Stability and Hopf bifurcation analysis of a fractional-order ring-hub structure neural network with delays under parameters delay feedback control

Yuan Ma; Yunxian Dai; Yuan Ma; Yunxian Dai

doi:10.3934/mbe.2023890

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 11: 20093-20115. doi: 10.3934/mbe.2023890

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Stability and Hopf bifurcation analysis of a fractional-order ring-hub structure neural network with delays under parameters delay feedback control

Yuan Ma ,
Yunxian Dai ^,

Department of System Science and Applied Mathematics, Kunming University of Science and Technology, Kunming 650500, China

Academic Editor: Mingji Zhang

Received: 07 September 2023 Revised: 17 October 2023 Accepted: 25 October 2023 Published: 03 November 2023

In this paper, a fractional-order two delays neural network with ring-hub structure is investigated. Firstly, the stability and the existence of Hopf bifurcation of proposed system are obtained by taking the sum of two delays as the bifurcation parameter. Furthermore, a parameters delay feedback controller is introduced to control successfully Hopf bifurcation. The novelty of this paper is that the characteristic equation corresponding to system has two time delays and the parameters depend on one of them. Selecting two time delays as the bifurcation parameters simultaneously, stability switching curves in $ (\tau_{1}, \tau_{2}) $ plane and crossing direction are obtained. Sufficient criteria for the stability and the existence of Hopf bifurcation of controlled system are given. Ultimately, numerical simulation shows that parameters delay feedback controller can effectively control Hopf bifurcation of system.
- fractional-order two-delay neural network,
- ring-hub structure,
- Hopf bifurcation,
- parameters delay feedback control,
- stability switching curves
Citation: Yuan Ma, Yunxian Dai. Stability and Hopf bifurcation analysis of a fractional-order ring-hub structure neural network with delays under parameters delay feedback control[J]. Mathematical Biosciences and Engineering, 2023, 20(11): 20093-20115. doi: 10.3934/mbe.2023890

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Abstract

In this paper, a fractional-order two delays neural network with ring-hub structure is investigated. Firstly, the stability and the existence of Hopf bifurcation of proposed system are obtained by taking the sum of two delays as the bifurcation parameter. Furthermore, a parameters delay feedback controller is introduced to control successfully Hopf bifurcation. The novelty of this paper is that the characteristic equation corresponding to system has two time delays and the parameters depend on one of them. Selecting two time delays as the bifurcation parameters simultaneously, stability switching curves in $ (\tau_{1}, \tau_{2}) $ plane and crossing direction are obtained. Sufficient criteria for the stability and the existence of Hopf bifurcation of controlled system are given. Ultimately, numerical simulation shows that parameters delay feedback controller can effectively control Hopf bifurcation of system.

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