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为考查白噪声参激的具有非半简双零特征值的一类余维二分叉系统的样本稳定性并确定其首次分叉点的位置，本文使用Ｌ．Ａｒｎｏｌｄ的渐近分析方法研究了系统最大Ｌｙａｐｕｎｏｖ指数的渐近分析式．为进一步研究噪声对于此系统退化分叉的影响，本文将使用一维扩散过程的奇异边界理论，考查“隐藏在余维２分叉点之后”同宿分叉系统受参激白噪声影响的分叉行为．
In order to examine the sample stability of a class of I-dimensional bifurcation system with non-semi-simple double zero eigenvalue and the location of its first bifurcation point, L is used in this paper. Arnold’s asymptotic analysis method is used to study the asymptotic analysis of the largest Lyapunov exponent of the system. In order to further study the effect of noise on the degenerate bifurcation of this system, we use the singular boundary theory of one-dimensional diffusion process to examine the bifurcation of the homoclinic bifurcation system affected by white noise due to parametric ghost behavior.