The basins of attraction in a modified May-Holling-Tanner predator-prey model with Allee affect

DOI10.1016/j.na.2019.03.004zbMath1421.34032arXiv1901.01118OpenAlexW2908189435WikidataQ115568774 ScholiaQ115568774MaRDI QIDQ2312554

Claudio Arancibia-Ibarra

Publication date: 17 July 2019

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.01118

zbMATH Keywords

basin of attractionbifurcationspredator-prey modelAllee effect

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Population dynamics (general) (92D25) Stability of solutions to ordinary differential equations (34D20) Qualitative investigation and simulation of ordinary differential equation models (34C60) Asymptotic properties of solutions to ordinary differential equations (34D05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (15)

Relaxation Oscillations and Canard Explosion of a Leslie–Gower Predator–Prey System with Addictive Allee Effect ⋮ Stability and Bifurcation in a Leslie–Gower Predator–Prey Model with Allee Effect ⋮ Evolutionary dynamics of single species model with allee effect ⋮ Modeling Allee Effect in the Leslie-Gower Predator–Prey System Incorporating a Prey Refuge ⋮ Bifurcation analysis of a modified May-Holling-Tanner predator-prey model with Allee effect ⋮ Bifurcations in a Leslie-Gower model with constant and proportional prey refuge at high and low density ⋮ Bifurcations in a discontinuous Leslie-Gower model with harvesting and alternative food for predators and constant prey refuge at low density ⋮ Modelling and analysis of a modified May-Holling-Tanner predator-prey model with allee effect in the prey and an alternative food source for the predator ⋮ Bifurcation analysis of a predator-prey model with predator intraspecific interactions and ratio-dependent functional response ⋮ Turing patterns in a diffusive Holling-Tanner predator-prey model with an alternative food source for the predator ⋮ A modified May-Holling-Tanner predator-prey model with multiple allee effects on the prey and an alternative food source for the predator ⋮ Dynamics of a modified Leslie-Gower predation model considering a generalist predator and the hyperbolic functional response ⋮ Canards and homoclinic orbits in a slow-fast modified May-Holling-Tanner predator-prey model with weak multiple allee effect ⋮ Dynamics in a diffusive predator–prey system with double Allee effect and modified Leslie–Gower scheme ⋮ Dynamics of a delayed predator–prey interaction incorporating nonlinear prey refuge under the influence of fear effect and additional food

Uses Software

• MATCONT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamical complexities in the Leslie-Gower predator-prey model as consequences of the Allee effect on prey
• Global asymptotic stability of a predator-prey model with modified Leslie-Gower and Holling-type II schemes
• Dynamics of a modified Leslie-Gower model with double Allee effects
• Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes
• A Lyapunov function for Leslie-Gower predator-prey models
• Allee effect acting on the prey species in a Leslie-Gower predation model
• Complex dynamics of a diffusive Holling-Tanner predator-prey model with the Allee effect
• Impulsive perturbations of a predator-prey system with modified Leslie-Gower and Holling type II schemes
• Qualitative theory of planar differential systems
• Stabilization of modified Leslie-Gower prey-predator model
• The number of limit cycles of certain polynomial differential equations
• Dynamics of a Predator-Prey Model
• Travelling waves in the Holling–Tanner model with weak diffusion
• MATCONT

This page was built for publication: The basins of attraction in a modified May-Holling-Tanner predator-prey model with Allee affect