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

TL;DR

This paper establishes the existence, uniqueness, and long-term behavior of solutions to a complex stochastic predator-prey model with jumps, providing conditions for persistence, extinction, and boundedness.

Contribution

It introduces a comprehensive analysis of a non-autonomous stochastic predator-prey system with jumps, extending prior models by including non-centered Poisson noises and deriving new stability conditions.

Findings

Existence and uniqueness of global positive solutions

Conditions for stochastic permanence and extinction

Analysis of long-term behavior under various noise disturbances

Abstract

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.