A Holling-Tanner predator-prey model with strong Allee effect
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A Holling-Tannerpdf.pdf. Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0. |
Description
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.
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| ID Code: | 197361 | ||
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| Item Type: | Contribution to Journal (Journal Article) | ||
| Refereed: | Yes | ||
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| Measurements or Duration: | 16 pages | ||
| Keywords: | bifurcations, Holling-Tanner type II, strong Allee effect | ||
| DOI: | 10.1142/S0218127419300325 | ||
| ISSN: | 0218-1274 | ||
| Pure ID: | 43492303 | ||
| Divisions: | Past > Institutes > Institute for Future Environments Past > QUT Faculties & Divisions > Science & Engineering Faculty |
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| Copyright Owner: | Consult author(s) regarding copyright matters | ||
| Copyright Statement: | This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the document is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recognise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to qut.copyright@qut.edu.au | ||
| Deposited On: | 12 Jun 2020 02:27 | ||
| Last Modified: | 14 Jul 2024 11:08 |
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