Stability Analysis of a Modified Leslie–Gower Predation Model With Weak Allee Effect in the Prey

Claudio Arancibia-Ibarra,Peter Van Heijster,José D Flores

doi:10.3389/fams.2021.731038

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.

Highlights

Predator-prey models are studied in both applied mathematics [1,2,3] and ecology [4,5,6,7]
New technologies used to study biological and physical phenomenon reveal that species’ interactions are more complex than previously used in the models [7, 12,13,14]. The importance of these more complex interactions are becoming increasingly apparent as research findings have shown that ecosystem dynamics depend on the particular nature of the interaction processes, such as the functional response and predation rate [6, 7, 15, 16]
The Allee effect can prevent the oscillation of both populations. In this manuscript, we find that the Leslie–Gower model with weak Allee effect supports the coexistence and oscillation of both populations

Summary

Introduction

Predator-prey models are studied in both applied mathematics [1,2,3] and ecology [4,5,6,7] The goal of these studies is to describe and analyse the predation interaction between the predator and the prey and predict how they respond to future interventions [8, 9]. New technologies used to study biological and physical phenomenon reveal that species’ interactions are more complex than previously used in the models [7, 12,13,14] The importance of these more complex interactions are becoming increasingly apparent as research findings have shown that ecosystem dynamics depend on the particular nature of the interaction processes, such as the functional response and predation rate [6, 7, 15, 16]

Objectives

Results

Conclusion