Dynamics of a prey-predator system with modified Leslie-Gower and Holling type II schemes incorporating a prey refuge

Long-time behavior of a non-autonomous stochastic predator-prey model with jumps

It is proved the existence and uniqueness of the global positive solution to the system of stochastic differential equations describing a non-autonomous stochastic predator-prey model with a modified version of Leslie-Gower and Holling-type II functional response disturbed by white noise, centered and non-centered Poisson noises. We obtain sufficient conditions of stochastic ultimate boundedness, stochastic permanence, non-persistence in the mean, weak persistence in the mean, and extinction of the solution to the considered system.