Long-time dynamics of a stochastic density dependent predator-prey model with Holling II functional response and jumps

TL;DR

This paper analyzes the long-term behavior of a stochastic predator-prey model with Holling II response, establishing conditions for solution existence, boundedness, persistence, and extinction under random disturbances.

Contribution

It provides the first rigorous analysis of global solutions and long-term dynamics for a stochastic predator-prey model with jumps and Holling II response.

Findings

Proves existence and uniqueness of global positive solutions.

Derives conditions for stochastic boundedness and persistence.

Identifies scenarios leading to extinction or non-persistence.

Abstract

The existence and uniqueness of a global positive solution is proven for 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. Sufficient conditions are obtained for stochastic ultimate boundedness, stochastic permanence, non-persistence in the mean, weak persistence in the mean and extinction of a population densities in the considered stochastic predator-prey model.