Effects of noise in nonlinear systems exhibiting simple bifurcations

Abstract

Simple bifurcation in the presence of noise is investigated and some results are presented. The effect of additive noise on gradient systems is examined by using Laplace's method of steepest descent. Reduced governing equations for multidimensional systems which exhibit simple bifurcation are obtained with the stochastic normal forms method and are applied to the stochastic Lorenz equations. The resulting equations are similar to those obtained by extended averaging. First passage time and stationary densities are also obtained and numerical examples are presented.