Travelling waves in the Holling-Tanner model with weak diffusion

For a wide range of parameters, we study travelling waves in a diffusive version of the Holling-Tanner predator-prey model from population dynamics. Fronts are constructed using geometric singular perturbation theory and the theory of rotated vector fields. We focus on the appearance of the fronts i...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2015-05, Vol.471 (2177), p.20150045-20150045
Main Authors: Ghazaryan, Anna, Manukian, Vahagn, Schecter, Stephen
Format: Article
Language:English
Subjects:
Diffusive Holling-Tanner Model
Entry-Exit Function
Geometric Singular Perturbation Theory
Periodic Wave Train
Predator-Prey Model
Travelling Front
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Summary:For a wide range of parameters, we study travelling waves in a diffusive version of the Holling-Tanner predator-prey model from population dynamics. Fronts are constructed using geometric singular perturbation theory and the theory of rotated vector fields. We focus on the appearance of the fronts in various singular limits. In addition, periodic travelling waves of relaxation oscillation type are constructed using a recent generalization of the entry-exit function.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2015.0045