scholarly journals Phase and Antiphase Synchronization between 3-Cell CNN and Volta Fractional-Order Chaotic Systems via Active Control

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Zahra Yaghoubi ◽  
Hassan Zarabadipour
Keyword(s):  
Dynamical Systems ◽  
Active Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Secure Communications ◽  
Digital Signals ◽  
Chaotic Dynamical Systems ◽  
Synchronization Method ◽  
Active Control Method

Synchronization of fractional-order chaotic dynamical systems is receiving increasing attention owing to its interesting applications in secure communications of analog and digital signals and cryptographic systems. In this paper, a drive-response synchronization method is studied for “phase and antiphase synchronization” of a class of fractional-order chaotic systems via active control method, using the 3-cell and Volta systems as an example. These examples are used to illustrate the effectiveness of the synchronization 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 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.

Synchronization of fractional order chaotic systems using active control method

2012 ◽  
Vol 45 (6) ◽  
pp. 737-752 ◽  
Author(s):  
S.K. Agrawal ◽  
M. Srivastava ◽  
S. Das
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Active Control Method

Comparative study of synchronization methods of fractional order chaotic systems

2016 ◽  
Vol 5 (3) ◽  
Author(s):  
Ajit K. Singh ◽  
Vijay K. Yadav ◽  
S. Das
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Salient Feature ◽  
Backstepping Method ◽  
Backstepping Approach ◽  
Active Control Method ◽  
Methods Numerical ◽  
Better Than

AbstractIn this article, the active control method and the backstepping method are used during the synchronization of fractional order chaotic systems. The salient feature of the article is the analysis of time of synchronization between fractional order Chen and Qi systems using both the methods. Numerical simulation and graphical results clearly exhibit that backstepping approach is better than active control method for synchronization of the considered pair of systems, as it takes less time to synchronize while using the first one compare to second one.

Anti-synchronization between identical and non-identical fractional-order chaotic systems using active control method

2013 ◽  
Vol 76 (2) ◽  
pp. 905-914 ◽  
Author(s):  
M. Srivastava ◽  
S. P. Ansari ◽  
S. K. Agrawal ◽  
S. Das ◽  
A. Y. T. Leung
Keyword(s):  
Active Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Active Control Method

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.

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.

ACTIVE CONTROL OF UNCERTAIN CHAOTIC SYSTEMS WITH PARAMETRIC PERTURBATION

2006 ◽  
Vol 20 (16) ◽  
pp. 2255-2264
Author(s):  
HAO ZHANG ◽  
XI-KUI MA
Keyword(s):  
Active Control ◽  
Control Strategy ◽  
Chaotic Systems ◽  
Control Method ◽  
Sufficient Condition ◽  
Parametric Perturbation ◽  
Uncertain Chaotic Systems ◽  
The Stability ◽  
Parameters Perturbation ◽  
Active Control Method

This paper presents an active control method for controlling general uncertain chaotic systems with parameters perturbation. And a sufficient condition is drawn for the stability of the controlled chaotic systems and is applied to guiding the design of the controllers. Finally, numerical results are used to show the robustness and effectiveness of the proposed control strategy.

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