Hopf bifurcation and stability analysis on discrete-time Hopfield neural network with delay. (English) Zbl 1136.93039

Summary: A discrete-time Hopfield neural network with delay is considered. We give some sufficient conditions ensuring the local stability of the equilibrium point for this model. By choosing the delay as a bifurcation parameter, we demonstrated that Neimark-Sacker bifurcation (or Hopf bifurcation for map) would occur when the delay exceeds a critical value. A formula for determining the direction bifurcation and stability of bifurcation periodic solutions is given by applying the normal form theory and the center manifold theorem. Some numerical simulations for justifying the theoretical results are also provided.


93D99 Stability of control systems
92B20 Neural networks for/in biological studies, artificial life and related topics
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