Firing activities in a fractional-order Hindmarsh-Rose neuron with multistable memristor as autapse |
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| Affiliation: | 1.School of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, China;2.School of Physics and Optoelectronics, Xiangtan University, Xiangtan 411105, China |
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| 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. |
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| Keywords: | fractional-order multistable neuron firing locally-active memristor |
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