实噪声参激一类余维2分叉系统的最大Lyapunov指数(Ⅰ)

On the Maximal Lyapunov Exponent for a Real Noise Parametrically Excited Co_Dimension Two Bifurcation System(Ⅰ)

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，并满足细致平衡条件· 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ｅｍａｘ 的渐近展式·

For a real noise parametrically excited co_dimension two bifurcation systems on a three_dimensional central manifold, 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 diffusion process that satisfies the detailed balance condition. On such basis, asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are established by use of Arnold asymptotic analysis approach in parallel with the eigenvalue spectrum of Fokker_Planck operator.