Stability and Hopf bifurcation analysis on a two-neuron network with discrete and distributed delays

In this paper, a two-neuron network with both discrete and distributed delays is considered. Local stability of this system is investigated by analyzing its associated transcendental characteristic equation. By taking the discrete time delay as a bifurcation parameter, it is found that this system undergoes a sequence of Hopf bifurcations. Moreover, formulae for determining the direction of Hopf bifurcation and the stability and period of bifurcating periodic solutions are derived. Finally, numerical simulations are given to illustrate the theoretical analysis.