Asymptotic Behavior of Predator-Prey Systems Perturbed by White Noise

摘要

In this paper, we develop the results in Rudnicki (Stoch. Process. Appl. 108:93–107, 2003) to a stochastic predator-prey system where the random factor acts on the coefficients of environment. We show that there exists the density functions of the solutions and then, study the asymptotic behavior of these densities. It is proved that the densities either converges in L 1 to an invariant density or converges weakly to a singular measure on the boundary.