Comparison principle and synchronization analysis of fractional-order complex networks with parameter uncertainties and multiple time delays

Hongguang Fan; Jihong Zhu; Hui Wen; Hongguang Fan; Jihong Zhu; Hui Wen

doi:10.3934/math.2022719

AIMS Mathematics

2022, Volume 7, Issue 7: 12981-12999. doi: 10.3934/math.2022719

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Comparison principle and synchronization analysis of fractional-order complex networks with parameter uncertainties and multiple time delays

Hongguang Fan ^{1
,
,},
Jihong Zhu ²,
Hui Wen ^{3
,
,}

1.
College of Computer, Chengdu University, Chengdu 610106, China
2.
Jiangxi Environmental Engineering Vocational College, Ganzhou, Jiangxi 341000, China
3.
Institute of New Engineering Industry, Putian University, Putian 351100, China

Received: 16 March 2022 Revised: 15 April 2022 Accepted: 18 April 2022 Published: 07 May 2022
MSC : 26A33

This paper investigates the global synchronization problems of fractional-order complex dynamical networks with uncertain inner coupling and multiple time delays. In particular, both internal time delays and coupling time delays are introduced into our model. To overcome the difficulties caused by various delays and uncertainties, a generalized delayed comparison principle with fractional-order and impulsive effects is established by using the Laplace transform. Based on the Lyapunov stability theory and mixed impulsive control technologies, some new synchronization criteria for concerned complex dynamical networks are derived. In addition, the synchronization criteria are related to the impulsive interval, network topology structure, fractional-order, and control gains. The theoretical results obtained in this paper can enhance the value of previous related works. Finally, numerical simulations are presented to show the correctness of our main results.
- fractional-order,
- complex network,
- synchronization,
- impulsive control,
- uncertainty,
- delay
Citation: Hongguang Fan, Jihong Zhu, Hui Wen. Comparison principle and synchronization analysis of fractional-order complex networks with parameter uncertainties and multiple time delays[J]. AIMS Mathematics, 2022, 7(7): 12981-12999. doi: 10.3934/math.2022719

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Abstract

This paper investigates the global synchronization problems of fractional-order complex dynamical networks with uncertain inner coupling and multiple time delays. In particular, both internal time delays and coupling time delays are introduced into our model. To overcome the difficulties caused by various delays and uncertainties, a generalized delayed comparison principle with fractional-order and impulsive effects is established by using the Laplace transform. Based on the Lyapunov stability theory and mixed impulsive control technologies, some new synchronization criteria for concerned complex dynamical networks are derived. In addition, the synchronization criteria are related to the impulsive interval, network topology structure, fractional-order, and control gains. The theoretical results obtained in this paper can enhance the value of previous related works. Finally, numerical simulations are presented to show the correctness of our main results.

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