A Holling-Tanner Predator-Prey Model with Strong Allee Effect

Claudio Arancibia-Ibarra, José D. Flores, Graeme Pettet, Peter Van Heijster

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)

Abstract

We analyze a modified Holling-Tanner predator-prey model where the predation functional response is of Holling type II and we incorporate a strong Allee effect associated with the prey species production. The analysis complements the results of previous articles by Saez and González-Olivares [1999] and Arancibia-Ibarra and González-Olivares [2015] discussing Holling-Tanner models which incorporate a weak Allee effect. The extended model exhibits rich dynamics and we prove the existence of separatrices in the phase plane separating basins of attraction related to coexistence and extinction of the species. We also show the existence of a homoclinic curve that degenerates to form a limit cycle and discuss numerous potential bifurcations such as saddle-node, Hopf, and Bogdanov-Takens bifurcations.

Original languageEnglish
Article number1930032
JournalInternational Journal of Bifurcation and Chaos
Volume29
Issue number11
DOIs
Publication statusPublished - 1 Oct 2019
Externally publishedYes

Keywords

  • bifurcations
  • Holling-Tanner type II
  • strong Allee effect

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