scholarly journals Hybrid Chaos Synchronization of Four–Scroll Systems via Active Control

2014 ◽  
Vol 65 (2) ◽  
pp. 97-103 ◽  
Author(s):  
Rajagopal Karthikeyan ◽  
Vaidyanathan Sundarapandian
Keyword(s):  
Numerical Simulations ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Hybrid Synchronization ◽  
Active Control Method

Abstract This paper investigates the hybrid chaos synchronization of identical Wang four-scroll systems (Wang, 2009), identical Liu-Chen four-scroll systems (Liu and Chen, 2004) and non-identical Wang and Liu-Chen four-scroll systems. Active control method is the method adopted to achieve the hybrid chaos synchronization of the four-scroll chaotic systems addressed in this paper and our synchronization results are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to hybrid synchronize identical and different Wang and Liu-Chen four-scroll chaotic systems. Numerical simulations are also shown to illustrate and validate the hybrid synchronization results derived in this paper.

ANTI-SYNCHRONIZATION OF UNIFIED HYPERCHAOTIC SYSTEMS

2014 ◽  
Vol 28 (05) ◽  
pp. 1450014
Author(s):  
PI LI ◽  
XING-YUAN WANG ◽  
PENG SUN ◽  
CHAO LUO ◽  
XIU-KUN WANG
Keyword(s):  
Adaptive Control ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Control Methods ◽  
System Parameters ◽  
Hyperchaotic Systems ◽  
Active Control Method

In this paper, active control and adaptive control methods are applied, respectively. Adaptive control method is implemented when system parameters are unknown and active control method is applied when system parameters are known. Based on the Lyapunov stability theory, the controllers are designed to realize anti-synchronization, meanwhile, the update laws of parameters are proposed. The theoretical proof is given. And two groups of examples are shown to verify the effectiveness of the proposed schemes.

Synchronization of Hyperchaotic Memristor-Based Chua’s Circuits

2014 ◽  
Vol 644-650 ◽  
pp. 3485-3488
Author(s):  
Hai Long Huang ◽  
Yan Peng ◽  
Jun Jian Huang
Keyword(s):  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Sufficient Condition ◽  
Global Synchronization ◽  
Error System ◽  
The Stability ◽  
Active Control Method

This paper further investigates the problem of synchronization of hyperchaotic memristor-based Chua’s circuits. An active control method is employed to design a controller to achieve the global synchronization of two identical memristor-based systems. Based on Lyapunov stability theory, a sufficient condition is given to guarantee the stability of the synchronization error system.

scholarly journals On Full-State Hybrid Projective Synchronization of General Discrete Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Adel Ouannas
Keyword(s):  
Lyapunov Stability ◽  
Discrete Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Full State ◽  
Hybrid Projective Synchronization ◽  
Nonlinear Control Method

The problems of full-state hybrid projective synchronization (FSHPS) and inverse full-state hybrid projective synchronization (IFSHPS) for general discrete chaotic systems are investigated in 2D. Based on nonlinear control method and Lyapunov stability theory, new controllers are designed to study FSHPS and IFSHPS, respectively, for 2D arbitrary chaotic systems in discrete-time. Numerical example and simulations are used to validate the main results of this paper.

scholarly journals The Synchronization of N Cascade-Coupled Chaotic Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Pengyu Li ◽  
Juan Du ◽  
Shouliang Li ◽  
Yazhao Zheng ◽  
Bowen Jia
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
General Criterion ◽  
Synchronization Method ◽  
Bidirectional Coupling ◽  
Coupling Parameters

In this paper, we investigate a novel synchronization method, which consists of nn≥2 cascade-coupled chaotic systems. Furthermore, as the number of chaotic systems decreases from n to 2, the proposed synchronization will transform into bidirectional coupling synchronization. Based on Lyapunov stability theory, a general criterion is proposed for choosing the appropriate coupling parameters to ensure cascading synchronization. Moreover, 4 Lü systems are taken as an example and the corresponding numerical simulations demonstrate the effectiveness of our idea.

