Delayed stability switches in singularly perturbed predator–prey models
| dc.contributor.author | Banasiak, Jacek | |
| dc.contributor.author | Tchamga, M. S. Seuneu | |
| dc.contributor.email | jacek.banasiak@up.ac.za | en_ZA |
| dc.date.accessioned | 2017-01-23T07:49:34Z | |
| dc.date.issued | 2017-06 | |
| dc.description.abstract | In this paper we provide an elementary proof of the existence of canard solutions for a class of singularly perturbed planar systems in which there occurs a transcritical bifurcation of the quasi steady states. The proof uses the one-dimensional result proved by V. F. Butuzov, N. N. Nefedov and K. R. Schneider, and an appropriate monotonicity assumption on the vector eld. The result is applied to identify all possible predator-prey models with quadratic vector elds allowing for the existence of canard solutions. | en_ZA |
| dc.description.department | Mathematics and Applied Mathematics | en_ZA |
| dc.description.embargo | 2018-06-30 | |
| dc.description.librarian | hb2017 | en_ZA |
| dc.description.uri | http://www.elsevier.com/locate/nonrwa | en_ZA |
| dc.identifier.citation | Banasiak, J & Tchamga, MSS 2017, 'Delayed stability switches in singularly perturbed predator–prey models', Nonlinear Analysis : Real World Applications, vol. 35, pp. 312-335. | en_ZA |
| dc.identifier.issn | 1468-1218 (print) | |
| dc.identifier.issn | 1878-5719 (online) | |
| dc.identifier.other | 10.1016/j.nonrwa.2016.10.013 | |
| dc.identifier.uri | http://hdl.handle.net/2263/58593 | |
| dc.language.iso | en | en_ZA |
| dc.publisher | Elsevier | en_ZA |
| dc.rights | © 2016 Elsevier Ltd. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Nonlinear Analysis : Real World Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. A definitive version was subsequently published in Nonlinear Analysis : Real World Applications, vol. 35, pp. 312-335, 2017. doi : 10.1016/j.nonrwa.2016.10.013. | en_ZA |
| dc.subject | Singularly perturbed dynamical systems | en_ZA |
| dc.subject | Multiple time scales | en_ZA |
| dc.subject | Tikhonov theorem | en_ZA |
| dc.subject | Delayed stability | en_ZA |
| dc.subject | Switch | en_ZA |
| dc.subject | Non-isolated quasi steady states | en_ZA |
| dc.subject | Predator-prey models | en_ZA |
| dc.subject | Canard solutions | en_ZA |
| dc.title | Delayed stability switches in singularly perturbed predator–prey models | en_ZA |
| dc.type | Postprint Article | en_ZA |