Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 42 No. 2 (2024): Revista Integración, temas de matemáticas
Accepted articles: Preprint

Stability and bifurcation analysis in a predator prey model involving additive Allee effect

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  • Jocirei Dias-Ferreira,
  • Wilmer L. Molina,
  • Jaime Tobar
Jocirei Dias-Ferreira
Federal University of Mato Grosso
Wilmer L. Molina
University of the Cauca
Jaime Tobar
Universidad del Cauca
DOI: https://doi.org/10.18273/revint.v42n2-2024003

Published 2024-08-23

Keywords

  • Predator-prey system,
  • Allee effect,
  • positivity,
  • dissipation,
  • boundedness,
  • permanence,
  • Stability,
  • bifurcation
    • ...More
    Less

How to Cite

Dias Ferreira, J., Molina Yepez, W. L., & Tobar Muñoz, J. (2024). Stability and bifurcation analysis in a predator prey model involving additive Allee effect. Revista Integración, Temas De matemáticas, 42(2), 23–53. https://doi.org/10.18273/revint.v42n2-2024003

Copyright (c) 2024 Revista Integración, temas de matemáticas

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

In this paper we study codimension 1 Hopf bifurcation for a two dimensional autonomous nonlinear ordinary differential equations system, modeling a predator-prey interaction with Holling type II functional response and additive Allee effect in the prey equation. Positivity, dissipation, boundedness and permanence of the solutions are analyzed.
Furthermore, stability and bifurcation analysis are carried out to show the existence of periodic orbits due to the occurrence of codimension 1 Hopf bifurcation, involving weak Allee effect as well as strong Allee effect. In the case of strong Allee effect, through computer simulations carried in MAPLE 13, we conjecture that this model may admit a heteroclinic bifurcation.
We present some simulations which allow one to verify the analytical results.

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