scholarly journals Synchronization of Different Fractional Order Time-Delay Chaotic Systems Using Active Control

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Jianeng Tang
Keyword(s):  
Time Delay ◽  
Laplace Transform ◽  
Numerical Simulations ◽  
Active Control ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Technique ◽  
The Laplace Transform

Chaos synchronization of different fractional order time-delay chaotic systems is considered. Based on the Laplace transform theory, the conditions for achieving synchronization of different fractional order time-delay chaotic systems are analyzed by use of active control technique. Then numerical simulations are provided to verify the effectiveness and feasibility of the developed method. At last, effects of the fraction order and the time delay on synchronization are further researched.

Synchronization of Different Fractional Order Time-Delay Chaotic Systems Using Active Control

2013 ◽  
Vol 805-806 ◽  
pp. 1975-1978
Author(s):  
Jia Neng Tang
Keyword(s):  
Time Delay ◽  
Laplace Transform ◽  
Numerical Simulations ◽  
Active Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Technique ◽  
The Laplace Transform

In this paper, based on the Laplace transform theory, the conditions for achieving synchronization of different fractional order time-delay chaotic systems are analyzed by use of active control technique. Then numerical simulations are provided to verify the effectiveness and feasibility of the developed method.

CHAOS SYNCHRONIZATION OF FRACTIONAL-ORDER DIFFERENTIAL SYSTEMS

2006 ◽  
Vol 20 (07) ◽  
pp. 791-803 ◽  
Author(s):  
CHANGPIN LI ◽  
WEIHUA DENG
Keyword(s):  
Laplace Transform ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Fractional Systems ◽  
Coupling Methods ◽  
The Laplace Transform ◽  
Fractional Orders

Chaos synchronization of the Duffing, Lorenz and Rössler systems with fractional orders are studied theoretically and numerically. Three methods are applied in this paper: combination of active-passive decomposition (APD) and one-way coupling methods, Pecora–Carroll method, bidirectional coupling method. The sufficient conditions of achieving synchronization between two identical fractional systems are derived by using the Laplace transform theory. Numerical simulations demonstrate the effectiveness of the proposed synchronization schemes for these fractional systems.

scholarly journals Chaos Synchronization between Two Different Fractional Systems of Lorenz Family

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
A. E. Matouk
Keyword(s):  
Theoretical Analysis ◽  
Laplace Transform ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Order Parameter ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Chen System ◽  
Fractional Systems ◽  
Lü System

This work investigates chaos synchronization between two different fractional order chaotic systems of Lorenz family. The fractional order Lü system is controlled to be the fractional order Chen system, and the fractional order Chen system is controlled to be the fractional order Lorenz-like system. The analytical conditions for the synchronization of these pairs of different fractional order chaotic systems are derived by utilizing Laplace transform. Numerical simulations are used to verify the theoretical analysis using different values of the fractional order parameter.

Synchronization of fractional-order different memristor-based chaotic systems using active control

2014 ◽  
Vol 92 (12) ◽  
pp. 1688-1695 ◽  
Author(s):  
R. Rakkiyappan ◽  
R. Sivasamy ◽  
Ju H. Park
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Active Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Control Technique ◽  
Fractional Order Differential Equations ◽  
Predictor Corrector

In this article, synchronization of two different fractional-order memristor-based chaotic systems is considered. To achieve synchronization, an active control technique is used. The main proof is concerned with the problem of synchronization of memristor-based Lorenz systems with memristor-based Chua’s circuits. Numerical simulations of fractional-order memristor-based chaotic systems are performed by using the Caputo version and a predictor–corrector algorithm for fractional-order differential equations, which is a generalization of the Adams–Bashforth–Moulton method. From the simulations, it will be verified that the proposed control method is effective in achieving synchronization.

