实噪声参激一类余维2分叉系统的最大Lyapunov指数(Ⅱ)

On the Maximal Lyapunov Exponent for a Real Noise Parametrically Excited Co-Dimension Two Bifurcation System(Ⅱ)

对于三维中心流形上实噪声参激的一类余维2分叉系统,为使模型更具有一般性,取系统的参激实噪声为一线性滤波系统的输出_零均值的平稳高斯扩散过程,满足细致平衡条件· 并在此基础上首次使用Arnold的渐近方法以及Fokker_Planck算子的特征谱展式,求解不变测度以及最大的Lyapunov指数的渐近展式·

For a co_dimension two bifurcation system on a three_dimensional central manifold, which is parametrically excited by a real noise, a rather general model is obtained by assuming that the real noise is an output of a linear filter system_a zeromean stationary Gaussian diffusion process which satisfies detailed balance condition. By means of the asymptotic analysis approach given by L. Arnold and the expression of the eigenvalue spectrum of Fokker_Planck operator, the asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are obtained.