Bifurcation analysis on a two-neuron system with distributed delays

A general two-neuron model with distributed delays is studied in this paper. Its local linear stability is analyzed by using the Routh–Hurwitz criterion. If the mean delay is used as a bifurcation parameter, we prove that Hopf bifurcation occurs for a weak kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Some numerical simulations for justifying the theoretical analysis are also given.