Multi-switching combination-combination synchronization of non-identical fractional-order chaotic systems

2017 ◽  
Vol 40 (15) ◽  
pp. 5654-5667 ◽  
Author(s):  
Ayub Khan ◽  
Muzaffar Ahmad Bhat
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Combination Synchronization

scholarly journals Combination synchronization of fractional order n-chaotic systems using active backstepping design

2019 ◽  
Vol 8 (1) ◽  
pp. 597-608 ◽  
Author(s):  
Vijay K. Yadav ◽  
S. Das
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Design Method ◽  
Backstepping Design ◽  
Fractional Order Systems ◽  
Combination Synchronization

Abstract In this article, a scheme using active backstepping design method is proposed to achieve combination synchronization of n number of fractional order chaotic systems. In the proposed method the controllers are designed with the help of a new lemma and Lyapunov function in a systematic way. Synchronization among three/four fractional order systems have been shown as examples of synchronization of n-chaotic systems. Numerical simulation and graphical results clearly exhibit that the method of this new procedure is easy to implement and reliable for synchronization of fractional order chaotic systems.

scholarly journals Special Characteristics and Synchronizations of Multi Hybrid-Order Chaotic Systems

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 664
Author(s):  
Jiaxun Liu ◽  
Zuoxun Wang ◽  
Fangfang Zhang ◽  
Yankai Yin ◽  
Fengying Ma
Keyword(s):  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Combination Synchronization ◽  
Simulation Results ◽  
Total Dimension ◽  
Hybrid Forms

Based on advantages of integer and fractional chaotic systems, hybrid chaotic systems and their definitions and some fundamental concepts are proposed, such as hybrid degree (HD), the lowest order (LO) and the total dimension order (TDO). The preliminary properties of hybrid Lorenz systems and hybrid forms of some classic chaotic systems are studied. Then, the relations between HD, LO and TDO with different parameters is investigated in chaotic systems. To be specific, HD is associated with fractional order. It is a directional method to search LO and TDO in chaotic systems. Finally, based on the incommensurate fractional stability theory, we accomplish combination synchronization for three different hybrid order chaotic systems. The simulation results verify the effectiveness of the synchronization controller.

Real combination synchronization of three fractional-order complex-variable chaotic systems

Optik ◽  
2016 ◽  
Vol 127 (23) ◽  
pp. 11460-11468 ◽  
Author(s):  
Junwei Sun ◽  
Wei Deng ◽  
Guangzhao Cui ◽  
Yanfeng Wang
Keyword(s):  
Fractional Order ◽  
Complex Variable ◽  
Chaotic Systems ◽  
Order Complex ◽  
Combination Synchronization

scholarly journals Combination Synchronization of Three Different Fractional-Order Delayed Chaotic Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Bo Li ◽  
Xiaobing Zhou ◽  
Yun Wang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Time Delays ◽  
Chaotic Systems ◽  
Multiple Time ◽  
Engineering Systems ◽  
Fractional Order Systems ◽  
Combination Synchronization ◽  
Multiple Time Delays ◽  
Practical Engineering

Time delay is a frequently encountered phenomenon in some practical engineering systems and introducing time delay into a system can enrich its dynamic characteristics. There has been a plenty of interesting results on fractional-order chaotic systems or integer-order delayed chaotic systems, but the problem of synchronization of fractional-order chaotic systems with time delays is in the primary stage. Combination synchronization of three different fractional-order delayed chaotic systems is investigated in this paper. It is an extension of combination synchronization of delayed chaotic systems or combination synchronization of fractional-order chaotic systems. With the help of stability theory of linear fractional-order systems with multiple time delays, we design controllers to achieve combination synchronization of three different fractional-order delayed chaotic systems. In addition, numerical simulations have been performed to demonstrate and verify the theoretical analysis.

Dual Combination Synchronization of the Fractional Order Complex Chaotic Systems

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Ajit K. Singh ◽  
Vijay K. Yadav ◽  
S. Das
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Communication Theory ◽  
Lyapunov Stability Theory ◽  
Real Space ◽  
Projective Synchronization ◽  
Order Complex ◽  
Combination Synchronization ◽  
Special Cases ◽  
Complex Chaotic Systems

In this article, the authors have proposed a novel scheme for the dual combination synchronization among four master systems and two slave systems for the fractional order complex chaotic systems. Dual combination synchronization for the integer order has already been investigated in real space; but for the case of fractional order in complex space, it is the first of its kind. Due to complexity and presence of additional variable, it will be more secure and interesting to transmit and receive signals in communication theory. Based on the Lyapunov stability theory, six complex chaotic systems are considered and corresponding controllers are designed to achieve synchronization. The special cases, such as combination synchronization, projective synchronization, complete synchronization, and many more, can be derived from the proposed scheme. The corresponding theoretical analysis and numerical simulations are shown to verify the feasibility and effectiveness of the proposed dual combination synchronization scheme.

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