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

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Book cover Computational Problems in Engineering

Part of the book series: Lecture Notes in Electrical Engineering ((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.

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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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Authors and Affiliations

  1. Grupo de Ecología Matemática, Instituto de Matemáticas, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile

    Eduardo González-Olivares & Jaime Huincahue-Arcos

  2. Departamento de Matemáticas, Universidad de Playa Ancha, Valparaíso, Chile

    Jaime Huincahue-Arcos

Authors
  1. Eduardo González-Olivares
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  2. Jaime Huincahue-Arcos
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Corresponding author

Correspondence to Eduardo González-Olivares .

Editor information

Editors and Affiliations

  1. Technical University of Sofia, Sofia, Bulgaria

    Nikos Mastorakis

  2. Technical University of Sofia, Sofia, Bulgaria

    Valeri Mladenov

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González-Olivares, E., Huincahue-Arcos, J. (2014). Double Allee Effects on Prey in a Modified Rosenzweig-MacArthur Predator-Prey Model. In: Mastorakis, N., Mladenov, V. (eds) Computational Problems in Engineering. Lecture Notes in Electrical Engineering, vol 307. Springer, Cham. https://doi.org/10.1007/978-3-319-03967-1_9

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  • DOI: https://doi.org/10.1007/978-3-319-03967-1_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03966-4

  • Online ISBN: 978-3-319-03967-1

  • eBook Packages: EngineeringEngineering (R0)

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