  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.
