Stochastic Stability and Bifurcation Analysis on Hopfield Neural Networks with Noise.

A stochastic differential equation modelling a Hopfield neural network with two neurons is investigated. Its dynamics are studied in terms of local stability analysis and Hopf bifurcation analysis. By analyzing the Lyapunov exponent, invariant measure and singular boundary theory, its nonlinear stability is investigated and Hopf bifurcations are demonstrated. The stability and direction of the Hopf bifurcation are determined from the dynamical and phenomenological points of view.