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Spatiotemporal instabilities and pattern formation in systems of diffusively coupled Izhikevich neurons

Mondal, Argha and Hens, Chittaranjan and Mondal, Arnab and Antonopoulos, Chris G (2021) 'Spatiotemporal instabilities and pattern formation in systems of diffusively coupled Izhikevich neurons.' Chaos, Solitons and Fractals, 152. ISSN 0960-0779

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Abstract

Neurons are often connected, spatially and temporally, in phenomenal ways that promote wave propagation. There- fore, it is essential to analyze the emergent spatiotemporal patterns to understand the working mechanism of brain activity, especially in cortical areas. Here, we present an explicit mathematical analysis, corroborated by numerical results, to identify and investigate the spatiotemporal, non-uniform, patterns that emerge due to instability in an extended homogeneous 2D spatial domain, using the excitable Izhikevich neuron model. We examine diffusive instability and perform bifurcation and fixed-point analyses to characterize the patterns and their stability. Then, we derive analytically the amplitude equations that establish the activities of reaction-diffusion structures. We report on the emergence of diverse spatial structures including hexagonal and mixed-type patterns by providing a systematic mathematical approach, including variations in correlated oscillations, pattern variations and amplitude fluctuations. Our work shows that the emergence of spatiotemporal behavior, commonly found in excitable systems, has the potential to contribute significantly to the study of diffusively-coupled biophysical systems at large.

Item Type: Article
Uncontrolled Keywords: Izhikevich model, Bifurcation analysis, Diffusive instabilities, Amplitude equations, Spatiotemporal patterns
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 24 Aug 2021 15:38
Last Modified: 20 Oct 2021 12:15
URI: http://repository.essex.ac.uk/id/eprint/30939

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