Permanence and Extinction of a Diffusive Predator–Prey Model with Robin Boundary Conditions

Permanence and Extinction of a Diffusive Predator–Prey Model with Robin Boundary Conditions Acta Biotheor (2018) 66:367–378 https://doi.org/10.1007/s10441-018-9332-0 REGULAR ARTICLE Permanence and Extinction of a Diffusive Predator–Prey Model with Robin Boundary Conditions 1 2 3 M. A. Aziz‑Alaoui  · M. Daher Okiye  · A. Moussaoui Received: 30 November 2017 / Accepted: 16 May 2018 / Published online: 28 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract The main concern of this paper is to study the dynamic of a predator– prey system with diffusion. It incorporates the Holling-type-II and a modified Les - lie–Gower functional responses under Robin boundary conditions. More concretely, we study the dissipativeness of the system by using the comparison principle, and we derive a criteria for permanence and for predator extinction. Keywords Reaction–diffusion · Robin boundary conditions · Predator–prey · Permanence · Extinction Mathematics Subject Classification 35B40 · 37N25 * M. A. Aziz-Alaoui aziz.alaoui@univ-lehavre.fr M. Daher Okiye madina_daher@univ.edu.dj A. Moussaoui moussaouidz@yahoo.fr Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, BP 540, 76600 Le Havre, France Faculté des Sciences, Université de Djibouti, Avenue Djanaleh, BP 1904 Djibouti City, Djibouti Department of Mathematics, Faculty of Sciences, University of Tlemcen, B.P. 119, 13000 Tlemcen, Algeria 1 3 368 M. A. Aziz-Alaoui et al. 1 Introduction, Mathematical Model and Preliminaries 1.1 Introduction and Mathematical Model One of the dominant themes in both ecology and mathematical ecology is the dynamic relationship between predators and their prey due http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Biotheoretica Springer Journals

Permanence and Extinction of a Diffusive Predator–Prey Model with Robin Boundary Conditions

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Philosophy; Philosophy of Biology; Evolutionary Biology
ISSN
0001-5342
eISSN
1572-8358
D.O.I.
10.1007/s10441-018-9332-0
Publisher site
See Article on Publisher Site

Abstract

Acta Biotheor (2018) 66:367–378 https://doi.org/10.1007/s10441-018-9332-0 REGULAR ARTICLE Permanence and Extinction of a Diffusive Predator–Prey Model with Robin Boundary Conditions 1 2 3 M. A. Aziz‑Alaoui  · M. Daher Okiye  · A. Moussaoui Received: 30 November 2017 / Accepted: 16 May 2018 / Published online: 28 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract The main concern of this paper is to study the dynamic of a predator– prey system with diffusion. It incorporates the Holling-type-II and a modified Les - lie–Gower functional responses under Robin boundary conditions. More concretely, we study the dissipativeness of the system by using the comparison principle, and we derive a criteria for permanence and for predator extinction. Keywords Reaction–diffusion · Robin boundary conditions · Predator–prey · Permanence · Extinction Mathematics Subject Classification 35B40 · 37N25 * M. A. Aziz-Alaoui aziz.alaoui@univ-lehavre.fr M. Daher Okiye madina_daher@univ.edu.dj A. Moussaoui moussaouidz@yahoo.fr Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, BP 540, 76600 Le Havre, France Faculté des Sciences, Université de Djibouti, Avenue Djanaleh, BP 1904 Djibouti City, Djibouti Department of Mathematics, Faculty of Sciences, University of Tlemcen, B.P. 119, 13000 Tlemcen, Algeria 1 3 368 M. A. Aziz-Alaoui et al. 1 Introduction, Mathematical Model and Preliminaries 1.1 Introduction and Mathematical Model One of the dominant themes in both ecology and mathematical ecology is the dynamic relationship between predators and their prey due

Journal

Acta BiotheoreticaSpringer Journals

Published: May 28, 2018

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