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. By analyzing the Lyapunov exponent, invariant measure and singular boundary theory, its nonlinear stochastic stability is investigated and stochastic D (P)-bifurcations are demonstrated. The stochastic stability and D (P)-bifurcation are determined from the random dynamical and phenomenological points of view. Numerical simulation results are given to support the theoretical predictions.