Existence of periodic travelling waves solutions in predator prey model with diffusion |
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Authors: | Radouane Yafia MA Aziz-Alaoui |
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Institution: | 1. Ibn Zohr University, Polydisciplinary Faculty of Ouarzazate, B.P: 638, Ouarzazate, Morocco;2. Laboratoire de Mathématiques Appliquées, 25 Rue Ph. Lebon, BP 540, 76058 Le Havre Cedex, France |
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Abstract: | This paper deals with the qualitative analysis of the travelling waves solutions of a reaction diffusion model that refers to the competition between the predator and prey with modified Leslie–Gower and Holling type II schemes. The well posedeness of the problem is proved. We establish sufficient conditions for the asymptotic stability of the unique nontrivial positive steady state of the model by analyzing roots of the forth degree exponential polynomial characteristic equation. We also prove the existence of a Hopf bifurcation which leads to periodic oscillating travelling waves by considering the diffusion coefficient as a parameter of bifurcation. Numerical simulations are given to illustrate the analytical study. |
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Keywords: | Predator prey model Diffusion Stability Periodic travelling waves Hopf bifurcation |
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