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

doi:10.1088/1674-1056/ac65f7

中国物理B ›› 2023, Vol. 32 ›› Issue (1): 10503-010503.doi: 10.1088/1674-1056/ac65f7

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

Zhi-Jun Li(李志军)^1,†, Wen-Qiang Xie(谢文强)¹, Jin-Fang Zeng(曾金芳)², and Yi-Cheng Zeng(曾以成)²

1 School of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, China;
2 School of Physics and Optoelectronics, Xiangtan University, Xiangtan 411105, China

收稿日期:2022-03-04 修回日期:2022-03-28 接受日期:2022-04-11 出版日期:2022-12-08 发布日期:2022-12-23
通讯作者: Zhi-Jun Li E-mail:lizhijun_320@163.com
基金资助:
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).

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

Zhi-Jun Li(李志军)^1,†, Wen-Qiang Xie(谢文强)¹, Jin-Fang Zeng(曾金芳)², and Yi-Cheng Zeng(曾以成)²

1 School of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, China;
2 School of Physics and Optoelectronics, Xiangtan University, Xiangtan 411105, China

Received:2022-03-04 Revised:2022-03-28 Accepted:2022-04-11 Online:2022-12-08 Published:2022-12-23
Contact: Zhi-Jun Li E-mail:lizhijun_320@163.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: fractional-order, multistable, neuron, firing, locally-active memristor

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.

Key words: fractional-order, multistable, neuron, firing, locally-active memristor

中图分类号: (Numerical simulations of chaotic systems)

05.45.Pq

87.19.ll (Models of single neurons and networks) 87.19.lj (Neuronal network dynamics)

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[J]. 中国物理B, 2023, 32(1): 10503-010503.

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

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

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