Dynamical stability in a delayed neural network with reaction-diffusion and coupling

In this paper, a delayed neural network with reaction-diffusion and coupling is considered. The network consists of two sub-networks each with two neurons. In the first instance, some parameter regions are identified by employing partial functional differential equation theory. Moreover, sufficient conditions of stationary bifurcation and Bogdanov-Takens bifurcation are also derived. Further, analytical results and illustrations are proved for the case where the unstable trivial equilibrium point becomes stable in the presence of reaction-diffusion terms with appropriate values. We emphasize that the non-trivial role of diffusions is enlarging the stability region in the system described by PDE, comparing with the corresponding system described by DDE. Finally, numerical simulations are carried out to verify the efficiency of the theoretical analysis and provide comparisons with some existing literature.