The coexistence of a stochastic Lotka–Volterra model with two predators competing for one prey

摘要

In this paper, we consider a stochastic Lotka–Volterra model with two predators competing for one prey. We give the sufficient conditions which guarantee that the principle of coexistence holds for this perturbed model via Markov semigroup theory. Furthermore, we prove that the densities of the solution can converge in L1 to an invariant density under appropriate conditions. Finally we make simulations to illustrate our analytical results.