Dynamics of a modified Leslie-Gower predation model considering a generalist predator and the hyperbolic functional response
type: Item
instance of: scholarly article
title: Dynamics of a modified Leslie-Gower predation model considering a generalist predator and the hyperbolic functional response
zbMATH Open document ID: 1472.92176
author: Claudio Arancibia-Ibarra
author: Alejandro Rojas-Palma
author: Betsabé González-Yañez
author: Eduardo González-Olivares
published in: Mathematical Biosciences and Engineering
publication date: 2021-08-13T00:00:00Z
review text: The paper studies the following modified Leslie--Gower type model \begin{align*} \dot x &=\left(r_1 - b_1x - \frac{a_1 y}{x+k_1}\right)x,\\ \dot y &= \left( r_2 - \frac{a_2 y}{x+ k_2}\right) y, \tag{1}\end{align*} where \(x\) and \(y\) represent the size of the prey and predator population, respectively, and the parameters \(r_1, b_1, a_1, k_1, r_2, a_2, k_2\) are assumed to be positive. The authors determine the number and stability of the (biologically relevant) equilibria and show that in certain parameter regions limit cycles arise as a result of either a Hopf or a homoclinic bifurcation. The stability of these limit cycles is also analyzed. The results illustrate that system (1) has the flexibility to model several different population dynamical phenomena.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 7381747
zbMATH Keywords: predator-prey model
zbMATH Keywords: modified Leslie--Gower model
zbMATH Keywords: bifurcation
zbMATH Keywords: limit cycle
zbMATH Keywords: separatrix curve
zbMATH Keywords: stability
Wikidata QID: Q91168099
describes a project that uses: MATCONT
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: mbe.2019403
OpenAlex ID: W2971717955
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DOI: 10.3934/MBE.2019403
description: scientific article; zbMATH DE number 7381747