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arXiv · 1809.05854

A Holling-Tanner predator-prey model with strong Allee effect

Claudio Arancibia-Ibarra·Jose D. Flores·Graeme J. Pettet·Peter van Heijster
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Abstract

We analyse 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 results of previous articles by Saez and Gonzalez-Olivares (SIAM J. Appl. Math. 59 1867-1878, 1999) and Arancibia-Ibarra and Gonzalez-Olivares (Proc. CMMSE 2015 130-141, 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 co-existence 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 Bogadonov-Takens bifurcations.

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Claudio Arancibia-Ibarra, Jose D. Flores, Graeme J. Pettet, Peter van Heijster. 2018-09-16. A Holling-Tanner predator-prey model with strong Allee effect. https://doi.org/10.1142/s0218127419300325

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