一类非线性时滞Fokker-Planck方程的近似平稳解

研究了一类非线性随机时滞动力系统,特别考虑到描述这一系统的非线性随机时滞微分方程扩散项含有时间延迟效应;为此首先利用摄动理论导出了相应于非线性随机时滞微分方程的非线性时滞Fokker-Planck方程,然后利用平稳概率密度的一阶近似法得出了在时间延迟很小的情况下非线性时滞Fokker-Planck方程的一阶近似平稳解。

Approximate stationary solution of one kind of nonlinear delay Fokker-Pianck equation

A stochastic dynamical system with time delay is investigated,where the delay effect is included in the diffusion term.The Fokker-Planck equation describing the evolution of system state transmission probability density is an effective and simple method to investigate dynamical behavior of a stochastic system.Therefore,the delay Fokker-Planck equation corresponding to the nonlinear stochastic delay differential equation is derived using the perturbation theory.And then,when the time delay is small,the first order approximate stationary solution of the nonlinear delay FPK equation is obtained in terms of the first order approximation of stationary probability density.