Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation

Li, X. and Mao, X., National Natural Science Foundation of China (Funder), Key Project of Chinese Ministry of Education (Funder), Key Laboratory for Applied Statistics of MOE (KLAS) (Funder) (2009) Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation. Discrete and Continuous Dynamical Systems - Series A, 24 (2). pp. 523-593. ISSN 1078-0947

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    Abstract

    In this paper, we consider a non-autonomous stochastic Lotka-Volterra competitive system dxi(t) = xi(t)[(bi(t)¡ nPj=1aij (t)xj (t))dt+¾i(t)dBi(t)], where Bi(t) (i = 1; 2; ¢ ¢ ¢ ; n) are independent standard Brownian motions. Some dynamical properties are discussed and the su±cient conditions for the existence of global positive solutions, stochastic permanence, extinction as well as global attractivity are obtained. In addition, the limit of the average in time of the sample paths of solutions is estimated.