ADAPTIVE GENERALIZED SYNCHRONIZATION OF HYPERCHAOS SYSTEMS

2011 ◽  
Vol 25 (32) ◽  
pp. 4563-4571 ◽  
Author(s):  
XINGYUAN WANG ◽  
YAQIN WANG
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
Lyapunov Stability Theory ◽  
New Method ◽  
Generalized Synchronization ◽  
Chen System ◽  
Response Systems ◽  
Hyperchaotic Lorenz System ◽  
Linear And Nonlinear ◽  
Simulation Results

This paper studies the generalized synchronization of hyperchaos systems, and a new method, by which adaptive generalized synchronization of chaotic systems with a kind of linear and nonlinear relationship between the drive and response systems can be achieved, is proposed. This new method has more extensive application scope. Based on the Lyapunov stability theory, the correctness of the proposed scheme is strictly demonstrated. It is also illustrated by applications to hyperchaotic Chen system and hyperchaotic Lorenz system and the simulation results show the effectiveness of the proposed scheme.

GENERALIZED SYNCHRONIZATION OF NONIDENTICAL FRACTIONAL-ORDER CHAOTIC SYSTEMS

2013 ◽  
Vol 27 (30) ◽  
pp. 1350195 ◽  
Author(s):  
XING-YUAN WANG ◽  
ZUN-WEN HU ◽  
CHAO LUO
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Pole Placement ◽  
Generalized Synchronization ◽  
Chen System ◽  
Hyperchaotic Lorenz System ◽  
The Stability ◽  
Synchronization Scheme ◽  
Placement Technique

In this paper, a chaotic synchronization scheme is proposed to achieve the generalized synchronization between two different fractional-order chaotic systems. Based on the stability theory of fractional-order systems and the pole placement technique, a controller is designed and theoretical proof is given. Two groups of examples are shown to verify the effectiveness of the proposed scheme, the first one is to realize the generalized synchronization between the fractional-order Chen system and the fractional-order Rössler system, the second one is between the fractional-order Lü system and the fractional-order hyperchaotic Lorenz system. The corresponding numerical simulations verify the effectiveness of the proposed scheme.

GENERALIZED SYNCHRONIZATION OF DIFFERENT DIMENSIONAL CHAOTIC SYSTEMS BASED ON PARAMETER IDENTIFICATION

2009 ◽  
Vol 23 (22) ◽  
pp. 2593-2606 ◽  
Author(s):  
YONGGUANG YU ◽  
HAN-XIONG LI ◽  
JUNZHI YU
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Generalized Synchronization ◽  
Unknown Parameters ◽  
Chen System ◽  
Response System ◽  
Generalized Lorenz System ◽  
The One

This paper investigates the generalized synchronization issue for two different dimensional chaotic systems with unknown parameters. Based on Lyapunov stability theory and adaptive control theory, an adaptive controller is derived to achieve the generalized synchronization whether the dimension of drive system is greater than the one of the response system or not. Meanwhile, corresponding parameter updating laws can be obtained so as to exactly identify uncertain parameters. This technique has been successfully applied to two examples, the generalized synchronization of hyperchaotic Rössler system and chaotic Lorenz system, chaotic Chen system and generalized Lorenz system. Numerical simulations are finally shown to illustrate the effectiveness of the proposed approach.

ACTIVE TRACKING CONTROL OF THE HYPERCHAOTIC LORENZ SYSTEM

2008 ◽  
Vol 22 (19) ◽  
pp. 1859-1865 ◽  
Author(s):  
XINGYUAN WANG ◽  
DAHAI NIU ◽  
MINGJUN WANG
Keyword(s):  
Numerical Simulation ◽  
Tracking Control ◽  
Chaotic Systems ◽  
Lorenz System ◽  
The Self ◽  
Hyperchaotic System ◽  
Reference Signals ◽  
Tracking Controller ◽  
Hyperchaotic Lorenz System ◽  
Simulation Results

A nonlinear active tracking controller for the four-dimensional hyperchaotic Lorenz system is designed in the paper. The controller enables this hyperchaotic system to track all kinds of reference signals, such as the sinusoidal signal. The self-synchronization of the hyperchaotic Lorenz system and the different-structure synchronization with other chaotic systems can also be realized. Numerical simulation results show the effectiveness of the controller.

scholarly journals Inverse Projective Synchronization between Two Different Hyperchaotic Systems with Fractional Order

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Yi Chai ◽  
Liping Chen ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Lorenz System ◽  
Projective Synchronization ◽  
Generalized Synchronization ◽  
Fractional Order Systems ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Hyperchaotic Lorenz System ◽  
The Stability ◽  
Hyperchaotic Systems

This paper mainly investigates a novel inverse projective synchronization between two different fractional-order hyperchaotic systems, that is, the fractional-order hyperchaotic Lorenz system and the fractional-order hyperchaotic Chen system. By using the stability theory of fractional-order differential equations and Lyapunov equations for fractional-order systems, two kinds of suitable controllers for achieving inverse projective synchronization are designed, in which the generalized synchronization, antisynchronization, and projective synchronization of fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system are also successfully achieved, respectively. Finally, simulations are presented to demonstrate the validity and feasibility of the proposed method.

