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

TL;DR

This paper analyzes a complex prey-predator model with prey refuge, exploring local and global dynamics, cycles, and stochastic effects to understand ecological stability and extinction risks.

Contribution

It introduces a prey refuge into a modified Leslie-Gower and Holling type II model, expanding understanding of predator-prey interactions with refuge effects.

Findings

Identification of conditions for prey and predator extinction

Existence of stable cycles under certain parameters

Impact of stochastic perturbations on system stability

Abstract

We study a modified version of a prey-predator system with modified Leslie-Gower and Holling type II functional response studied by M.A. Aziz-Alaoui and M. Daher-Okiye. The modification consists in incorporating a refuge for preys, and substantially complicates the dynamics of the system. We study the local and global dynamics and the existence of cycles. We also investigate conditions for extinction or existence of a stationary distribution, in the case of a stochastic perturbation of the system.