Double Hopf Bifurcation for an Hopfield Eural Network Model With Time Delayed Feedback

Abstract

In this paper, we consider a system of delay differential equations which represents the general model of a Hopfield neural networks type. We focus on the case that the corresponding linear system has two pairs of purely imaginary eigenvalues at the trivial equilibrium, giving rise to double Hopf bifurcations. An analytical approach is used to find the explicit expressions for the critical values of the system parameters at which nonresonant or resonant double Hopf bifurcations may occur. We also investigate the occurrence of an double Hopf bifurcation about the trivial equilibrium.