Effect of cross diffusion on the FitzHugh-Rinzel model

Abstract The article explores the FitzHugh-Rinzel model in the context of reaction-diffusion systems, focusing on both self-diffusion and cross-diffusion mechanisms. The conditions under which a stable equilibrium in the absence of diffusion can become unstable following the introduction of diffusive terms are highlighted, showing the onset of Turing instability. Explicit examples are considered, and intervals in which Turing instability occurs are identified.