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On a predator-prey system of Holling type
Author(s):
Jitsuro
Sugie;
Rie
Kohno;
Rinko
Miyazaki
Journal:
Proc. Amer. Math. Soc.
125
(1997),
2041-2050.
MSC (1991):
Primary 34C05, 92D25;
Secondary 58F21, 70K10
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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.
References:
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- 2.
- S.-H. Ding, On a kind of predator-prey system, SIAM J. Math. Anal. 20 (1989), 1426-1435. MR 91f:92018
- 3.
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- 4.
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- 5.
- C. S. Holling, The functional response of predators to prey density and its role in mimicry and population regulation, Mem. Ent. Soc. Can. 45 (1965), 1-60.
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- 7.
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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:
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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