Firing activities in a fractional-order Hindmarsh-Rose neuron with multistable memristor as autapse

doi:10.1088/1674-1056/ac65f7

Abstract Considering the fact that memristors have the characteristics similar to biological synapses, a fractional-order multistable memristor is proposed in this paper. It is verified that the fractional-order memristor has multiple local active regions and multiple stable hysteresis loops, and the influence of fractional-order on its nonvolatility is also revealed. Then by considering the fractional-order memristor as an autapse of Hindmarsh-Rose (HR) neuron model, a fractional-order memristive neuron model is developed. The effects of the initial value, external excitation current, coupling strength and fractional-order on the firing behavior are discussed by time series, phase diagram, Lyapunov exponent and inter spike interval (ISI) bifurcation diagram. Three coexisting firing patterns, including irregular asymptotically periodic (A-periodic) bursting, A-periodic bursting and chaotic bursting, dependent on the memristor initial values, are observed. It is also revealed that the fractional-order can not only induce the transition of firing patterns, but also change the firing frequency of the neuron. Finally, a neuron circuit with variable fractional-order is designed to verify the numerical simulations.

Keywords: fractional-order multistable neuron firing locally-active memristor

Received: 04 March 2022
Revised: 28 March 2022
Accepted manuscript online: 11 April 2022

PACS:	05.45.Pq	(Numerical simulations of chaotic systems)
	87.19.ll	(Models of single neurons and networks)
	87.19.lj	(Neuronal network dynamics)

Fund: Project supported by the National Key Research and Development Program of China (Grant No. 2018AAA0103300) and the National Natural Science Foundation of China (Grant Nos. 62171401 and 62071411).

Corresponding Authors: Zhi-Jun Li
E-mail: lizhijun_320@163.com

Cite this article:

Zhi-Jun Li(李志军), Wen-Qiang Xie(谢文强), Jin-Fang Zeng(曾金芳), and Yi-Cheng Zeng(曾以成) Firing activities in a fractional-order Hindmarsh-Rose neuron with multistable memristor as autapse 2023 Chin. Phys. B 32 010503

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Firing activities in a fractional-order Hindmarsh-Rose neuron with multistable memristor as autapse

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