ON CO-DIMENSION 2 BIFURCATION SYSTEM EXCITED PARAMETRICALLY BY WHITE NOISES
白噪声参激余维2分叉系统研究

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 on the influence of noises upon the degenerate bifurcation of such system is made to study the bifurcation behaviors of the white noise parametrically excited homoclinic bifurcation system which is hidden behind the co-dimension 2 bifurcation point.