Permanence and asymptotic behaviors of stochastic competitive Lotka-Volterra system with Markov switching and L\'{e}vy noise

Abstract

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