Codimension two bifurcation in a delayed neural network with unidirectional coupling

In this paper, a delayed neural network model with unidirectional coupling is considered. Zero–Hopf bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm form at the zero–Hopf singularity and show that the model can exhibit pitchfork, Hopf bifurcation, and double Hopf bifurcation is also found to occur in this model. Some numerical simulations are given to support the analytic results.