scholarly journals Lag Synchronization of Coupled Multidelay Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Luo Qun ◽  
Peng Hai-Peng ◽  
Xu Ling-Yu ◽  
Yang Yi Xian
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Theory ◽  
Sufficient Condition ◽  
Improved Method ◽  
Lag Synchronization

Chaos synchronization is an active topic, and its possible applications have been studied extensively. In this paper we present an improved method for lag synchronization of chaotic systems with coupled multidelay. The Lyapunov theory is used to consider the sufficient condition for synchronization. The specific examples will demonstrate and verify the effectiveness of the proposed approach.

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.

scholarly journals Symplectic Synchronization of Lorenz-Stenflo System with Uncertain Chaotic Parameters via Adaptive Control

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Cheng-Hsiung Yang
Keyword(s):  
Adaptive Control ◽  
Secure Communication ◽  
Communication Systems ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Asymptotical Stability ◽  
Sufficient Condition ◽  
Null Solution ◽  
Special Cases ◽  
Error Dynamics

A new symplectic chaos synchronization of chaotic systems with uncertain chaotic parameters is studied. The traditional chaos synchronizations are special cases of the symplectic chaos synchronization. A sufficient condition is given for the asymptotical stability of the null solution of error dynamics and a parameter difference. The symplectic chaos synchronization with uncertain chaotic parameters may be applied to the design of secure communication systems. Finally, numerical results are studied for symplectic chaos synchronized from two identical Lorenz-Stenflo systems in three different cases.

$\mathcal{H}_{\infty}$ LAG SYNCHRONIZATION FOR CHAOTIC SYSTEMS

2011 ◽  
Vol 25 (21) ◽  
pp. 2801-2812 ◽  
Author(s):  
CHOON KI AHN
Keyword(s):  
Chaotic Systems ◽  
External Disturbance ◽  
Lyapunov Theory ◽  
Linear Matrix ◽  
Lag Synchronization ◽  
Convex Optimization Problem ◽  
Synchronization Problem ◽  
Norm Constraint ◽  
Synchronization Scheme ◽  
New Formula

In this paper, we propose a new [Formula: see text] lag synchronization scheme for a general class of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) approach, the [Formula: see text] lag synchronization controller is presented to not only guarantee exponential lag synchronization but also reduce the effect of external disturbance to an [Formula: see text] norm constraint. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. As an application of the proposed method, the [Formula: see text] lag synchronization problem for Genesio–Tesi system is investigated.

scholarly journals Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems

2017 ◽  
Vol 7 (6) ◽  
pp. 3446 ◽  
Author(s):  
Hamed Tirandaz ◽  
Mohsen Ahmadnia ◽  
Hamid Reza Tavakoli
Keyword(s):  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Lag Synchronization ◽  
Synchronization Problem ◽  
Projective Lag Synchronization ◽  
Control And Synchronization

In this paper, the synchronization problem of T chaotic system and Lu chaotic system is studied. The parameter of the drive T chaotic system is considered unknown. An adaptive projective lag control method and also parameter estimation law are designed to achieve chaos synchronization problem between two chaotic systems. Then Lyapunov stability theorem is utilized to prove the validity of the proposed control method. After that, some numerical simulations are performed to assess the performance of the proposed method. The results show high accuracy of the proposed method in control and synchronization of chaotic systems.

Chaos Anti-Synchronization between Chen System and Lu System

2014 ◽  
Vol 631-632 ◽  
pp. 710-713 ◽  
Author(s):  
Xian Yong Wu ◽  
Hao Wu ◽  
Hao Gong
Keyword(s):  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Theory ◽  
State Variables ◽  
Chen System ◽  
System Parameters ◽  
Control Scheme ◽  
Error Dynamics ◽  
The Stability ◽  
Different Chaotic Systems

Anti-synchronization of two different chaotic systems is investigated. On the basis of Lyapunov theory, adaptive control scheme is proposed when system parameters are unknown, sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed using the sum of the state variables in chaotic systems. Numerical simulations are performed for the Chen and Lu systems to demonstrate the effectiveness of the proposed control strategy.

Optimal Synchronization of a Memristive Chaotic Circuit

2016 ◽  
Vol 26 (06) ◽  
pp. 1650093 ◽  
Author(s):  
Michaux Kountchou ◽  
Patrick Louodop ◽  
Samuel Bowong ◽  
Hilaire Fotsin ◽  
Jurgen Kurths
Keyword(s):  
Numerical Simulations ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Analog Circuit ◽  
Electronic Circuit ◽  
Dynamical Behavior ◽  
Circuit Implementation ◽  
Chaotic Circuit ◽  
Dynamical Properties ◽  
Analog Circuit Implementation

This paper deals with the problem of optimal synchronization of two identical memristive chaotic systems. We first study some basic dynamical properties and behaviors of a memristor oscillator with a simple topology. An electronic circuit (analog simulator) is proposed to investigate the dynamical behavior of the system. An optimal synchronization strategy based on the controllability functions method with a mixed cost functional is investigated. A finite horizon is explicitly computed such that the chaos synchronization is achieved at an established time. Numerical simulations are presented to verify the effectiveness of the proposed synchronization strategy. Pspice analog circuit implementation of the complete master-slave-controller systems is also presented to show the feasibility of the proposed scheme.

An Adaptive Chaos Synchronization with Controller and Secure Communication

2013 ◽  
Vol 401-403 ◽  
pp. 1657-1660
Author(s):  
Bin Zhou ◽  
Xiang Wang ◽  
Yu Gao ◽  
Shao Cheng Qu
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Secure Communication ◽  
Chaos Synchronization ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
Sufficient Condition ◽  
Control Parameters

An adaptive controller with adaptive rate is presented to synchronize two chaos systems and to apply to secure communication. Based on Lyapunov stability theory, a sufficient condition and adaptive control parameters are obtained. Finally, the simulation with synchronization and secure communication is given to show the effectiveness of the proposed method. Keywords: adaptive; synchronization; observer; controller.

Noninvertible Piecewise Linear Maps Applied to Chaos Synchronization and Secure Communications

1997 ◽  
Vol 07 (07) ◽  
pp. 1617-1634 ◽  
Author(s):  
G. Millerioux ◽  
C. Mira
Keyword(s):  
Dynamical Systems ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Piecewise Linear ◽  
A Priori ◽  
Secure Communications ◽  
Technological Parameters ◽  
Linear Maps ◽  
Piecewise Linear Maps ◽  
Necessary And Sufficient

Recently, it was demonstrated that two chaotic dynamical systems can synchronize each other, leading to interesting applications as secure communications. We propose in this paper a special class of dynamical systems, noninvertible discrete piecewise linear, emphasizing on interesting advantages they present compared with continuous and differentiable nonlinear ones. The generic aspect of such systems, the simplicity of numerical implementation, and the robustness to mismatch of technological parameters make them good candidates. The classical concept of controllability in the control theory is presented and used in order to choose and predict the number of appropriate variables to be transmitted for synchronization. A necessary and sufficient condition of chaotic synchronization is established without computing numerical quantities, introducing a state affinity structure of chaotic systems which provides an a priori establishment of synchronization.

Reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems

2009 ◽  
Vol 59 (4) ◽  
pp. 529-534 ◽  
Author(s):  
Liping Zhang ◽  
Haibo Jiang ◽  
Qinsheng Bi
Keyword(s):  
Chaotic Systems ◽  
Lag Synchronization

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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