Neimark-Sacker Bifurcation For A Discrete-Time Neural Network Model With Multiple Delays

In this paper, we investigate a discrete-time neural network model with multiple delays. By analyzing the corresponding characteristic equation of the system, we discuss the stability and the existence of Neimark-Sacker bifurcation for the model. Applying the normal form method and the center manifold theory for discrete time system developed by Kuznetsov, we derive the explicit formula for determining the direction of Neimark-Sacker bifurcation and the stability of bifurcating periodic solution. Some numerical simulations which are in a good agreement with our theoretical analysis are carried out. Our results are new and complement previously known studies.