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Chin. Phys. B, 2023, Vol. 32(1): 010503    DOI: 10.1088/1674-1056/ac65f7
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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
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:

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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