Stochastic Lotka-Volterra systems with Levy noise

This paper is concerned with stochastic Lotka-Volterra models perturbed by Levy noise. Firstly, stochastic logistic models with Levy noise are investigated. Sufficient and necessary conditions for stochastic permanence and extinction are obtained. Then three stochastic Lotka-Volterra models of two interacting species perturbed by Levy noise (i.e., predator-prey system, competition system and cooperation system) are studied. For each system, sufficient and necessary conditions for persistence in the mean and extinction of each population are established. The results reveal that firstly, both persistence and extinction have close relationships with Levy noise; Secondly, the interaction rates play very important roles in determining the persistence and extinction of the species. (C) 2013 Elsevier Inc. All rights reserved.