Dynamics and stability of neural systems with indirect interactions involved energy levels

Yan Shao, Fuqiang Wu and Qingyun Wang

Chaos, Solitons & Fractals, 2024, vol. 183, issue C

Abstract: Dynamical modelling for neural systems with direct and indirect connections is to understand how these connections contribute to neural dynamics. Despite recent findings suggesting the existence of indirect connections in neural systems, their dynamical characteristics remain poorly understood. In this paper, we propose a simplified circuit model with indirect interactions inspired by the indirect connection between two neurons, from an energy perspective. Through bifurcation and dynamics analysis, we find that the presented model has a striking resemblance with the classical Hodgkin-Huxley neuronal model. Moreover, stability in a neural network coupled with energy is demonstrated by combining stability analysis and numerical simulation. Our analysis sheds light on the excitability dynamics and multi-stability that can emerge in biophysical systems with nonlinear interactions inspired by the neural systems and highlights the role of energy in propagating electrical activities.

Keywords: Nonlinear dynamics; Neural modelling; Stability; Energy (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924005198

DOI: 10.1016/j.chaos.2024.114967

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