DIGITAL CRYPTOGRAPHY AND FEEDBACK SYNCHRONIZATION OF CHAOTIC SYSTEMS

2011 ◽  
Vol 25 (04) ◽  
pp. 521-529 ◽  
Author(s):  
MALA MITRA ◽  
SANTO BANERJEE
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Coupled System ◽  
Lyapunov Stability Theory ◽  
Chaotic Synchronization ◽  
Feedback Controller ◽  
New Method ◽  
Secure Communications

Secure communications via chaotic synchronization is demonstrated in this literature. At first we have designed a feedback controller for chaotic synchronization utilizing the Lyapunov stability theory for cascade-connected systems.The method has been applied successfully to make two identical systems globally asymptotically synchronized. The result of numerical simulations are given to validate the effectiveness of this method. Then we have discussed a new method of cryptography for this coupled system which is very simple to implement and effective.

Dual Combination Synchronization of Six Chaotic Systems

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Junwei Sun ◽  
Suxia Jiang ◽  
Guangzhao Cui ◽  
Yanfeng Wang
Keyword(s):  
Adaptive Control ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Combination Synchronization

Based on combination synchronization of three chaotic systems and combination–combination synchronization of four chaotic systems, a novel scheme of dual combination synchronization is investigated for six chaotic systems in the paper. Using combined adaptive control and Lyapunov stability theory of chaotic systems, some sufficient conditions are attained to realize dual combination synchronization of six chaotic systems. The corresponding theoretical proofs and numerical simulations are presented to demonstrate the effectiveness and correctness of the dual combination synchronization. Due to the complexity of dual combination synchronization, it will be more secure and interesting to transmit and receive signals in application of communication.

Robust Finite-Time Stabilization of Fractional-Order Chaotic Systems based on Fractional Lyapunov Stability Theory

2012 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Pourmahmood Aghababa
Keyword(s):  
Fractional Order ◽  
Lyapunov Stability ◽  
Finite Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Convergence Time ◽  
Control Approach ◽  
Finite Time Stability

This paper concerns the problem of stabilization of uncertain fractional-order chaotic systems in finite time. On the basis of fractional Lyapunov stability theory, a robust finite-time fractional controller is introduced to control chaos of fractional-order chaotic systems in the presence of system uncertainties. The finite-time stability of the closed-loop system is analytically proved. An estimation of the convergence time is also given. Some numerical simulations are provided to illustrate the usefulness and applicability of the proposed robust finite-time control approach. It is worth noting that the proposed fractional control method is applicable for stabilizing a broad range of uncertain fractional-order nonlinear systems in a given finite time.

PARAMETER IDENTIFICATION AND ADAPTIVE SYNCHRONIZATION CONTROL OF A LORENZ-LIKE SYSTEM

2008 ◽  
Vol 22 (15) ◽  
pp. 2453-2461 ◽  
Author(s):  
XINGYUAN WANG ◽  
YONG WANG
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Uncertain System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
Synchronization Control ◽  
System Parameters

This paper analyzes the synchronization control of new chaotic systems called Lorenz-like systems. Based on the Lyapunov stability theory, an adaptive controller and a parameter update rule are designed. It is proved that the controller and update rule not only achieve self-synchronization of Lorenz-like systems but can also make the Lorenz-like system asymptotically synchronized with the Rössler system, and further identify the uncertain system parameters. Numerical simulations have shown the effectiveness of the adaptive controller.

scholarly journals Combination-Combination Synchronization of Four Nonlinear Complex Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaobing Zhou ◽  
Lianglin Xiong ◽  
Xiaomei Cai
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Combination Synchronization ◽  
Special Cases ◽  
Complex Chaotic Systems

This paper investigates the combination-combination synchronization of four nonlinear complex chaotic systems. Based on the Lyapunov stability theory, corresponding controllers to achieve combination-combination synchronization among four different nonlinear complex chaotic systems are derived. The special cases, such as combination synchronization and projective synchronization, are studied as well. Numerical simulations are given to illustrate the theoretical analysis.

Anti-Synchronization of Pan and Lorenz-Lu-Liu-Cai Chaotic Systems by Active Nonlinear Control

2012 ◽  
Vol 3 (2) ◽  
pp. 15-25 ◽  
Author(s):  
Ayub Khan ◽  
Ram Pravesh Prasad
Keyword(s):  
Nonlinear Control ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Exponential Synchronization ◽  
Global Exponential Synchronization

In this paper, the authors investigate the anti-synchronization of chaotic Pan, Lorenz, and Lu systems and anti-synchronization of Liu and Cai systems. Global exponential synchronization of Pan, Lorenz, Lu, Liu, and Cai chaotic systems are established by using Lyapunov stability theory. Numerical simulations are performed to illustrate the effectiveness of the proposed synchronization schemes for Pan, Lorenz, Lu, Liu, and Cai chaotic systems.

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