Bifurcation analysis on a discrete-time tabu learning model

In this paper, we consider a discrete-time tabu learning single neuron model. After investigating the stability of the given system, we demonstrate that Pichfork bifurcation, Flip bifurcation and Neimark-Sacker bifurcation will occur when the bifurcation parameter exceed a critical value, respectively. A formula is given for determining the direction and stability of Neimark-Sacker bifurcation by applying the normal form theory and the center manifold theorem. Some numerical simulations for justifying the theoretical results are also provided.