Bifurcation analysis on a two-neuron system with distributed delays in the frequency domain

In this paper, a general two-neuron model with distributed delays and a strong kernel is investigated. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of bifurcation parameter for the model is determined. Furthermore, if the mean delay used as a bifurcation parameter, it is found that Hopf bifurcation occurs for the strong 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 Nyquist criterion and the graphical Hopf bifurcation theorem. Some numerical simulations are given to justify the theoretical analysis results.