A modified may-holling-tanner predator-prey model with multiple allee effects on the prey and an alternative food source for the predator

Claudio Arancibia-Ibarra*, José Flores, Michael Bode, Graeme Pettet, Peter van Heijster

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We study a predator-prey model with Holling type I functional response, an alternative food source for the predator, and multiple Allee effects on the prey. We show that the model has at most two equilibrium points in the first quadrant, one is always a saddle point while the other can be a repeller or an attractor. Moreover, there is always a stable equilibrium point that corresponds to the persistence of the predator population and the extinction of the prey population. Additionally, we show that when the parameters are varied the model displays a wide range of different bifurcations, such as saddle-node bifurcations, Hopf bifurcations, Bogadonov-Takens bifurcations and homoclinic bifurcations. We use numerical simulations to illustrate the impact changing the predation rate, or the non-fertile prey population, and the proportion of alternative food source have on the basins of attraction of the stable equilibrium point in the first quadrant (when it exists). In particular, we also show that the basin of attraction of the stable positive equilibrium point in the first quadrant is bigger when we reduce the depensation in the model.

Original languageEnglish
Pages (from-to)943-962
Number of pages20
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume26
Issue number2
DOIs
Publication statusPublished - Feb 2021
Externally publishedYes

Keywords

  • Bifurcations
  • Homoclinic curve
  • May-Holling-Tanner model
  • Multiple Allee effect
  • Strong Allee effect

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