Bifurcation Analysis for a Discrete-time Hopfield Neural Network with Multiple Delays

摘要

In this paper, a discrete-time Hopfield neural network with multiple delays is investigated. We firstly consider the local asymptotic stability of the null solution and the existence of Neimark-Sacker bifurcations. By using the normal form theory and center manifold reduction, we derive explicit formulae that determine the stability, direction and other properties of bifurcating periodic solutions. Finally, some numerical simulations for justifying the theoretical results are provided.