非高斯噪声激励下非线性漂移Fokker-Planck方程的非稳态解及其应用

非高斯噪声广泛存在于各种非线性系统，对非高斯噪声所驱动系统的非稳态演化行为进行研究可以更为深入的了解其内在的演化机理．本文对非高斯噪声和高斯白噪声共同驱动的非线性动力学系统的非稳态演化问题进行研究．首先应用格林函数的 $\Omega$ 展开理论在初始区域对非线性动力学系统进行线性化，然后结合本征值和本征矢理论推导出了该系统 Fokker-Planck 方程的近似非稳态解的表达式，最后以 Logistic 系统模型为例分析了非高斯噪声强度，关联时间及非高斯噪声偏离参数对非稳态解以及一阶矩的影响．研究结果表明，用 Logistic 模型描述产品产量增长时，其非稳态解可更好地反映产品产量在不稳定点附近的演化行为．

The Non-stationary State Solution of Non-linear Drift Fokker-Planck Equation with Non-Gaussian Noise and its Application

Non-Gaussian noise widely exists in many kinds of nonlinear systems. The study about the non-stationary state evolution behavior of the system driven by non-Gaussian noise can help us to understand its inherent evolution mechanism more deeply. In this paper, we investigate the non-stationary state evolution problem of the non-linear dynamical system driven by both non-Gaussian noise and Gaussian white noise. First, the non-linear dynamical system is linearized in the initial area by using the $\Omega$-expansion of the Green function. Then, we obtain the expression for the approximate non-stationary state solution through the eigenvalue and eigenvector theory. Finally, taking the Logistic model as an example, we examine the influences of the non-Gaussian noise intensity, the correlation time and the deviation parameter on the non-stationary state solution and its mean. The results show that when the Logistic model is used to describe the growth of product output, the non-stationary state solution can better reflect the evolution behavior of the product output near the unstable point.