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

Argha Mondal, Chittaranjan Hens, Arnab Mondal, Chris G. Antonopoulos

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Neurons are often connected, spatially and temporally, in phenomenal ways that promote wave propagation. Therefore, 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.

Original languageEnglish
Article number111375
JournalChaos, Solitons and Fractals
StatePublished - Nov 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Ltd


  • Amplitude equations
  • Bifurcation analysis
  • Diffusive instabilities
  • Izhikevich model
  • Spatiotemporal patterns


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