Abstract: In this paper, in order to investigate the sample stability of a class of white noises parametrically excited co-dimension 2 bifurcation system which possesses non-semisimple double zero eigenvalues and then to fix the first bifurcation point, the approach of asymptotic analysis of L. Arnold is used to obtain the asymptotic expression of the maximum Lyapunov exponent of the relevant system. In addition, with the aid of the theory of singular boundary of one-dimensional diffusion process, a further research ...