Frequency domain analysis for bifurcation in a simplified tri-neuron BAM network model with two delays

Abstract

In this paper, a class of simplified tri-neuron BAM network model with two delays is considered. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of bifurcation parameter point is determined. If the sum tau of delays tau(1) and tau(2) is chosen as a bifurcation parameter, it is found that Hopf bifurcation occurs when the sum tau passes through a series of critical values. The direction and the stability of Hopf bifurcation periodic solutions are determined by the Nyquist criterion and the graphical Hopf bifurcation theorem. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, main conclusions are given.