This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is studied. Moreover, we show that the solution is stochastically bounded, uniformly continuous and stochastic permanence. The sufficient conditions for the system to be extinct are given and the condition for the system to be persistent are also established. At last, some figures are presented to illustrate our main results.
Generalized KdV equation subject to a stochastic perturbation
我们证明了次临界广义Korteweg-de Vries方程（mKdV和gKdV与四次幂的非线性）的全局适定性。更精确地说，我们证明了如果驱动噪声是$L^2(\mathbb{R})$上的圆柱Wiener过程，协方差算子是适当的索伯列夫空间中的Hilbert-Schmidt，那么具有$H^1(\mathbb{R})$数据的解在$H^1(\mathbb{R})$中是全局适定性的.这推广了A. de Bouard和A.德彪西的随机KdV方程。
Spectral Convergence of the Stochastic Galerkin Approximation to the Boltzmann Equation with Multiple Scales and Large Random Perturbation in the Collision Kernel
Stochastic perturbation of sweeping process and a convergence result for an associated numerical scheme
CNRS - Université Lille 1（法国国家科学研究中心-里尔第一大学）；Laboratoire de mathématiques Paul Painlevé（保罗·潘勒韦数学实验室）；LAMAV Université de Valenciennes et du Hainaut-Cambrésis（瓦朗谢纳与康布雷-汉诺威大学拉马夫研究所）
