The stability and bifurcation analysis in high dimensional neural networks with discrete and distributed delays

This paper studies the stability and Hopf bifurcation in a high-dimension neural network involving the discrete and distributed delays. Such model extends the existing models of neural networks from low-dimension to high-dimension. Therefore, our model is much close to large real neural networks. Here, the delay is chosen as the bifurcation parameter and we obtain the sufficient conditions for the system keeping stable and undergoing the Hopf bifurcation. Moreover, the software package DDE-BIFTOOL is introduced to better display the properties of the system and the effect of gain parameters of the system and delay kernel on the onset of the bifurcation. The simulation results further justify the validity of our theoretical analysis.