Bifurcations and complex dynamics of a two dimensional neural network model with delayed discrete time

Abstract

This paper focuses on the different bifurcations of fixed points of a delayed discrete neural network model analytically and numerically. The conditions and critical values of different bifurcations including the pitchfork, flip, Neimark–Sacker, and flip–Neimark–Sacker are analyzed. By using the critical coefficients, the structure for each bifurcation are determined. By taking one and two parameters, the critical coefficients are calculated and the curves associated with each bifurcation are plotted. The numerical simulation results demonstrate the effectiveness and feasibility of the proposed method.