Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


A predator-prey system with Holling-type functional response
HTML articles powered by AMS MathViewer

by Nabil Beroual and Tewfik Sari PDF
Proc. Amer. Math. Soc. 148 (2020), 5127-5140 Request permission


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 $0<p<1$.
Similar Articles
Additional Information
  • Nabil Beroual
  • Affiliation: Department of Mathematics, University Ferhat Abbes, Sétif, Algeria
  • MR Author ID: 756169
  • Email:
  • Tewfik Sari
  • Affiliation: ITAP, Univ Montpellier, INRAE, Institut Agro, Montpellier, France
  • MR Author ID: 154625
  • ORCID: 0000-0002-6274-7826
  • Email:
  • 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 for financial support.
  • Communicated by: Wenxian Shen
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 5127-5140
  • MSC (2010): Primary 34A12, 34C05, 34D23; Secondary 70K05, 92D25
  • DOI:
  • MathSciNet review: 4163827