Chaos Hybrid Generalized Synchronization of Liu-Chen System by GYC Partial Region Stability Theory

2013 ◽  
Vol 10 (4) ◽  
pp. 825-831 ◽  
Author(s):  
Cheng-Hsiung Yang
Keyword(s):  
Stability Theory ◽  
Generalized Synchronization ◽  
Chen System ◽  
Partial Region

PARAMETER IDENTIFICATION AND ADAPTIVE SYNCHRONIZATION OF UNCERTAIN HYPERCHAOTIC CHEN SYSTEM

2008 ◽  
Vol 22 (08) ◽  
pp. 1015-1023 ◽  
Author(s):  
XINGYUAN WANG ◽  
XIANGJUN WU
Keyword(s):  
Adaptive Control ◽  
Parameter Identification ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Adaptive Synchronization ◽  
Control Law ◽  
Uncertain Parameters ◽  
Chen System ◽  
Adaptive Control Law

This paper studies the adaptive synchronization and parameter identification of an uncertain hyperchaotic Chen system. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical hyperchaotic Chen systems asymptotically synchronized. With this approach, the synchronization and parameter identification of the hyperchaotic Chen system with five uncertain parameters can be achieved simultaneously. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

scholarly journals Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Shih-Yu Li ◽  
Shi-An Chen ◽  
Chin-Teng Lin ◽  
Li-Wei Ko ◽  
Cheng-Hsiung Yang ◽  
...  
Keyword(s):  
Control Strategy ◽  
Stability Theory ◽  
High Performance ◽  
Chaotic Systems ◽  
Control Function ◽  
Homogeneous Function ◽  
Functional System ◽  
Generalized Synchronization ◽  
High Efficient ◽  
Lyapunov Control

A novel bioinspired control strategy design is proposed for generalized synchronization of nonlinear chaotic systems, combining the bioinspired stability theory, fuzzy modeling, and a novel, simple-form Lyapunov control function design of derived high efficient, heuristic and bioinspired controllers. Three main contributions are concluded: (1) apply the bioinspired stability theory to further analyze the stability of fuzzy error systems; the high performance of controllers has been shown in previous study by Li and Ge 2009, (2) a new Lyapunov control function based on bioinspired stability theory is designed to achieve synchronization without using traditional LMI method, which is a simple linear homogeneous function of states and the process of designing controller to synchronize two fuzzy chaotic systems becomes much simpler, and (3) three different situations of synchronization are proposed; classical master and slave Lorenz systems, slave Chen’s system, and Rossler’s system as functional system are illustrated to further show the effectiveness and feasibility of our novel strategy. The simulation results show that our novel control strategy can be applied to different and complicated control situations with high effectiveness.

LINEAR GENERALIZED CHAOTIC SYNCHRONIZATION VIA SINGLE CHANNEL

2011 ◽  
Vol 25 (21) ◽  
pp. 2879-2887
Author(s):  
XING-YUAN WANG ◽  
MING-JUN WANG
Keyword(s):  
Numerical Simulations ◽  
Single Channel ◽  
Chaotic Synchronization ◽  
Drive System ◽  
Generalized Synchronization ◽  
Chen System ◽  
Response System ◽  
Replacement Method ◽  
Simulation Results ◽  
Transitional System

In this paper, the drive system and the response system can be in a state of linear generalized synchronization via transmitting single signal. By means of a transitional system, the response system is obtained by variable replacement method. Chen system and hyperchaotic Chen system are used as examples in numerical simulations. Simulation results show the effectiveness of the method.

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.

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.

scholarly journals Generalized synchronization of identical and nonidentical chaotic dynamical systems via master approaches

2017 ◽  
Vol 7 (3) ◽  
pp. 248-254
Author(s):  
Shko Ali-Tahir ◽  
Murat Sari ◽  
Abderrahman Bouhamidi
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Generalized Synchronization ◽  
Chaotic Dynamical Systems

The main objective of this work is to discuss a generalized synchronization of a coupled chaotic identicaland nonidentical dynamical systems. We propose a method used to study generalized synchronization in masterslavesystems. This method, is based on the classical Lyapunov stability theory, utilizes the master continuous timechaotic system to monitor the synchronized motions. Various numerical simulations are performed to verify theeffectiveness of the proposed approach.

Generalized Synchronization of Chaos in RCL-Shunted Josephson Junction with Uncertain Parameters

2012 ◽  
Vol 157-158 ◽  
pp. 752-756
Author(s):  
Na Fang ◽  
Jie Fang
Keyword(s):  
Numerical Simulation ◽  
Adaptive Control ◽  
Josephson Junction ◽  
Stability Theory ◽  
Chaotic Dynamics ◽  
Control Method ◽  
Uncertain Parameters ◽  
Generalized Synchronization ◽  
Nonlinear Feedback ◽  
Scaling Factors

This paper investigates the generalized synchronization of chaotic dynamics in resistive capacitive inductance (RCL)-shunted Josephson junctions with uncertain parameters.Based on Lyapunove stability theory and adaptive control method, unified nonlinear feedback controller and the parameter update laws are pesented .Numerical simulation illustrate that the system can realize generalized synchronization by different scaling factors .

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