The Hopf bifurcation analysis on a time-delayed recurrent neural network in the frequency domain

In this paper, a class of recurrent neural networks with distributed delays and a strong kernel is studied. It is shown that the Hopf bifurcation occurs as the bifurcation parameter, the mean delay, passes a critical value where a family of periodic solutions emanates from the equilibrium. The existence and stability of such solutions are determined by the Hopf bifurcation theorem in the frequency domain and the generalized Nyquist stability criterion.