Acta Biotheoretica

, Volume 66, Issue 4, pp 367–378 | Cite as

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

  • M. A. Aziz-AlaouiEmail author
  • M. Daher Okiye
  • A. Moussaoui
Regular Article


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 Leslie–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.


Reaction–diffusion Robin boundary conditions Predator–prey Permanence Extinction 

Mathematics Subject Classification

35B40 37N25 



This work was partially supported by the ERDF (XTerm Project) and Normandie Region, France. And also by The LMAH-FR-CNRS-3335.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • M. A. Aziz-Alaoui
    • 1
    Email author
  • M. Daher Okiye
    • 2
  • A. Moussaoui
    • 3
  1. 1.Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCNLe HavreFrance
  2. 2.Faculté des SciencesUniversité de DjiboutiDjibouti CityDjibouti
  3. 3.Department of Mathematics, Faculty of SciencesUniversity of TlemcenTlemcenAlgeria

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