Hybrid Synchronization of Three Identical Coupled Chaotic Systems Using the Direct Design Method

2014 ◽  
Vol 912-914 ◽  
pp. 695-699 ◽  
Author(s):  
Xiu Huan Ji
Keyword(s):  
Nonlinear System ◽  
Theoretical Analysis ◽  
Stability Criterion ◽  
Chaotic Systems ◽  
Design Method ◽  
Complete Synchronization ◽  
Numerical Example ◽  
Direct Design ◽  
Error System ◽  
Hybrid Synchronization

This paper investigates the hybrid synchronization behavior (coexistence of anti-synchronization and complete synchronization) in three coupled chaotic systems with ring connections. We employ the direct design method to design the hybird synchronization controllers, which transform the error system into a nonlinear system with a special antisymmetric structure. A simple stability criterion is then derived for reaching hybrid synchronization. Finally, numerical example is provided to demonstrate the effectiveness of the theoretical analysis.

scholarly journals Synchronization of Coupled Chaotic Systems with Ring Connection Based on Special Antisymmetric Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xiangyong Chen ◽  
Jianlong Qiu ◽  
Qiang Song ◽  
Ancai Zhang
Keyword(s):  
Theoretical Analysis ◽  
Chaotic Systems ◽  
Design Method ◽  
Stable System ◽  
Stability Criteria ◽  
Complete Synchronization ◽  
Numerical Examples ◽  
Synchronization Problem ◽  
Direct Design ◽  
Error System

This paper considers the complete synchronization problem for coupled chaotic systems with ring connections. First, we use a direct design method to design a synchronization controller. It transforms the error system into a stable system with special antisymmetric structure. And then, we get some simple stability criteria of achieving the complete synchronization. These criteria are not only easily verified but also improve and generalize previous known results. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical analysis.

scholarly journals Synchronization ofNDifferent Chaotic Systems Based on Antisymmetric Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Xiangyong Chen ◽  
Jianlong Qiu
Keyword(s):  
Nonlinear System ◽  
Chaotic Systems ◽  
Control Method ◽  
Stability Conditions ◽  
Complete Synchronization ◽  
Direct Design ◽  
Sufficient Stability ◽  
Error System ◽  
Different Chaotic Systems ◽  
Sufficient Stability Conditions

The problem of synchronization ofNdifferent chaotic systems is investigated. By using the direct design control method, the synchronization controler is designed to transform the error system into a nonlinear system with a special antisymmetric structure. The sufficient stability conditions are presented for such systems, and the complete synchronization of chaotic systems is realized. Finally, the corresponding numerical simulations demonstrate the effectiveness of the proposed schemes.

scholarly journals Parameter Identification and Hybrid Synchronization in an Array of Coupled Chaotic Systems with Ring Connection: An Adaptive Integral Sliding Mode Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Nazam Siddique ◽  
Fazal ur Rehman
Keyword(s):  
Sliding Mode Control ◽  
Parameter Identification ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Design Method ◽  
Integral Sliding Mode Control ◽  
Integral Sliding Mode ◽  
Mode Control ◽  
Error System ◽  
Hybrid Synchronization

This article presents an adaptive integral sliding mode control (SMC) design method for parameter identification and hybrid synchronization of chaotic systems connected in ring topology. To employ the adaptive integral sliding mode control, the error system is transformed into a special structure containing nominal part and some unknown terms. The unknown terms are computed adaptively. Then the error system is stabilized using integral sliding mode control. The controller of the error system is created that contains both the nominal control and the compensator control. The adapted laws and compensator controller are derived using Lyapunov stability theory. The effectiveness of the proposed technique is validated through numerical examples.

scholarly journals Synchronization of bidirectional N-coupled fractional-order chaotic systems with ring connection based on antisymmetric structure

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Cuimei Jiang ◽  
Akbar Zada ◽  
M. Tamer Şenel ◽  
Tongxing Li
Keyword(s):  
Fractional Order ◽  
Lyapunov Functions ◽  
Chaotic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Order Error ◽  
Synchronization Problem ◽  
Direct Design ◽  
Error System ◽  
Theoretical Results

Abstract This paper discusses the synchronization problem of N-coupled fractional-order chaotic systems with ring connection via bidirectional coupling. On the basis of the direct design method, we design the appropriate controllers to transform the fractional-order error dynamical system into a nonlinear system with antisymmetric structure. By choosing appropriate fractional-order Lyapunov functions and employing the fractional-order Lyapunov-based stability theory, several sufficient conditions are obtained to ensure the asymptotical stabilization of the fractional-order error system at the origin. The proposed method is universal, simple, and theoretically rigorous. Finally, some numerical examples are presented to illustrate the validity of theoretical results.

