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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a predator-prey system of Holling type


Authors: Jitsuro Sugie, Rie Kohno and Rinko Miyazaki
Journal: Proc. Amer. Math. Soc. 125 (1997), 2041-2050
MSC (1991): Primary 34C05, 92D25; Secondary 58F21, 70K10
MathSciNet review: 1396998
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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
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

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03901-4
PII: S 0002-9939(97)03901-4
Keywords: Limit cycles, global asymptotic stability, predator-prey system, functional response
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
Article copyright: © Copyright 1997 American Mathematical Society