DYNAMICS OF A STOCHASTIC LOTKA–VOLTERRA MUTUALISTIC PARASITE–HOST SYSTEM WITH LÉVY JUMPS

Abstract

This paper is concerned with a two-dimensional stochastic Lotka–Volterra mutualistic parasite–host system with Lévy jumps. First, the study reveals that each species is either extinct or persistent in the mean, relying on some critical values. The result shows that both the environmental noises and Lévy jumps play important roles in determining the persistent in the mean or extinction of each species. Then, we establish the sufficient criteria for stability on distribution of the system. Finally, we give some numerical simulations to support the main results. Some recent works are extended and improved greatly.