Complex modified projective synchronization of two fractional-order complex-variable chaotic systems

2016 ◽  
Author(s):  
Xiaomin Tian ◽  
Zhong Yang ◽  
Shumin Fei
Keyword(s):  
Fractional Order ◽  
Complex Variable ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Order Complex ◽  
Modified Projective Synchronization

scholarly journals Complex Modified Projective Synchronization of Fractional-Order Complex-Variable Chaotic System with Unknown Complex Parameters

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 407
Author(s):  
Zhang ◽  
Feng ◽  
Yang
Keyword(s):  
Fractional Order ◽  
Complex Variable ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Order Complex ◽  
Modified Projective Synchronization ◽  
Simulation Results ◽  
Synchronization Scheme ◽  
Complex Valued ◽  
Variable Inequality

This paper investigates the problem of complex modified projective synchronization (CMPS) of fractional-order complex-variable chaotic systems (FOCCS) with unknown complex parameters. By a complex-variable inequality and a stability theory for fractional-order nonlinear systems, a new scheme is presented for constructing CMPS of FOCCS with unknown complex parameters. The proposed scheme not only provides a new method to analyze fractional-order complex-valued systems but also significantly reduces the complexity of computation and analysis. Theoretical proof and simulation results substantiate the effectiveness of the presented synchronization scheme.

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.

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

Adaptive Modified Hybrid Robust Projective Synchronization Between Identical and Nonidentical Fractional-Order Complex Chaotic Systems With Fully Unknown Parameters

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Hadi Delavari ◽  
Milad Mohadeszadeh
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Order Complex ◽  
Unknown Parameters ◽  
Adaptive Sliding Mode Controller ◽  
Robust Adaptive ◽  
Complex Chaotic Systems

In this paper, a robust adaptive sliding mode controller is proposed. Under the existence of external disturbances, modified hybrid projective synchronization (MHPS) between two identical and two nonidentical fractional-order complex chaotic systems is achieved. It is shown that the response system could be synchronized with the drive system up to a nondiagonal scaling matrix. An adaptive controller and parameter update laws are investigated based on the Lyapunov stability theorem. The closed-loop stability conditions are derived based on the fractional-order Lyapunov function and Mittag-Leffler function. Finally, numerical simulations are given to verify the theoretical analysis.

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