Bifurcation and control of a neuron model with delays and reaction-diffusion

The paper deals with the stability and Hopf bifurcation of a class of a neuron model with reaction-diffusion and delay-dependent parameter. Based on stability and bifurcation theory, determining the delay as the bifurcation parameter, we give some criteria for stability and Hopf bifurcation. Numerical simulations are given to validate the theoretical analysis. It shows that controllers which are designed in this paper can control the occurrence of bifurcation effectively and can dominate the amplitude of the bifurcation limit cycle.