Hopf Bifurcation Analysis on a Tabu Learning Single Neuron Model in the Frequency Domain

In this paper, a tabu learning single neuron model is investigated. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of bifurcation parameter for this model is determined. Furthermore, we found that if the memory decay rate is used as a bifurcation parameter, Hopf bifurcation occurs in the neuron. This means that a family of periodic solutions bifurcates out from the equilibrium when the bifurcation parameter exceeds a critical value. The direction and stability of the bifurcating periodic solutions are determine by the Nyquist criterion and the graphical Hopf bifurcation theorem. Some numerical simulations for justifying the theoretical analysis are also given.