A stochastic predator-prey model that depends on the population density of the predator

Abstract

The system of stochastic differential equations describing a nonautonomous stochastic density-dependent predator-prey model with Holling-type II functional response disturbed by white noise, centered and non-centered Poisson noises is considered. So, in this model we take into account levels of predator density dependence and jumps, corresponding to the centered and non-centered Poisson measures. The existence and uniqueness theorem for the positive, global (no explosions in the finite time) solution of the considered system is proved. We obtain sufficient conditions of stochastic ultimate boundedness and stochastic permanence in the considered stochastic predator-prey model.