Dynamics of a two-predator one-prey stochastic delay model with Lévy noise

Abstract

In this paper, the stability in distribution of the solutions (SDS) of a two-predator one-prey stochastic delay model with Lévy noise is considered. We show that under some simple conditions, the complete dynamic scenarios of SDS are characterized by three parameters η1>η2>η3, which depend on the interaction and Lévy noise. We prove that if η1<1, then limt→+∞yi(t)=0 almost surely, i=1,2,3; if ηi>1>ηi+1, then limt→+∞yj(t)=0 almost surely, j=i+1,…,3, and the distributions of (y1(t),⋯,yi(t))T converge weakly to a unique ergodic invariant distribution (UEID); if η3>1, then the distributions of (y1(t),y2(t),y3(t))T converge weakly to a unique ergodic invariant distribution (UEID).