Hopf bifurcation analysis of a BAM neural network with multiple time delays and diffusion

In this paper, a BAM neural network with multiple time delays and diffusion under homogeneous Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equations, the local stability of the trivial uniform steady state and the existence of Hopf bifurcation under two different cases are established, respectively. By using the normal form theory and the center manifold reduction of partial functional differential equations (PFDEs), explicit formulae are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results.