Synchronization between fractional order complex chaotic systems

2016 ◽  
Vol 5 (3) ◽  
pp. 756-770 ◽  
Author(s):  
Ajit K. Singh ◽  
Vijay K. Yadav ◽  
S. Das
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Order Complex ◽  
Complex Chaotic Systems

scholarly journals Synchronization of Fractional-Order Complex Chaotic Systems Based on Observers

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 481 ◽  
Author(s):  
Zhonghui Li ◽  
Tongshui Xia ◽  
Cuimei Jiang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Pole Placement ◽  
Order Complex ◽  
Order Error ◽  
New Type ◽  
Modified Projective Synchronization ◽  
The Stability ◽  
Complex Chaotic Systems

By designing a state observer, a new type of synchronization named complex modified projective synchronization is investigated in a class of nonlinear fractional-order complex chaotic systems. Combining stability results of the fractional-order systems and the pole placement method, this paper proves the stability of fractional-order error systems and realizes complex modified projective synchronization. This method is so effective that it can be applied in engineering. Additionally, the proposed synchronization strategy is suitable for all fractional-order chaotic systems, including fractional-order hyper-chaotic systems. Finally, two numerical examples are studied to show the correctness of this new synchronization strategy.

Module-phase synchronization of fractional-order complex chaotic systems based on RBF neural network and sliding mode control

2020 ◽  
Vol 34 (07) ◽  
pp. 2050050 ◽  
Author(s):  
Fuzhong Nian ◽  
Xinmeng Liu ◽  
Yaqiong Zhang ◽  
Xuelong Yu
Keyword(s):  
Neural Network ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Phase Synchronization ◽  
Sliding Mode ◽  
Rbf Neural Network ◽  
Order Complex ◽  
Mode Control ◽  
Complex Chaotic Systems

Combined with RBF neural network and sliding mode control, the synchronization between drive system and response system was achieved in module space and phase space, respectively (module-phase synchronization). The RBF neural network is used to estimate the unknown nonlinear function in the system. The module-phase synchronization of two fractional-order complex chaotic systems is implemented by the Lyapunov stability theory of fractional-order systems. Numerical simulations are provided to show the effectiveness of the analytical results.

Adaptive impulsive synchronization for a class of fractional order complex chaotic systems

2019 ◽  
Vol 25 (10) ◽  
pp. 1614-1628 ◽  
Author(s):  
Xingpeng Zhang ◽  
Dong Li ◽  
Xiaohong Zhang
Keyword(s):  
Number Field ◽  
Fractional Order ◽  
Complex Number ◽  
Chaotic Systems ◽  
Direct Method ◽  
Order Complex ◽  
Lyapunov Direct Method ◽  
Impulsive Synchronization ◽  
Complex Chaotic Systems ◽  
Order Extension

In this paper, a new lemma is proposed to study the stability of a fractional order complex chaotic system without dividing the complex number into real and imaginary parts. The proving process of the new lemma combines the fundamental properties of the complex field and the fractional order extension of the Lyapunov direct method. It extends the fractional order extension of the Lyapunov direct method from the real number field to the complex number field. Based on the new lemma, we propose a new impulsive synchronization scheme for fractional order complex chaotic systems. The numerical simulation results also show the validity of our conclusion.

Robust Control and Synchronization of Fractional-Order Complex Chaotic Systems with Hidden Attractor

2021 ◽  
pp. 199-210
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano ◽  
Nashwa Ahmad Kamal ◽  
Tulasichandra Sekhar Gorripotu ◽  
Ramana Pilla ◽  
...  
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Order Complex ◽  
Hidden Attractor ◽  
Control And Synchronization ◽  
Complex Chaotic Systems

Synchronization between fractional order complex chaotic systems with uncertainty

Optik ◽  
2017 ◽  
Vol 133 ◽  
pp. 98-107 ◽  
Author(s):  
Ajit K. Singh ◽  
Vijay K. Yadav ◽  
S. Das
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Order Complex ◽  
Complex Chaotic Systems
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