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.

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.

Comparison of Times of Synchronization of Chaotic Burke-Shaw Attractor with Active Control and Integer and Optimum Fractional-Order Pecaro Carroll Method

2021 ◽  
Author(s):  
Ali Durdu ◽  
Yılmaz Uyaroğlu
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Attractor ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Control Method ◽  
Initial Conditions ◽  
Data Communication ◽  
Experimental Results ◽  
Active Control Method

Abstract Many studies have been introduced in the literature showing that two identical chaotic systems can be synchronized with different initial conditions. Secure data communication applications have also been made using synchronization methods. In the study, synchronization times of two popular synchronization methods are compared, which is an important issue for communication. Among the synchronization methods, active control, integer, and fractional-order Pecaro Carroll (P-C) method was used to synchronize the Burke-Shaw chaotic attractor. The experimental results showed that the P-C method with optimum fractional-order is synchronized in 2.35 times shorter time than the active control method. This shows that the P-C method using fractional-order creates less delay in synchronization and is more convenient to use in secure communication applications.

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.

The Projective Synchronization of Drive-Reponse Complex Dynamical Networks

2014 ◽  
Vol 687-691 ◽  
pp. 2458-2461
Author(s):  
Feng Ling Jia
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Complex Dynamical Networks ◽  
Projective Synchronization ◽  
Dynamical Networks ◽  
Fractional Order Differential Equations ◽  
The Stability ◽  
Response Complex

This paper investigates the projective synchronization of drive-response complex dynamical networks. Based on the stability theory for fractional-order differential equations, controllers are designed torealize the projective synchronization for complex dynamical networks. Morover, some simple synchronization conditions are proposed. Numerical simulations are presented to show the effectiveness of the proposed method.

scholarly journals Numerical behavior of a fractional order dynamical model of RNA silencing

2016 ◽  
Vol 4 (2) ◽  
pp. 52
Author(s):  
A.M.A. El-Sayed ◽  
M. Khalil ◽  
A.A.M. Arafa ◽  
Amaal Sayed
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Detailed Analysis ◽  
Fractional Order ◽  
Rna Silencing ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
The Stability ◽  
Predictor Corrector ◽  
With Memory

A class of fractional-order differential models of RNA silencing with memory is presented in this paper. We also carry out a detailed analysis on the stability of equilibrium and we show that the model established in this paper possesses non-negative solutions. Numerical solutions are obtained using a predictor-corrector method to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. Numerical simulations are presented to illustrate the results. Also, the numerical simulations show that, modeling the phenomena of RNA silencing by fractional ordinary differential equations (FODE) has more advantages than classical integer-order modeling.

scholarly journals Antisynchronization of Nonidentical Fractional-Order Chaotic Systems Using Active Control

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Sachin Bhalekar ◽  
Varsha Daftardar-Gejji
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Value Of Time ◽  
State Variables ◽  
Financial Systems ◽  
The Stability ◽  
First Time ◽  
Active Control Method

Antisynchronization phenomena are studied in nonidentical fractional-order differential systems. The characteristic feature of antisynchronization is that the sum of relevant state-variables vanishes for sufficiently large value of time variable. Active control method is used first time in the literature to achieve antisynchronization between fractional-order Lorenz and Financial systems, Financial and Chen systems, and Lü and Financial systems. The stability analysis is carried out using classical results. We also provide numerical results to verify the effectiveness of the proposed theory.

DIVERSE STRUCTURE SYNCHRONIZATION OF FRACTIONAL ORDER HYPER-CHAOTIC SYSTEMS

2013 ◽  
Vol 27 (11) ◽  
pp. 1350034 ◽  
Author(s):  
XING-YUAN WANG ◽  
GUO-BIN ZHAO ◽  
YU-HONG YANG
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Control Method ◽  
Rossler System ◽  
Rössler System ◽  
Predictor Corrector ◽  
Fractional Orders ◽  
Active Control Method

This paper studied the dynamic behavior of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system, then numerical analysis of the different fractional orders hyper-chaotic systems are carried out under the predictor–corrector method. We proved the two systems are in hyper-chaos when the maximum and the second largest Lyapunov exponential are calculated. Also the smallest orders of the systems are proved when they are in hyper-chaos. The diverse structure synchronization of the fractional order hyper-chaotic Lorenz system and the fractional order hyper-chaotic Rössler system is realized using active control method. Numerical simulations indicated that the scheme was always effective and efficient.

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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