中文摘要：

在现在的纸，最大的 Lyapunov 代表为一种合作尺寸被调查在上的二个分叉系统一三维中央对由围住的噪音的参量的刺激歧管、使 \O 遭到。由使用一个不安方法，一个一个维的阶段散开过程的不变的措施的表情为三个案例被获得，在哪个矩阵 B 的不同形式，那在噪音刺激术语被包括，被假定然后作为结果，为一个维的阶段散开过程的所有三种单个边界被分析。经由 Monte-Carlo 模拟，我们发现不变的措施的分析表情遇见数字的很好。并且而且， P 分叉行为为一个维的阶段散开过程被调查。为为一个维的阶段散开过程的单个边界的三个案例，最后，最大的 Lyapunov 代表的分析表达式为随机的分叉系统被介绍。

英文摘要：

In the present paper, the maximal Lyapunov ex- ponent is investigated for a co-dimension two bifurcation system that is on a three-dimensional central manifold and subjected to parametric excitation by a bounded noise. By using a perturbation method, the expressions of the invari- ant measure of a one-dimensional phase diffusion process are obtained for three cases, in which different forms of the matrix B, that is included in the noise excitation term, are assumed and then, as a result, all the three kinds of singular boundaries for one-dimensional phase diffusion process are analyzed. Via Monte-Carlo simulation, we find that the an- alytical expressions of the invariant measures meet well the numerical ones. And furthermore, the P-bifurcation behav- iors are investigated for the one-dimensional phase diffusion process. Finally, for the three cases of singular botmdaries for one-dimensional phase diffusion process, analytical ex- pressions of the maximal Lyapunov exponent are presented for the stochastic bifurcation system.