Permanence and asymptotic behaviors of stochastic competitive Lotka-Volterra system with Markov switching and Lévy noise

Abstract

This paper concerns the dynamics of a stochastic competitive Lotka-Volterra system with Markov switching and Lévy noise. The results show that stochastic permanence and extinction are characterized by two parameters B 1 and B 2 : if B 1 B 2 0, then the system is either stochastically permanent or extinctive. That is, it is extinctive if and only if B 1 < 0 and B 2 < 0; otherwise, it is stochastically permanent. Some existing results are included as special cases.