A study of the FitzHugh-Nagumo Model with diffusion term
Résumé
This article aims to provide a theoretical background for the FitzHugh-Nagumo Model, a reaction-diffusion system originating from the field of neuroscience modeling. We begin by examining a linear reaction-diffusion system, establishing conditions under which Hopf bifurcations exist. We then bridge these findings to the nonlinear and nonhomogeneous FitzHugh-Nagumo (nhFHN) system, demonstrating the conditions necessary for generating oscillatory behavior in this system. Finally, we present numerical simulations of the nhFHN system.
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