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Dynamics of a memristive FitzHugh–Rinzel neuron model: application to information patterns

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Abstract

In this work, a memristive FitzHugh–Rinzel (mFHR) neuron prototype is introduced and investigated. The memristive device is exploited to simulate the impact of a magnetic radiation on the FitzHugh–Rinzel (FHR) neuron’s behavior. Depending on the strength of the electromagnetic induction and the intensity of the external stimulus, it is found that the model experiences self-excited firing activity. The two-parameter charts of the largest Lyapunov exponent and the bifurcation diagram investigation revealed the model exhibited hysteretic dynamics, which induced the coexistence of bifurcation of sets of parameters not yet revealed in such a model. The energy necessary to provide each firing activity in the proposed model is also estimated based on the Helmholtz theorem. Finally, results of the information patterns with a chain of 100 mFHR neurons are obtained by numerical calculations using Runge–Kutta (fourth-order) calculation method, which approaches solutions of the resulting dynamic equations. The spatiotemporal patterns and time series plots for membrane potential revealed regular localized structures made of alternate bright and dark bands identified as spikes, which are sensitive to external stimulation current, electromagnetic induction coefficients and synaptic coupling strength.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The data used to support the findings of this study are available from the corresponding author upon request.]

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Acknowledgements

This work is funded by the Center for Nonlinear Systems, Chennai Institute of Technology, India, vide funding number CIT/CNS/2023/RP/009. Jan Awrejcewicz has been supported by the Polish National Science Centre under the Grant OPUS 18No.2019/35/B/ST8/00980.

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O.Box 63, Buea, Cameroon

    Zeric Tabekoueng Njitacke & Clovis Ntahkie Takembo

  2. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, ul. Stefanowskiego 1/15, 90-537, Lodz, Poland

    Jan Awrejcewicz

  3. Centre for Computational Modelling, Chennai Institute of Technology, Chennai, India

    Sriram Parthasarathy

  4. Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, India

    Karthikeyan Rajagopal

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  1. Zeric Tabekoueng Njitacke
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  2. Sriram Parthasarathy
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Correspondence to Zeric Tabekoueng Njitacke.

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Njitacke, Z.T., Parthasarathy, S., Takembo, C.N. et al. Dynamics of a memristive FitzHugh–Rinzel neuron model: application to information patterns. Eur. Phys. J. Plus 138, 473 (2023). https://doi.org/10.1140/epjp/s13360-023-04120-z

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