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.
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)
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)。