SYNCHRONIZATION BETWEEN TWO DIFFERENT HYPERCHAOTIC SYSTEMS WITH UNCERTAIN PARAMETERS

2013 ◽  
Vol 27 (13) ◽  
pp. 1350044
Author(s):  
XING-YUAN WANG ◽  
YU-HONG YANG ◽  
MING-KU FENG
Keyword(s):  
Lyapunov Stability ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Sufficient Condition ◽  
Uncertain Parameters ◽  
Hyperchaotic Lorenz System ◽  
Hyperchaotic Systems

This paper studies the problem of chaos synchronization between two different hyperchaotic systems with uncertain parameters. Based on the Lyapunov stability theory, we obtain the sufficient condition of synchronization between two different hyperchaotic systems with uncertain parameters. A new adaptive controller with parameter update laws is designed to synchronize these chaotic systems. We proved it in theory with an uncertain hyperchaotic Lorenz system and an uncertain hyperchaotic Rössler system. Numerical results verified the validation of the proposed scheme.

GENERALIZED (LAG, ANTICIPATED AND COMPLETE) PROJECTIVE SYNCHRONIZATION IN TWO NONIDENTICAL CHAOTIC SYSTEMS WITH UNKNOWN PARAMETERS

2012 ◽  
Vol 26 (16) ◽  
pp. 1250121
Author(s):  
XINGYUAN WANG ◽  
LULU WANG ◽  
DA LIN
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Control Method ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Chen System ◽  
Control Approach ◽  
Response System ◽  
Hyperchaotic Lorenz System

In this paper, a generalized (lag, anticipated and complete) projective synchronization for a general class of chaotic systems is defined. A systematic, powerful and concrete scheme is developed to investigate the generalized (lag, anticipated and complete) projective synchronization between the drive system and response system based on the adaptive control method and feedback control approach. The hyperchaotic Chen system and hyperchaotic Lorenz system are chosen to illustrate the proposed scheme. Numerical simulations are provided to show the effectiveness of the proposed schemes. In addition, the scheme can also be extended to research generalized (lag, anticipated and complete) projective synchronization between nonidentical discrete-time chaotic systems.

scholarly journals ROBUST SYNCHRONIZATION WITH UNIFORM ULTIMATE BOUND BETWEEN TWO DIFFERENT CHAOTIC SYSTEMS WITH UNCERTAINTIES

2011 ◽  
Vol 25 (16) ◽  
pp. 2217-2227
Author(s):  
JIANPING CAI ◽  
ZHENGZHONG YUAN
Keyword(s):  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Unknown Parameters ◽  
Chen System ◽  
Adaptive Controllers ◽  
External Perturbations ◽  
Response Systems ◽  
The Lorenz System ◽  
Different Chaotic Systems ◽  
Ultimate Bound

Adaptive controllers are designed to synchronize two different chaotic systems with uncertainties, including unknown parameters, internal and external perturbations. Lyapunov stability theory is applied to prove that under some conditions the drive-response systems can achieve synchronization with uniform ultimate bound even though the bounds of uncertainties are not known exactly in advance. The designed controllers contain only feedback terms and partial nonlinear terms of the systems, and they are easy to implement in practice. The Lorenz system and Chen system are chosen as the illustrative example to verify the validity of the proposed method. Simulation results also show that the present control has good robustness against different kinds of disturbances.

GENERALIZED SYNCHRONIZATION OF FRACTIONAL ORDER HYPERCHAOTIC LORENZ SYSTEM

2009 ◽  
Vol 23 (17) ◽  
pp. 2167-2178 ◽  
Author(s):  
TIANSHU WANG ◽  
XINGYUAN WANG
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Lorenz System ◽  
Order System ◽  
Generalized Synchronization ◽  
Response System ◽  
Hyperchaotic Lorenz System ◽  
Simulation Results ◽  
The Stability ◽  
Predictor Corrector

In this paper, a type of new fractional order hyperchaotic Lorenz system is proposed. Based on the fractional calculus predictor-corrector algorithm, the fractional order hyperchaotic Lorenz system is investigated numerically, and the simulation results show that the lowest orders for hyperchaos in hyperchaotic Lorenz system is 3.884. According to the stability theory of fractional order system, an improved state-observer is designed, and the response system of generalized synchronization is obtained analytically, whose feasibility is proved theoretically. The synchronization method is adopted to realize the generalized synchronization of 3.884-order hyperchaotic Lorenz system, and the numerical simulation results verify the effectiveness.

scholarly journals Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Liping Chen ◽  
Shanbi Wei ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Unknown Parameters ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Response Systems ◽  
The Stability ◽  
Adaptive Control Law

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

scholarly journals A Research on the Synchronization of Two Novel Chaotic Systems Based on a Nonlinear Active Control Algorithm

2015 ◽  
Vol 5 (1) ◽  
pp. 739-747 ◽  
Author(s):  
I. Ahmad ◽  
A. Saaban ◽  
A. Ibrahin ◽  
M. Shahzad
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Closed Loop System ◽  
Feedback Controllers ◽  
Control Techniques ◽  
Synchronization Problem ◽  
Response Systems ◽  
Globally Stable ◽  
Time Evaluation

The problem of chaos synchronization is to design a coupling between two chaotic systems (master-slave/drive-response systems configuration) such that the chaotic time evaluation becomes ideal and the output of the slave (response) system asymptotically follows the output of the master (drive) system. This paper has addressed the chaos synchronization problem of two chaotic systems using the Nonlinear Control Techniques, based on Lyapunov stability theory. It has been shown that the proposed schemes have outstanding transient performances and that analytically as well as graphically, synchronization is asymptotically globally stable. Suitable feedback controllers are designed to stabilize the closed-loop system at the origin. All simulation results are carried out to corroborate the effectiveness of the proposed methodologies by using Mathematica 9.

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