Stability and bifurcation for discrete-time Cohen–Grossberg neural network

摘要

This paper investigates a discrete-time Cohen–Grossberg neural network model. Some sufficient criteria ensuring the asymptotic stability of the equilibrium point for this model are derived. Moreover, by choosing the appropriate bifurcation parameter, we prove that Neimark–Sacker bifurcation occurs when the bifurcation parameter exceeds a critical value. We determine the direction and stability of bifurcation by applying the normal form theory and the center manifold theorem. Some numerical simulations for justifying the theoretical analysis are also given.