Limit cycles in a Gause-type predator-prey model with sigmoid functional response and weak Allee effect on prey

DOI10.1002/MMA.2509zbMath1241.92072OpenAlexW2168262807MaRDI QIDQ2894260

Alejandro Rojas-Palma, Eduardo González-Olivares

Publication date: 29 June 2012

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.2509

zbMATH Keywords

bifurcations

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Dynamical systems in biology (37N25) Bifurcation theory for ordinary differential equations (34C23) Ecology (92D40) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Related Items (11)

ROLE OF ALLEE EFFECT AND HARVESTING OF A FOOD-WEB SYSTEM IN THE PRESENCE OF SCAVENGERS ⋮ Complexity analysis of a modified predator-prey system with Beddington-DeAngelis functional response and Allee-like effect on predator ⋮ High codimension bifurcations of a predator-prey system with generalized Holling type III functional response and Allee effects ⋮ Analysis of stability and Hopf bifurcation in a fractional Gauss-type predator-prey model with Allee effect and Holling type-III functional response ⋮ Allee effect acting on the prey species in a Leslie-Gower predation model ⋮ Maturation delay for the predators can enhance stable coexistence for a class of prey-predator models ⋮ 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 ⋮ Multiple limit cycles in a Leslie–Gower-type predator–prey model considering weak Allee effect on prey ⋮ Consequences of weak Allee effect on prey in the May-Holling-Tanner predator-prey model ⋮ A general class of predation models with multiplicative Allee effect

Uses Software

• Mathematica

Cites Work

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• Global asymptotic stability of a predator–prey system of Holling type
• On a predator-prey system of Holling type
• On the uniqueness and nonexistence of limit cycles for predator prey systems
• Speeds of invasion in a model with strong or weak Allee effects
• Absence of limit cycles of a predator-prey system with a sigmoid functional response

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