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December 2020 Hopf bifurcation of the fractional-order Hindmarsh–Rose neuron model with time-delay
Min Shi, Yajuan Yu, Qi Xu
Rocky Mountain J. Math. 50(6): 2213-2222 (December 2020). DOI: 10.1216/rmj.2020.50.2213

Abstract

The Hopf bifurcation problem of the fractional-order Hindmarsh–Rose neuron model with time-delay is investigated. The effects of time-delay to the bifurcation behavior of system is considered by linearizing the system at the equilibria method. With the bifurcation theory, the condition for the existence of Hopf bifurcation is obtained when considering time-delay τ as variable parameter. As illustrated by the numerical example, the proposed theoretical results work effectively and accurately.

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Min Shi. Yajuan Yu. Qi Xu. "Hopf bifurcation of the fractional-order Hindmarsh–Rose neuron model with time-delay." Rocky Mountain J. Math. 50 (6) 2213 - 2222, December 2020. https://doi.org/10.1216/rmj.2020.50.2213

Information

Received: 19 February 2020; Revised: 1 July 2020; Accepted: 3 July 2020; Published: December 2020
First available in Project Euclid: 5 January 2021

Digital Object Identifier: 10.1216/rmj.2020.50.2213

Subjects:
Primary: 34A08

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 6 • December 2020
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