Continuous non-autonomous memristive Rulkov model with extreme multistability

doi:10.1088/1674-1056/ac2f30

Abstract Based on the two-dimensional (2D) discrete Rulkov model that is used to describe neuron dynamics, this paper presents a continuous non-autonomous memristive Rulkov model. The effects of electromagnetic induction and external stimulus are simultaneously considered herein. The electromagnetic induction flow is imitated by the generated current from a flux-controlled memristor and the external stimulus is injected using a sinusoidal current. Thus, the presented model possesses a line equilibrium set evolving over the time. The equilibrium set and their stability distributions are numerically simulated and qualitatively analyzed. Afterwards, numerical simulations are executed to explore the dynamical behaviors associated to the electromagnetic induction, external stimulus, and initial conditions. Interestingly, the initial conditions dependent extreme multistability is elaborately disclosed in the continuous non-autonomous memristive Rulkov model. Furthermore, an analog circuit of the proposed model is implemented, upon which the hardware experiment is executed to verify the numerically simulated extreme multistability. The extreme multistability is numerically revealed and experimentally confirmed in this paper, which can widen the future engineering employment of the Rulkov model.

Keywords: extreme multistability memristor electromagnetic induction Rulkov model

Received: 15 July 2021
Revised: 09 October 2021
Accepted manuscript online: 13 October 2021

PACS:	87.50.-a	(Effects of electromagnetic and acoustic fields on biological systems)
	87.19.ll	(Models of single neurons and networks)
	87.23.Kg	(Dynamics of evolution)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12172066, 61801054, and 51777016), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20160282), and the Postgraduate Research and Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX21_2823).

Corresponding Authors: Bo-Cheng Bao
E-mail: mervinbao@126.com

Cite this article:

Quan Xu(徐权), Tong Liu(刘通), Cheng-Tao Feng(冯成涛), Han Bao(包涵), Hua-Gan Wu(武花干), and Bo-Cheng Bao(包伯成) Continuous non-autonomous memristive Rulkov model with extreme multistability 2021 Chin. Phys. B 30 128702

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Continuous non-autonomous memristive Rulkov model with extreme multistability

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