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. (C) 2011 Elsevier Ltd. All rights reserved.
stochastic stability and bifurcation hopfield neural network lyapunov exponent invariant measure