一类随机分叉系统概率1分叉研究

ON THE BIFURCATION IN PROBABILITY 1 SENSE FOR A KIND OF STOCHASTIC BIFURCATION SYSTEM

对于三维中心流形上实噪声参激的一类余维 2分叉系统 ,使用Arnold的渐近方法以及Fokker Planck算子的特征谱展式 。

For a co dimension two bifurcation system on a three dimensional central manifold, which is parametrically excited by a real noise, a model of enhanced generality is developed in the present paper by assuming the real noise to be an output of a linear filter system, namely, a zero mean stationary Gaussian process that satisfies the detailed balance condition. On such basis, asymptotic expansions of invariant measure and maximal Lyapunov exponent for relevant system are established by the use of Arnold asymptotic analysis approach in parallel with the eigenvalue spectrum expansions of Fokker Planck operator.