Stability analysis of a modified Leslie-Gower predation model with weak Allee effect on the prey

TL;DR

This paper analyzes a predator-prey model incorporating a weak Allee effect and hyperbolic response, revealing conditions for coexistence, oscillations, and various bifurcations in the system.

Contribution

It introduces a modified Leslie-Gower model with weak Allee effect and thoroughly investigates its stability and bifurcation phenomena.

Findings

Coexistence and oscillations are supported under certain conditions.

Multiple bifurcations, including saddle-node, Hopf, and Bogdanov-Takens, are identified.

Parameter regions for different dynamic behaviors are mapped.

Abstract

In this manuscript, we study a Leslie-Gower predator-prey model with a hyperbolic functional response and weak Allee effect. The results reveal that the model supports coexistence and oscillation of both predator and prey populations. We also identify regions in the parameter space in which different kinds of bifurcations, such as saddle-node bifurcations, Hopf bifurcations and Bogdanov-Takens bifurcations.