LINEAR AND NONLINEAR GENERALIZED SYNCHRONIZATION OF CHAOTIC SYSTEMS

2010 ◽  
Vol 24 (31) ◽  
pp. 6143-6155
Author(s):  
XING-YUAN WANG ◽  
JING ZHANG
Keyword(s):  
Numerical Simulations ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
State Observer ◽  
Drive System ◽  
Generalized Synchronization ◽  
Response System ◽  
Linear And Nonlinear ◽  
Synchronization Scheme ◽  
Application Scope

In this paper, the linear and nonlinear generalized synchronization of chaotic systems is investigated. Based on the modified state observer method, a new synchronization approach is proposed with more extensive application scope. The proposed synchronization scheme can realize the linear and nonlinear generalized synchronizations of same dimensional or different dimensional chaotic systems. Sufficient conditions of global asymptotic generalized synchronization between the drive system and the response system are gained on the basis of the state observer theory. Numerical simulations further illustrate the effectiveness of the proposed scheme.

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.

ROBUST DEAD-BEAT SYNCHRONIZATION AND COMMUNICATION FOR DISCRETE-TIME CHAOTIC SYSTEMS

2002 ◽  
Vol 12 (04) ◽  
pp. 835-846 ◽  
Author(s):  
KUANG-YOW LIAN ◽  
PETER LIU ◽  
CHIAN-SONG CHIU ◽  
TUNG-SHENG CHIANG
Keyword(s):  
Numerical Simulations ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Chaotic Systems ◽  
Performance Criterion ◽  
Drive System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Chaotic Communication ◽  
Response System

This paper proposes synchronization and chaotic communication for a class of Lur'e type discrete-time chaotic systems. The scalar outputs are suitably chosen in a flexible manner to be linear, nonlinear, or predictive, and along with the drive system are then written in an output injection form. Then with a suitable design of an observer-based response system, dead-beat performance is achieved for synchronization and chaotic communications. Then disturbances in the drive system are considered. Using an ℋ∞performance criterion, the disturbance is attenuated to a prescribed level by solving linear matrix inequalities (LMIs). Numerical simulations are carried out to verify the dead-beat performance.

Generalized Synchronization for Two Different Fractional-Order Chaotic Systems

2013 ◽  
Vol 336-338 ◽  
pp. 404-407
Author(s):  
Dong Zhang ◽  
Ya Fei Zhou
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Generalized Synchronization ◽  
Control Scheme ◽  
Synchronization Scheme

A generalized synchronization scheme for two new different fractional-order chaotic systems is considered. The control scheme is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed synchronization scheme.

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.

Synchronization of Continuous Scalar Chaotic Signal from Uncertain Chaotic System

2013 ◽  
Vol 816-817 ◽  
pp. 843-846
Author(s):  
Jing Wang ◽  
Hui Zhong
Keyword(s):  
Canonical Form ◽  
Chaotic System ◽  
Chaotic Systems ◽  
System Simulation ◽  
Chaotic Signal ◽  
Response System ◽  
Synchronization Scheme

This paper presents the synchronizing problem of scalar chaotic signal. A class of nonlinear chaotic systems is discussed which has unknown part in model. The proposed approach is based on canonical form of the response system. Simulation result shows the effectiveness of our synchronization scheme.

PROJECTIVE SYNCHRONIZATION OF TWO DIFFERENT DIMENSIONAL NONLINEAR SYSTEMS

2013 ◽  
Vol 27 (21) ◽  
pp. 1350113 ◽  
Author(s):  
FUZHONG NIAN ◽  
XINGYUAN WANG
Keyword(s):  
Nonlinear Systems ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Drive System ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Response System ◽  
Opposite Situation ◽  
The One ◽  
Hyperchaotic Systems

Projective synchronization between two nonlinear systems with different dimension was investigated. The controllers were designed when the dimension of drive system greater than the one of response system. The opposite situation also was discussed. In addition, we found an approach to control the chaotic (hyperchaotic) system to exhibit the behaviors of hyperchaotic (chaotic) system. The numerical simulations were implemented on different chaotic (hyperchaotic) systems, and the results indicate that our methods are effective.

ANTI-SYNCHRONIZATION OF A CLASS OF COUPLED CHAOTIC SYSTEMS VIA LINEAR FEEDBACK CONTROL

2006 ◽  
Vol 16 (04) ◽  
pp. 1041-1047 ◽  
Author(s):  
CHUANDONG LI ◽  
XIAOFENG LIAO
Keyword(s):  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Linear Feedback ◽  
Generalized Synchronization ◽  
Lyapunov Stability Theorem ◽  
Linear Feedback Control ◽  
Relevant Variables ◽  
Special Case

As a special case of generalized synchronization, chaos anti-synchronization can be characterized by the vanishing of the sum of relevant variables. In this paper, based on Lyapunov stability theorem for ordinary differential equations, several sufficient conditions for guaranteeing the existence of anti-synchronization in a class of coupled identical chaotic systems via linear feedback or adaptive linear feedback methods are derived. Chua's circuit is presented as an example to demonstrate the effectiveness of the proposed approach by computer simulations.

scholarly journals Compound-combination synchronization of chaos in identical and different orders chaotic systems

2015 ◽  
Vol 25 (4) ◽  
pp. 463-490 ◽  
Author(s):  
K. S. Ojo ◽  
A. N. Njah ◽  
O. I. Olusola
Keyword(s):  
Chaotic Systems ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Backstepping Technique ◽  
Third Order ◽  
Combination Synchronization ◽  
Response Systems ◽  
Drive Systems ◽  
Synchronization Scheme ◽  
Insight Into

Abstract This paper proposes a new synchronization scheme called compound-combination synchronization. The scheme is investigated using six chaotic Josephson junctions evolving from different initial conditions based on the drive-response configuration via the active backstepping technique. The technique is applied to achieve compound-combination synchronization of: (i) six identical third order resistive-capacitive-inductive-shunted Josepshon junctions (RCLSJJs) (with three as drive and three as response systems); (ii) three third order RCLSJJs (as drive systems) and three second order resistive-capacitive-shunted Josepshon junctions (RCSJJs (as response systems). In each case, sufficient conditions for global asymptotic stability for compound-combination synchronization to any desired scaling factors are achieved. Numerical simulations are employed to verify the feasibility and effectiveness of the compound-combination synchronization scheme. The result shows that this scheme could be used to vary the junction signal to any desired level and also give a better insight into synchronization in biological systems wherein different organs of different dynamical structures and orders are involved. The scheme could also provide high security in information transmission due to the complexity of its dynamical formulation.

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.

A SIMPLE SYNCHRONIZATION SCHEME OF COULLET SYSTEMS WITH UNKNOWN PARAMETERS

2014 ◽  
Vol 28 (06) ◽  
pp. 1450021
Author(s):  
ZUO-LEI WANG ◽  
XUE-RONG SHI ◽  
YAOLIN JIANG
Keyword(s):  
Adaptive Control ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Unknown Parameters ◽  
Control Scheme ◽  
Single Controller ◽  
Synchronization Scheme ◽  
Adaptive Control Scheme

Synchronization of Coullet systems is investigated via back stepping method when parameters are unknown. A novel adaptive control scheme is presented, which contains a single controller. To achieve the synchronization of Coullet systems, sufficient conditions are derived and the unknown parameters are estimated. Finally, some numerical simulations are employed to verify the effectiveness of the proposed scheme.

Sign in / Sign up

Export Citation Format

Share Document