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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.

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On a predator-prey system of Holling type
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by Jitsuro Sugie, Rie Kohno and Rinko Miyazaki PDF
Proc. Amer. Math. Soc. 125 (1997), 2041-2050 Request permission

Abstract:

We consider the predator-prey system with a fairly general functional response of Holling type and give a necessary and sufficient condition under which this system has exactly one stable limit cycle. Our result extends previous results and is an answer to a conjecture which was recently presented by Sugie, Miyamoto and Morino.
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Additional Information
  • Jitsuro Sugie
  • Affiliation: Department of Mathematics, Faculty of Science, Shinshu University, Matsumoto 390, Japan
  • Address at time of publication: Department of Mathematics and Computer Science, Shimane University Matsue 690, Japan
  • MR Author ID: 168705
  • Email: jsugie@riko.shimane-u.ac.jp
  • Rie Kohno
  • Affiliation: Department of Mathematics, Faculty of Science, Shinshu University, Matsumoto 390, Japan
  • Rinko Miyazaki
  • Affiliation: Department of Mathematical Sciences, Osaka Prefecture University, Sakai 593, Japan
  • Email: rinko@ms.osakafu-u.ac.jp
  • Received by editor(s): January 25, 1996
  • Additional Notes: The first author was supported in part by Grant-in-Aid for Scientific Research 06804008.
  • Communicated by: Hal L. Smith
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 2041-2050
  • MSC (1991): Primary 34C05, 92D25; Secondary 58F21, 70K10
  • DOI: https://doi.org/10.1090/S0002-9939-97-03901-4
  • MathSciNet review: 1396998