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Memristor-induced mode transitions and extreme multistability in a map-based neuron model

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Abstract

Because of the advent of discrete memristor, memristor effect in discrete map has become the important subject deserving discussion. To this end, this paper constructs a memristor-based neuron model considering magnetic induction by combining an existing map-based neuron model and a discrete memristor with absolute value memductance. Taking the coupling strength and initial state of the memristor as variables, complex mode transition behaviors induced by the introduced memristor are disclosed using numerical methods, including spiking-bursting behaviors, mode transition behaviors, and hyperchaotic spiking behaviors. In particular, all of these behaviors are greatly dependent on the memristor initial state, resulting in the existence of extreme multistability in the memristive neuron model. Therefore, this memristive neuron model can be used to effectively imitate the magnetic induction effects when complex mode transition behaviors appear in the neuronal action potential. Besides, a hardware platform based on FPGA is developed for implementing the memristive neuron model and various spiking-bursting sequences are experimentally captured therein. The results show that when biophysical memory effect is present, the memristive neuron model can better represent the firing activities of biological neurons than the original map-based neuron model.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This work was supported by the National Natural Science Foundations of China under Grant Nos. 62201094, 62271088, and 12172066, the Scientific Research Foundation of Jiangsu Provincial Education Department, China, under Grant No. 22KJB510001, and the Postgraduate Research & Practice Innovation Program of Jiangsu Province, China, under Grant Nos. KYCX22_3051 and KYCX22_3046.

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  1. School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164, China

    Bocheng Bao, Jingting Hu, Jianming Cai, Xi Zhang & Han Bao

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  1. Bocheng Bao
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Correspondence to Han Bao.

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Bao, B., Hu, J., Cai, J. et al. Memristor-induced mode transitions and extreme multistability in a map-based neuron model. Nonlinear Dyn 111, 3765–3779 (2023). https://doi.org/10.1007/s11071-022-07981-8

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