AN ACTIVE CONTROL FOR CHAOS SYNCHRONIZATION OF REAL AND COMPLEX VAN DER POL OSCILLATORS

2007 ◽  
Vol 18 (05) ◽  
pp. 795-804 ◽  
Author(s):  
AHMED A. M. FARGHALY
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Active Control ◽  
Limit Cycles ◽  
Chaos Synchronization ◽  
Control Technique ◽  
Control Input ◽  
Van Der Pol ◽  
Van Der Pol Oscillators

In a recent paper [Chaos, Solitons Fractals21, 915 (2004)], both real and complex Van der Pol oscillators were introduced and shown to exhibit chaotic limit cycles. In the present work these oscillators are synchronized by applying an active control technique. Based on Lyapunov function, the control input vectors are chosen and activated to achieve synchronization. The feasibility and effectiveness of the proposed technique are verified through numerical simulations.

scholarly journals Adaptive - Synchronization of Fractional-Order Chaotic Systems with Nonidentical Structures

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li-xin Yang ◽  
Wan-sheng He
Keyword(s):  
Adaptive Control ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Technique ◽  
Adaptive Synchronization ◽  
Fractional Order Systems ◽  
The Stability ◽  
Different Chaotic Systems ◽  
Theoretical Results

This paper investigates the adaptive - synchronization of the fractional-order chaotic systems with nonidentical structures. Based on the stability of fractional-order systems and adaptive control technique, a general formula for designing the controller and parameters update law is proposed to achieve adaptive - synchronization between two different chaotic systems with different structures. The effective scheme parameters identification and - synchronization of chaotic systems can be realized simultaneously. Furthermore, two typical illustrative numerical simulations are given to demonstrate the effectiveness of the proposed scheme, for each case, we design the controller and parameter update laws in detail. The numerical simulations are performed to verify the effectiveness of the theoretical results.

Robust finite-time chaos synchronization of time-delay chaotic systems and its application in secure communication

2016 ◽  
Vol 40 (4) ◽  
pp. 1177-1187 ◽  
Author(s):  
Hua Wang ◽  
Jian-Min Ye ◽  
Zhong–Hua Miao ◽  
Edmond A Jonckheere
Keyword(s):  
Time Delay ◽  
Numerical Simulations ◽  
Finite Time ◽  
Secure Communication ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Chaotic Synchronization ◽  
Uncertain Parameters ◽  
Wide Range ◽  
Zero Items

This paper presents finite-time chaos synchronization of time-delay chaotic systems with uncertain parameters. According to the proposed method, a lot of coupled items can be treated as zero items. Thus, the whole system can be simplified greatly. Based on robust chaotic synchronization, secure communication can be realized with a wide range of parameter disturbance and time-delay. Numerical simulations are provided to illustrate the effectiveness of the proposed method.

A TYPE OF SINGLE SCROLL ATTRACTOR CHAOS SYNCHRONIZATION

2010 ◽  
Vol 24 (27) ◽  
pp. 5269-5283
Author(s):  
TIANSHU WANG ◽  
XINGYUAN WANG
Keyword(s):  
Numerical Simulations ◽  
Active Control ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Function ◽  
Function Parameter ◽  
Nonlinear Feedback ◽  
Global Synchronization ◽  
Linear And Nonlinear ◽  
Different Chaotic Systems

This paper studies a type of single scroll attractor chaos system. Based on the research of Jiang et al. the global synchronization method is designed, and moreover, the author uses a combined synchronization of linear and nonlinear feedback, active control, single vector and unidirectional coupling synchronization three methods else, the problem of synchronization between same and different chaotic systems are realized by the four methods, respectively. The range of control function parameter is discussed according to the Routh–Hurwitz criterion and numerical simulations show the effectiveness of them.

Active Control for Multi-Switching Combination Synchronization of Non-Identical Chaotic Systems

2018 ◽  
pp. 129-162 ◽  
Author(s):  
Shikha Singh ◽  
Ahmad Taher Azar ◽  
Muzaffar Ahmad Bhat ◽  
Sundarapandian Vaidyanathan ◽  
Adel Ouannas
Keyword(s):  
Information Security ◽  
Numerical Simulations ◽  
Active Control ◽  
Chaotic Systems ◽  
Control Technique ◽  
Slave System ◽  
Combination Synchronization ◽  
Wide Range ◽  
Synchronization Scheme ◽  
Theoretical Results

This chapter investigates the multi-switching combination synchronization of three non-identical chaotic systems via active control technique. In recent years, some advances have been made with the idea of multi-switching combination synchronization. The different states of the master systems are synchronized with the desired state of the slave system in multi-switching combination synchronization scheme. The relevance of such kinds of synchronization studies to information security is evident in the wide range of possible synchronization directions that exist due to multi-switching synchronization. Numerical simulations justify the validity of the theoretical results discussed.

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