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

作　　者：李志军 谢文强 曾金芳 曾以成 Zhi-Jun Li;Wen-Qiang Xie;Jin-Fang Zeng;Yi-Cheng Zeng(School of Automation and Electronic Information,Xiangtan University,Xiangtan 411105,China;School of Physics and Optoelectronics,Xiangtan University,Xiangtan 411105,China)

机构地区：[1]School of Automation and Electronic Information,Xiangtan University,Xiangtan 411105,China [2]School of Physics and Optoelectronics,Xiangtan University,Xiangtan 411105,China

出　　处：《Chinese Physics B》2023年第1期227-238,共12页中国物理B（英文版）

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

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 

分 类 号：TN60[电子电信—电路与系统] TP183[自动化与计算机技术—控制理论与控制工程]