scholarly journals Chaos generalized synchronization of new Mathieu–Van der Pol systems with new Duffing–Van der Pol systems as functional system by GYC partial region stability theory

2011 ◽  
Vol 35 (11) ◽  
pp. 5245-5264 ◽  
Author(s):  
Zheng-Ming Ge ◽  
Shih-Yu Li
Keyword(s):  
Stability Theory ◽  
Functional System ◽  
Generalized Synchronization ◽  
Van Der Pol ◽  
Partial Region

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.

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 .

GENERALIZED SYNCHRONIZATION OF FRACTIONAL ORDER CHAOTIC SYSTEMS

2011 ◽  
Vol 25 (09) ◽  
pp. 1283-1292 ◽  
Author(s):  
MING-JUN WANG ◽  
XING-YUAN WANG
Keyword(s):  
Theoretical Analysis ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Chaotic Synchronization ◽  
Generalized Synchronization ◽  
Fractional Order Systems ◽  
Different Dimensions ◽  
The Stability ◽  
Synchronization Scheme

In the paper, generalized chaotic synchronization of a class of fractional order systems is studied. Based on the stability theory of linear fractional order systems, a generalized synchronization scheme is presented, and theoretical analysis is provided to verify its feasibility. The proposed method can realize generalized synchronization not only of fractional order systems with same dimension, but also of systems with different dimensions. Besides, the function relation of generalized synchronization can be linear or nonlinear. Numerical simulations show the effectiveness of the scheme.

Chaos control and anticontrol of a tachometer system by Ge—Yao—Chen partial region stability theory

2008 ◽  
Vol 223 (5) ◽  
pp. 1069-1082
Author(s):  
Z-M Ge ◽  
C-Y Chiang
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Stability Theory ◽  
Chaos Control ◽  
Homogeneous Function ◽  
Lower Degree ◽  
Partial Region ◽  
Simulation Results

In this paper, chaos control and anticontrol of a tachometer system by Ge—Yao—Chen (GYC) partial region stability are proposed. The Lyapunov function becomes a simple linear homogeneous function and the controllers become simpler by using the GYC partial region stability theory. The simulation results are more precise because the controllers are in lower degree than that of traditional controllers. Finally, chaos control and anticontrol of the tachometer system by GYC partial region stability are obtained and verified by numerical simulations.

SYNCHRONIZATION AND GENERALIZED SYNCHRONIZATION OF FRACTIONAL ORDER CHAOTIC SYSTEMS

2009 ◽  
Vol 23 (13) ◽  
pp. 1695-1714 ◽  
Author(s):  
XING-YUAN WANG ◽  
JING ZHANG
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
State Observer ◽  
Generalized Synchronization ◽  
Fractional Order Systems ◽  
The Stability

In this paper, based on the modified state observer method, synchronization and generalized synchronization of a class of fractional order chaotic systems are presented. The two synchronization approaches are theoretically and numerically studied and two simple criterions are proposed. By using the stability theory of linear fractional order systems, suitable conditions for achieving synchronization and generalized synchronization are given. Numerical simulations coincide with the theoretical analysis.

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