Complex compound-combination multi switching anti-synchronization of fractional-order complex chaotic systems and integer-order 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.

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Modified hybrid projective synchronization of two fractional order complex chaotic systems with time delays

10.1063/5.0023589 ◽

2020 ◽

Author(s):

Jesu Nicholas George ◽

Rajendran Selvamani ◽

Quanxin Zhu

Keyword(s):

Fractional Order ◽

Time Delays ◽

Chaotic Systems ◽

Projective Synchronization ◽

Order Complex ◽

Hybrid Projective Synchronization ◽

Complex Chaotic Systems

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

International Journal of Modern Physics B ◽

10.1142/s0217979220500502 ◽

2020 ◽

Vol 34 (07) ◽

pp. 2050050 ◽

Cited By ~ 1

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.

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

Journal of Vibration and Control ◽

10.1177/1077546318822372 ◽

2019 ◽

Vol 25 (10) ◽

pp. 1614-1628 ◽

Cited By ~ 1

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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