scholarly journals Impulsive synchronization of fractional-order complex-variable dynamical network

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yu Xiong ◽  
Zhaoyan Wu
Keyword(s):  
Fractional Order ◽  
Complex Variable ◽  
Order Complex ◽  
Numerical Examples ◽  
Dynamical Network ◽  
Impulsive Synchronization

AbstractThe impulsive synchronization of a fractional-order complex-variable network is investigated. Firstly, static impulsive controllers are designed and the corresponding synchronization criteria are derived. From the criteria, the impulsive gains can be calculated. Secondly, adaptive impulsive controllers are designed. Noticeably, the impulsive gains can be adjusted to the needed values adaptively. Finally, numerical examples are provided to verify the results.

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.

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.

Pinning adaptive and impulsive synchronization of fractional-order complex dynamical networks

2016 ◽  
Vol 92 ◽  
pp. 142-149 ◽  
Author(s):  
Hong-Li Li ◽  
Cheng Hu ◽  
Yao-Lin Jiang ◽  
Zuolei Wang ◽  
Zhidong Teng
Keyword(s):  
Fractional Order ◽  
Complex Dynamical Networks ◽  
Order Complex ◽  
Dynamical Networks ◽  
Impulsive Synchronization

scholarly journals Structure Identification of Fractional-order Complex-variable Network With Complex Coupling

2021 ◽  
Author(s):  
Mingcong Zhou ◽  
Zhaoyan Wu
Keyword(s):  
Fractional Order ◽  
Complex Variable ◽  
Topological Structure ◽  
Dynamical Behavior ◽  
Critical Issue ◽  
Structure Identification ◽  
Order Complex ◽  
System Parameters ◽  
Lyapunov Function Method ◽  
Theoretical Results

Abstract Fractional-order complex-variable dynamical network with complex coupling is considered in this paper. The topological structures and system parameters are assumed to be unknown. As we know, the topological structure and system parameters play a key role on the dynamical behavior of complex network. Thus, how to effectively identify them is a critical issue for better studying the network. Through designing proper controllers and updating laws, two corresponding network estimators are constructed. Based on the Lyapunov function method and Gronwall-Bellman integral inequality, the results are analytically derived. Finally, two numerical examples are performed to illustrate the feasibility of the theoretical results.

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