Dual function projective synchronization of fractional order complex chaotic systems

Optik ◽  
2016 ◽  
Vol 127 (22) ◽  
pp. 10527-10538 ◽  
Author(s):  
Vijay K. Yadav ◽  
N. Srikanth ◽  
S. Das
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Dual Function ◽  
Order Complex ◽  
Function Projective Synchronization ◽  
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.

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.

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.

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.

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.

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