Excitable FitzHugh-Nagumo model with cross-diffusion: close and far-from-equilibrium coherent structures

Abstract In this paper, we shall study the formation of stationary patterns for a reaction-diffusion system in which FitzHugh-Nagumo (FHN) kinetics, its excitable regime, is coupled to linear cross-diffusion terms. (Gambino et al. Excitable Fitzhugh-Nagumo model with cross-diffusion: long-range activation instabilities, 2023), proved that supports emergence cross-Turing patterns, i.e., close-to-equilibrium structures occurring as an effect cross-diffusion. Here, construct close equilibrium on 1-D and 2-D rectangular domains. Through analysis, show species are out-of-phase spatially distributed derive amplitude equations govern pattern dynamics criticality. Moreover, classify bifurcation parameter space, distinguishing between super-and sub-critical transitions. final part numerically investigate impact terms large-amplitude pulse-like solutions existing outside showing their also case lateral short-range inhibition .