PARTIAL STATE IMPULSIVE SYNCHRONIZATION OF A CLASS OF NONLINEAR SYSTEMS

2009 ◽  
Vol 19 (01) ◽  
pp. 387-393 ◽  
Author(s):  
YAN-WU WANG ◽  
CHANGYUN WEN ◽  
YENG CHAI SOH ◽  
ZHI-HONG GUAN
Keyword(s):  
Nonlinear System ◽  
Theoretical Analysis ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Hyperchaotic System ◽  
Impulsive Synchronization ◽  
Partial State ◽  
Simulation Results ◽  
System States ◽  
Synchronization Scheme

Impulsive synchronization of chaotic systems is an attractive topic and a number of interesting results have been obtained in recent years. However, all of these results on impulsive synchronization need to employ full states of the system to achieve the desired objectives. In this paper, impulsive synchronization that needs only part of system states is studied for a class of nonlinear system. Typical chaotic systems, such as Lorenz system, Chen's system, and a 4D hyperchaotic system, are taken as examples. A new scheme is proposed to select the impulsive intervals. After some theoretical analysis, simulation results show the effectiveness of the proposed synchronization scheme.

scholarly journals Synchronization and Antisynchronization of N-Coupled Complex Permanent Magnet Synchronous Motor Systems with Ring Connection

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Cuimei Jiang ◽  
Shutang Liu
Keyword(s):  
Permanent Magnet ◽  
Chaotic Systems ◽  
Design Method ◽  
Permanent Magnet Synchronous Motor ◽  
Mathematical Expression ◽  
Permanent Magnet Synchronous Motors ◽  
Synchronous Motors ◽  
Direct Design ◽  
General Complex ◽  
Complex Chaotic Systems

This paper discusses synchronization and antisynchronization of N-coupled complex permanent magnet synchronous motors systems with ring connection. Based on the direct design method and antisymmetric structure, the appropriate controllers are designed to ensure the occurrence of synchronization and antisynchronization in an array of N-coupled general complex chaotic systems described by a unified mathematical expression with ring connection. The proposed method is flexible and is suitable both for design and for implementation in practice. Numerical results are plotted to show the rapid convergence of errors to zero and further verify the effectiveness and feasibility of the theoretical scheme.

Synchronization and anti-synchronization of N different coupled chaotic systems with ring connection

2014 ◽  
Vol 25 (05) ◽  
pp. 1440011 ◽  
Author(s):  
Xiangyong Chen ◽  
Chengyong Wang ◽  
Jianlong Qiu
Keyword(s):  
Chaotic Systems ◽  
Design Method ◽  
Stable System ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Synchronization Problem ◽  
Symmetric Structure ◽  
Direct Design

This paper considers the synchronization and anti-synchronization problem of N different coupled chaotic systems with ring connections. Employing the direct design method to design the synchronization and anti-synchronization controllers which can transform the error systems into a stable system with special anti-symmetric structure. Some simple stability criteria are then derived for reaching the synchronization in such systems. It is proved that these criteria not only are easily verified, but also improve and generalize previously known results. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical.

scholarly journals Generalized Synchronization of Different Chaotic Systems Based on Nonnegative Off-Diagonal Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Ling Guo ◽  
Xiaohong Nian ◽  
Huan Pan
Keyword(s):  
Chaotic Systems ◽  
Matrix Theory ◽  
Design Method ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Generalized Synchronization ◽  
Synchronization Problem ◽  
Direct Design ◽  
The Stability ◽  
Different Chaotic Systems

The generalized synchronization problem is studied in this paper for different chaotic systems with the aid of the direct design method. Based on Lyapunov stability theory and matrix theory, some sufficient conditions guaranteeing the stability of a nonlinear system with nonnegative off-diagonal structure are obtained. Then the control scheme is designed from the stable system by the direct design method. Finally, two numerical simulations are provided to verify the effectiveness and feasibility of the proposed method.

scholarly journals A Simple Hybrid Synchronization for a Class of Chaotic Financial Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Jiming Zheng ◽  
Xiaoshuang Li ◽  
Yang Qiu
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Financial System ◽  
Asymptotically Stable ◽  
Financial Systems ◽  
Master System ◽  
Error System ◽  
Hybrid Synchronization ◽  
Novel Algorithm

It is an important to achieve the hybrid synchronization of the chaotic financial system. Chaos synchronization is equivalent to the error system which is asymptotically stable. The hybrid synchronization for a class of finance chaotic systems is discussed. First, a simple single variable controller is obtained to synchronize two identical chaotic financial systems with different initial conditions. Second, a novel algorithm is proposed to determine the variables of the master system that should antisynchronize with corresponding variables of the slave system and use this algorithm to determine the corresponding variables in the chaotic financial systems. The hybrid synchronization of the chaotic financial systems is realized by a simple controller. At the same time, different controllers can implement the chaotic financial system hybrid synchronization. In comparison with the existing results, the obtained controllers in this paper are simpler than those of the existing results. Finally, numerical simulations show the effectiveness of the proposed results.

Sliding mode projective synchronization for fractional-order coupled systems based on network without strong connectedness

2021 ◽  
pp. 014233122110009
Author(s):  
Xin Meng ◽  
Baoping Jiang ◽  
Cunchen Gao
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Coupled Systems ◽  
Projective Synchronization ◽  
Slave System ◽  
Complete Synchronization ◽  
Synchronization Problem ◽  
Strong Connectedness ◽  
Master System ◽  
Error System

This paper considers the Mittag-Leffler projective synchronization problem of fractional-order coupled systems (FOCS) on the complex networks without strong connectedness by fractional sliding mode control (SMC). Combining the hierarchical algorithm with the graph theory, a new SMC strategy is designed to realize the projective synchronization between the master system and the slave system, which covers the globally complete synchronization and the globally anti-synchronization. In addition, some novel criteria are derived to guarantee the Mittag-Leffler stability of the projective synchronization error system. Finally, a numerical example is given to illustrate the validity of the proposed method.

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