Stability and bifurcation analysis on a discrete-time neural network

Using techniques developed by Kuznetsov to discrete-time systems, we study the stability of the equilibrium (0,0) and Neimark-Sacker bifurcation (also called Hopf bifurcation for map) of a discrete-time neural network system. The obtained results are less restrictive and improve upon the existing ones on Neimark-Sacker bifurcation of discrete-time neural network with special classes of transfer functions. The theoretical analyses are verified by numerical simulations. Our results have potential applications in neural networks.