By virtue of the stochastic bifurcation theory　the transition of the atom moveme nt at a crack tip in fatigue damage system is investigated.Using the singular po int theory of one－dimensional diffusion process and the stochastic averaging ap proach of energy envelope　a micro－model to describe the atom movement at the cr ack tip in homoclinic bifurcation fatigue damage system　which is in the presence of stochastic perturbation　is established.After the study on the characteristic of the diffusion exponent　the drift exponent and the character exponent of the fatigue damage diffusion process on singular boundary　the bifurcation behavior o f a homoclinic bifurcation fatigue damage system　which is in the presence of par ametric white noise　is examined.