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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 B1 and B2: if B1B2 , 0, then the system is either stochastically permanent or extinctive. That is, it is extinctive if and only if B1 < 0 and B2 < 0; otherwise, it is stochastically permanent. Some existing results are included as special cases.

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