Dynamical complexities in the Leslie-Gower predator-prey model as consequences of the Allee effect on prey

DOI10.1016/j.apm.2010.07.001zbMath1202.34079OpenAlexW2043233048WikidataQ115588053 ScholiaQ115588053MaRDI QIDQ614421

Jaime Mena-Lorca, José D. Flores, Alejandro Rojas-Palma, Eduardo González-Olivares

Publication date: 27 December 2010

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2010.07.001

zbMATH Keywords

limit cycle functional response bifurcations Allee effect Leslie-Gower predator-prey models separatrix curves

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Population dynamics (general) (92D25)

Related Items (60)

Relaxation Oscillations and Canard Explosion of a Leslie–Gower Predator–Prey System with Addictive Allee Effect ⋮ Influencia del efecto Allee débil en las presas en un modelo de depredación del tipo Leslie-Gower con respuesta funcional sigmoidea ⋮ Dynamics of a predator-prey model with strong Allee effect and nonconstant mortality rate ⋮ Spatial dynamics of predator-prey system with hunting cooperation in predators and type I functional response ⋮ A Leslie–Gower-type predator–prey model with sigmoid functional response ⋮ Limit cycles of multi-parameter polynomial dynamical systems ⋮ Dynamics of a ratio-dependent Leslie-Gower predator-prey model with Allee effect and fear effect ⋮ Stability and Bifurcation in a Leslie–Gower Predator–Prey Model with Allee Effect ⋮ Global Dynamics in the Leslie–Gower Model with the Allee Effect ⋮ Bifurcations and multistability on the May-Holling-Tanner predation model considering alternative food for the predators ⋮ Stability Analysis of a Leslie–Gower Model with Strong Allee Effect on Prey and Fear Effect on Predator ⋮ Modeling Allee Effect in the Leslie-Gower Predator–Prey System Incorporating a Prey Refuge ⋮ Dynamic complexities in 2-dimensional discrete-time predator-prey systems with Allee effect in the prey ⋮ Predator-prey models with component Allee effect for predator reproduction ⋮ Impact of prey refuge in a discontinuous Leslie-Gower model with harvesting and alternative food for predators and linear functional response ⋮ Stability and Hopf bifurcation in a modified Holling-Tanner predator-prey system with multiple delays ⋮ Bifurcations in a Leslie-Gower model with constant and proportional prey refuge at high and low density ⋮ Stability and Turing patterns of a predator-prey model with Holling type II functional response and Allee effect in predator ⋮ Erratum to ``Dynamical complexities in the Leslie-gower predator-prey model as consequences of the Allee effect on prey ⋮ Consequences of double Allee effect on the number of limit cycles in a predator-prey model ⋮ Complex dynamics of a diffusive Holling-Tanner predator-prey model with the Allee effect ⋮ Optimal harvesting in a predator-prey model with Allee effect and sigmoid functional response ⋮ Bifurcation analysis in a delayed diffusive Leslie-Gower model ⋮ Dynamics of a diffusive predator-prey model with Allee effect on predator ⋮ Relationship between exploitation, oscillation, MSY and extinction ⋮ A modified Leslie-Gower predator-prey model with ratio-dependent functional response and alternative food for the predator ⋮ Defining and detecting structural sensitivity in biological models: developing a new framework ⋮ Multiple Bifurcation Analysis in a Diffusive Eco-Epidemiological Model with Time Delay ⋮ Global qualitative analysis of a predator-prey system with Allee effect on the prey species ⋮ A new non-autonomous model for migratory birds with Leslie-Gower Holling-type II schemes and saturation recovery rate ⋮ Dynamical analysis in a hybrid bioeconomic system with multiple time delays and strong Allee effect ⋮ Dynamical behaviors of Bazykin-Berezovskaya model with fractional-order and its discretization ⋮ Global stability in a modified Leslie-Gower type predation model assuming mutual interference among generalist predators ⋮ Stability and Bifurcation Analysis of a Commensal Model with Additive Allee Effect and Nonlinear Growth Rate ⋮ Dynamic behavior analysis of phytoplankton-zooplankton system with cell size and time delay ⋮ Hopf bifurcation and steady-state bifurcation for a Leslie-Gower prey-predator model with strong allee effect in prey ⋮ Multiple limit cycles in a Gause type predator-prey model with Holling type III functional response and Allee effect on prey ⋮ Consequences of weak Allee effect on prey in the May–Holling–Tanner predator–prey model ⋮ Bifurcations and global dynamics in a predator-prey model with a strong Allee effect on the prey, and a ratio-dependent functional response ⋮ Bifurcation and Turing pattern formation in a diffusive ratio-dependent predator-prey model with predator harvesting ⋮ Dynamics of a modified Leslie-Gower predation model considering a generalist predator and the hyperbolic functional response ⋮ Predator-prey interaction system with mutually interfering predator: role of feedback control ⋮ Multiple limit cycles in a Leslie–Gower-type predator–prey model considering weak Allee effect on prey ⋮ Dynamics of a modified Leslie-Gower model with double Allee effects ⋮ Study of a tritrophic food chain model with non-differentiable functional response ⋮ Population dynamics with multiple Allee effects induced by fear factors -- a mathematical study on prey-predator interactions ⋮ Role of allee effect on prey-predator model with component allee effect for predator reproduction ⋮ The basins of attraction in a modified May-Holling-Tanner predator-prey model with Allee affect ⋮ Consequences of weak Allee effect on prey in the May-Holling-Tanner predator-prey model ⋮ A Holling–Tanner Predator–Prey Model with Strong Allee Effect ⋮ Dynamics of a Class of Leslie–Gower Predation Models with a Non-Differentiable Functional Response ⋮ Bifurcation manifolds in predator-prey models computed by Gröbner basis method ⋮ Dynamical behavior analysis of the Leslie-Gower model in random environment ⋮ Predator-prey interactions under fear effect and multiple foraging strategies ⋮ Rich Global Dynamics in a Prey–Predator Model with Allee Effect and Density Dependent Death Rate of Predator ⋮ Bifurcations on a discontinuous Leslie-Grower model with harvesting and alternative food for predators and Holling II functional response ⋮ Dynamics of a Leslie-Gower predator-prey model with additive Allee effect ⋮ Plastic energy allocation toward life-history functions in a consumer-resource interaction. Analyzing the temporal patterns of the consumer-resource dynamics ⋮ A general class of predation models with multiplicative Allee effect ⋮ Dynamic behaviors of a Lotka-Volterra type predator-prey system with Allee effect on the predator species and density dependent birth rate on the prey species

Uses Software

Mathematica

Cites Work

This page was built for publication: Dynamical complexities in the Leslie-Gower predator-prey model as consequences of the Allee effect on prey