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A predator-prey system with Holling-type functional response


Authors: Nabil Beroual and Tewfik Sari
Journal: Proc. Amer. Math. Soc. 148 (2020), 5127-5140
MSC (2010): Primary 34A12, 34C05, 34D23; Secondary 70K05, 92D25
DOI: https://doi.org/10.1090/proc/15166
Published electronically: September 11, 2020
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Abstract: We consider the Gause-type predator-prey system with a large class of growth and response functions, in the case where the response function is not smooth at the origin. We discuss the conditions under which this system has exactly one stable limit cycle or has a positive stable equilibrium point and we describe the basin of attraction of the stable limit cycle and the stable equilibrium point, respectively. Our results correct previous results of the existing literature obtained for the Holling response function $ x^p/(a+x^p)$, in the case where $ 0<p<1$.


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Additional Information

Nabil Beroual
Affiliation: Department of Mathematics, University Ferhat Abbes, Sétif, Algeria
MR Author ID: 756169
Email: n.beroual@univ-setif.dz

Tewfik Sari
Affiliation: ITAP, Univ Montpellier, INRAE, Institut Agro, Montpellier, France
MR Author ID: 154625
Email: tewfik.sari@inrae.fr

DOI: https://doi.org/10.1090/proc/15166
Received by editor(s): January 10, 2019
Received by editor(s) in revised form: November 4, 2019
Published electronically: September 11, 2020
Additional Notes: The authors thank the CNRS-PICS project CODYSYS 278552 and the Euro-Mediterranean research network TREASURE \url{http://www.inra.fr/treasure} for financial support.
Communicated by: Wenxian Shen
Article copyright: © Copyright 2020 American Mathematical Society