Abstract
<abstract> In this paper, critical conditions of Turing instability for Fitzhugh-Nagumo (FHN) model with diffusion under Neumann boundary conditions are derived. Moreover, different from previous works about the FHN model, we obtain simple bifurcation, double bifurcation, and four-fold bifurcation with stripe pattern, rectangular pattern, spot pattern, square pattern, and highly developed square pattern, respectively. Meanwhile, the theoretical results are applied to two coupled FHN model with diffusion, and the process of the coupling strengths affecting the stability of the model is presented by numerical simulations. </abstract>
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