A Holling-Tanner predator-prey model with strong Allee effect
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.
Keywords
Cite
@article{arxiv.1809.05854,
title = {A Holling-Tanner predator-prey model with strong Allee effect},
author = {Claudio Arancibia-Ibarra and Jose D. Flores and Graeme J. Pettet and Peter van Heijster},
journal= {arXiv preprint arXiv:1809.05854},
year = {2019}
}