Bifurcation and luring instability of a class of reaction-diffusion neural networks

The dynamics of neural networks with reaction-diffusion is very rich. In this paper, a class of neural network with diffusive coupling is considered. By choosing appropriate parameter and applying the Hopf and Turing instability theory, we investigate the local stability, Hopf bifurcation and Turing instability of this model and give some criteria. Numerical results have been presented to verify the analytical predictions. It shows that diffusion could destabilize a stable equilibrium of the reaction-diffusion system and lead to nonuniform spatial patterns, the formation of spatial structures may change as time is growing, finally form a relatively stable structure.