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Modes transition and network synchronization in extended Hindmarsh–Rose model driven by mutation of adaptation current under effects of electric field

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Abstract

Considering the influence of electric field and introducing the adaptation current as spike-burst firing mutation parameter, a novel variant Hindmarsh–Rose neural model is proposed to study the firing modes of neural systems. (1) In the case of single HR neural system, it is shown that the firing modal fusion absorption of neuron can be occurred with the increasing of current intensity. A higher sinusoidal current frequency transforms HR neuronal model from asymmetric dual-mode state to symmetric dual-mode state. There exists a singularity at which the neuron has a larger firing mode mutation when the adaptation current mutation parameter is applied. (2) In the case of three-dimensional network with the chemically coupled HR neurons, it is observed that the firing behavior of the core neuron of network has the strongest stability when the noise-like or the periodic electric field is imposed on the vertex neurons and edge center neurons of three-dimensional network. At the singular point of the mutation parameter, the synchronization of the neuron firing modes shows a relationship of nonlinear function when the electric field is not considered with the increasing of the chemical synapse intensity, the synchronization is firstly decreased and then increased. (3) In the case of star network with chemically coupled neurons, the phenomenon of bursting firing modal fusion and absorption can be observed when chemical synapse intensity is larger.

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Acknowledgments

This work is supported by Science and Technology Project of Jiangxi Provincial Department of Education under Grants Nos. GJJ2202903 & GJJ203111, Science and Technology Project of Yuzhang Normal University under Grants No. YZYB-21-17. Talent Introduction Project (No. NGRCZX-22-07), Special Fund for Doctor of Science and Technology Program of Nanchang Institute of Technology under Grants No. NGKJ-21-03.

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Authors and Affiliations

  1. School of Education, Nanchang Institute of Science and Technology, Nanchang, 300108, China

    G.-W. Wang

  2. School of Mathematics and Computer, Yuzhang Normal University, Nanchang, 300103, China

    Y. Fu

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  1. G.-W. Wang
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  2. Y. Fu
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Wang, GW., Fu, Y. Modes transition and network synchronization in extended Hindmarsh–Rose model driven by mutation of adaptation current under effects of electric field. Indian J Phys 97, 2327–2337 (2023). https://doi.org/10.1007/s12648-023-02613-2

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