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Double Allee Effects on Prey in a Modified Rosenzweig-MacArthur Predator-Prey Model

  • Eduardo González-OlivaresEmail author
  • Jaime Huincahue-Arcos
Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 307)

Abstract

In this work, a modified Rosenzweig-MacArthur predator-prey model is analyzed, which is a particular Gause type model, considering two Allee effect affecting the prey population.

This phenomenon may be expressed by different mathematical expressions; with the form here used, the existence of one limit cycle surrounding a positive equilibrium point is proved.

Conditions to the existence of equilibrium points and their local stability are established; moreover, the existence of a separatrix curve dividing the behavior of trajectories which can have different ω-limit sets.

Some simulations reinforced our results are given and the ecological consequences are discussed.

Keywords

Predator-prey model Functional response Allee effect Stability Bifurcation Limit cycle 

Notes

Acknowledgement

The authors thank the members of the Grupo de Ecología Matemática on the Instituto de Matemáticas at the Pontificia Universidad Católica de Valparaíso, for their valuable comments and suggestions. This work is partially financed by Projects Fondecyt No 1120218 and DIEA-PUCV 124.730/2012.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Eduardo González-Olivares
    • 1
    Email author
  • Jaime Huincahue-Arcos
    • 1
    • 2
  1. 1.Grupo de Ecología Matemática, Instituto de MatemáticasPontificia Universidad Católica de ValparaísoValparaísoChile
  2. 2.Departamento de MatemáticasUniversidad de Playa AnchaValparaísoChile

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