Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2010, Article ID 684926, 18 pages doi:10.1155/2010/684926 Research Article Existence, Uniqueness and Ergodicity of Positive Solution of Mutualism System with Stochastic Perturbation Chunyan Ji, 1, 2 Daqing Jiang, 2 Hong Liu, 2, 3 and Qingshan Yang 2 1 School of Mathematics and Statistics, Changshu Institute of Technology, Changshu, Jiangsu 215500, China 2 School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, China 3 China Economics and Management Academy, CIAS, Central University of Finance and Economics, Beijing 100081, China Correspondence should be addressed to Chunyan Ji, chunyanji80@hotmail.com Received 30 December 2009; Accepted 15 June 2010 Academic Editor: Ben T. Nohara Copyright q 2010 Chunyan Ji et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We discuss a two-species Lotka-Volterra mutualism system with stochastic perturbation. We show that there is a unique nonnegative solution of this system. Furthermore, we investigate that there exists a stationary distribution for this system, and it has ergodic property. 1. Introduction It is well known that the differential equation ˙ x 1 t x 1 tr 1 - a 11 x 1 t a 12 x 2 t, ˙ x 2 t x 2 tr 2 a 21 x 1 t - a 22 x 2 t 1.1 denotes the population growth of mutualism system for the two species. x 1 t and x 2 t represent the densities of the two species at time t, respectively, and the parameters r i ,a ij , i, j 1, 2 are all positive. Goh 1 showed that the asymptotic stability equilibrium state of 1.1 in local must be asymptotic stability in global. That is, if r i > 0,a ij > 0, i,j 1, 2, and a 11 a 22 - a 12 a 21 > 0, then x 1 t -→ x ∗ 1 , x 2 t -→ x ∗ 2 , as t -→ ∞, 1.2