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A discrete memristive neuron and its adaptive dynamics

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Abstract

Capacitive membrane and inductive channels enable the approach of neural activities in some equivalent neural circuits, and involvement of memristive term and magnetic flux can estimate the effect of electromagnetic induction. Based on the memristive neuron models, synaptic controllability and field coupling between neurons can be explored from physical aspect. Most of the biophysical neurons are defined in nonlinear oscillators, which can be mapped from the circuit equations under scale transformation, and the energy functions can be obtained in theoretical way. To enrich complex dynamics, specific terms are often introduced into the known models, and it requires the involvement of specific electric components for inducting special relation between the channel current and across voltage. Indeed, mathematical maps are effective to produce similar firing modes matching with neural activities in biological neurons. In this work, memristor is connected to a simple nonlinear circuit for building a memristive neuron, and its energy function is derived from two ways. Under linear transformation, the memristive neuron in oscillator form is converted into a memristive map, the energy function is confirmed, and an adaptive criterion is presented to regulate the intrinsic parameter, which the self-adaptive regulation property is released. The scheme provides clues to design discrete neuron models and understand its role of energy flow on the self-adaptive property and mode selection.

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Acknowledgements

This project is partially supported by National Natural Science Foundation of China under Grant No. 12072139.

Funding

Funding was provided by National Natural Science Foundation of China (Grant No. 12072139).

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Authors and Affiliations

  1. Department of Physics, Lanzhou University of Technology, Lanzhou, 730050, China

    Yanni Li & Jun Ma

  2. Faculty of Engineering, China University of Petroleum-Beijing at Karamay, Karamay, 834000, China

    Mi Lv

  3. School of Science, Chongqing University of Posts and Telecommunications, Chongqing, 430065, China

    Jun Ma & Xikui Hu

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  1. Yanni Li
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  4. Xikui Hu
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Contributions

Yanni Li and Mi Lv calculated all the numerical results and provided formal analysis. Jun Ma suggested this investigation and provided complete proof and wrote this manuscript. Xikui Hu verified the proof and numerical approach.

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Correspondence to Jun Ma.

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Li, Y., Lv, M., Ma, J. et al. A discrete memristive neuron and its adaptive dynamics. Nonlinear Dyn 112, 7541–7553 (2024). https://doi.org/10.1007/s11071-024-09361-w

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