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.

► A 3-node recurrent neural network model with multiple time delays is studied.
► Bifurcation and stability analysis associated with Hopf-zero singularity is given.
► A simple method based multiple time scales is used to derive normal forms.
► Numerical simulations are presented to verify the theoretical results.