proposed approach numerical simulation results are presented.

scholarly journals Robust Adaptive Generalized Projective Synchronization of Chaotic Systems with Uncertain Disturbances

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Zhen Jia ◽  
Guangming Deng
Keyword(s):  
Chaotic Systems ◽  
External Disturbance ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Response System ◽  
Adaptive Technique ◽  
Uncertain Disturbances ◽  
Response Systems ◽  
Generalized Projective Synchronization ◽  
Robust Adaptive

The generalized projective synchronization (GPS) of chaotic systems with uncertain parameter noise and external disturbance is discussed. Based on the adaptive technique, a response system is constructed, and a novel adaptive controller is designed to guarantee the GPS between the drive-response systems, and to eliminate the effect of external disturbance and parameters noise on GPS. The conclusion is proved theoretically, and corresponding numerical simulations are provided to verify the effectiveness of the proposed method.

LAG PROJECTIVE STOCHASTIC PERTURBED SYNCHRONIZATION FOR CHAOTIC SYSTEMS AND ITS APPLICATION IN SECURE COMMUNICATION

2008 ◽  
Vol 22 (24) ◽  
pp. 4175-4188 ◽  
Author(s):  
YANG TANG ◽  
JIAN-AN FANG ◽  
LIANG CHEN
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Stochastic Perturbation ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Adaptive Feedback ◽  
Communication Scheme ◽  
Simulation Results ◽  
Feedback Method

In this paper, a simple and systematic adaptive feedback method for achieving lag projective stochastic perturbed synchronization of a new four-wing chaotic system with unknown parameters is presented. Moreover, a secure communication scheme based on the adaptive feedback lag projective synchronization of the new chaotic systems with stochastic perturbation and unknown parameters is presented. The simulation results show the feasibility of the proposed method.

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