Hopf bifurcation analysis of a tabu learning two-neuron model

Tabu learning neural network applies the concept of tabu search to neural networks for solving optimization problems. In this paper, we study the nonlinear dynamical behaviors of a tabu learning two-neuron model with linear proximity function. By choosing the memory decay rate as the bifurcation parameter, we prove that Hopf bifurcation occurs in the model. The stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are determined by applying the normal form theory. A numerical example is also presented to verify the theoretical analysis.