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

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