Bifurcation analysis in a recurrent neural network model with delays

In this paper, we study the dynamical behaviors of a three-node recurrent neural network model with four discrete time delays. We study several types of bifurcation, and use the method of multiple time scales to derive the normal forms associated with Hopf-zero bifurcation, non-resonant and resonant double Hopf bifurcations. Moreover, bifurcations are classified in two-dimensional parameter space near these critical points, and numerical simulations are presented to demonstrate the applicability of the theoretical results.