Acta Biotheor 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 © 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 firstname.lastname@example.org M. Daher Okiye email@example.com A. Moussaoui firstname.lastname@example.org 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 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 to its universal existence and impor- tance in population
Acta Biotheoretica – Springer Journals
Published: May 28, 2018
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