Abstract
This paper investigates the dynamics of a discrete FitzHugh-Nagumo (FHN) model with self-diffusion on two-dimensional coupled map lattices. The primary objective is to analyze the complex dynamics of neuronal systems in a discrete setting. Through the application of central manifold and normal form analysis, it has been demonstrated that the system is capable of undergoing Neimark-Sacker and flip bifurcations even in the absence of diffusion. Additionally, when influenced by diffusion, the system can manifest pure Turing instability, Neimark-Sacker-Turing instability, and Flip-Turing instability. In the numerical simulation section, the path from bifurcation to chaos is explored by calculating the maximum Lyapunov exponent and drawing the bifurcation diagram. The interconversion between various Turing instabilities is simulated by varying the values of the time step and the self-diffusion coefficient. This study contributes to a deeper understanding of the complexity of neural network systems.
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