Bifurcation analysis in a class of neural network models with discrete and distributed delays

This paper investigates the stability and Hopf bifurcation in a class of neural networks with two neurons. This model involves discrete and distributed delays described by an integral with a strong delay kernel. By analysing the distribution of roots of the characteristic equation of the associated linearized system, the conditions for creating the Hopf bifurcation can be obtained. Besides, the delay is chosen as the bifurcation parameter and we find that the equilibrium is asymptotically stable when the delay is less than a critical value while the system undergoes a Hopf bifurcation when the delay exceeds the critical value. Finally, the software package DDE-BIFTOOL is applied to neural networks and the simulation results justify the validity of our theoretical analysis.