Long-time behavior of a nonautonomous stochastic predator–prey model with jumps

Abstract

The existence and uniqueness of a global positive solution is proven for the system of stochastic differential equations describing a nonautonomous stochastic predator–prey model with a modified version of the Leslie–Gower term and Holling-type II functional response disturbed by white noise, centered and noncentered Poisson noises. Sufficient conditions are obtained for stochastic ultimate boundedness, stochastic permanence, nonpersistence in the mean, weak persistence in the mean and extinction of a solution to the considered system.

Keywords

• Stochastic predator–prey model
• Leslie–Gower and Holling-type II functional response
• global solution
• stochastic ultimate boundedness
• stochastic permanence
• extinction