Memristive effect on a Hindmarsh-Rose neuron

doi:10.1088/1674-1056/ae0b3a

Abstract Considering the impact of electromagnetic induction on neurons, this paper presents a three-dimensional (3D) memristor Hindmarsh-Rose (HR) neuron model. This model exhibits diverse hidden chaotic dynamics due to the absence of equilibrium points, including bifurcation phenomena, coexisting attractors, transient chaos, state transitions, and offset-boosting control. Since equilibrium points are absent in this model, all observed dynamics are classified as hidden behaviors. The complex dynamics of this neuron model are illustrated through bifurcation diagrams, Lyapunov diagrams, time series plots, and phase portraits. Furthermore, an equivalent circuit for the memristor HR neuron is constructed, and the accuracy of numerical simulations is confirmed via circuit simulation results.

Keywords: chaos memristor HR neuron electromagnetic induction hidden attractor

Received: 03 August 2025
Revised: 04 September 2025
Accepted manuscript online: 25 September 2025

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	87.19.ll	(Models of single neurons and networks)
	84.35.+i	(Neural networks)

Fund: This work was supported by the Natural Science Foundation of Shandong Province (Grant No. ZR2024MF106), the National Natural Science Foundation of China (Grant Nos. 62371274 and 62401346), the China Postdoctoral Science Foundation (Grant No. 2023M742138), the Natural Science Foundation of Shandong Province (Grant Nos. ZR2023MF004 and ZR2022MA073), the Postdoctoral Innovation Project of Shandong Province (Grant No. SDCX-ZG-202400311), the Natural Science Foundation of Qingdao Municipality (Grant No. 23-2-1-151-zyydjch), the Qingdao Postdoctoral Innovation Project (Grant No. QDBSH20230202012), and in part by the Elite Project of Shandong University of Science and Technology.

Corresponding Authors: Tengfei Lei
E-mail: leitengfeicanhe@126.com

Cite this article:

Fei Gao(高飞), Xiangcheng Yu(于相成), Yue Deng(邓玥), Fang Yuan(袁方), Guangyi Wang(王光义), and Tengfei Lei(雷腾飞) Memristive effect on a Hindmarsh-Rose neuron 2025 Chin. Phys. B 34 120504

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