Uniqueness of the Limit Cycle for Gause-Type Predator-Prey Systems

Journal of Mathematical Analysis and Applications

Volumn 238, Issue 1, 1999, Pages 179-195

  Hwang, Tzy Wei ^a  

^a NATIONAL KAOHSIUNG NORMAL UNIVERSITY   (Taiwan)

Author keywords

Dulac criterion; Predator prey system; Uniqueness limit cycle

Indexed keywords

EID: 0002421472     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1999.6520     Document Type: Article

References (20)

1. Ardito A., Ricciardi P. Lyapunov functions for a generalized Gause-type model. J. Math. Biol. 33:1995;816-828.
2. Cheng K. S. Uniqueness of a limit cycle for a predator-prey system. SIAM J. Math. Anal. 12:1981;541-548.
3. Cheng K. S., Hsu S. B., Lin S. S. Some results on global stability of a predator-prey system. J. Math. Biol. 12:1981;115-126.
4. Ding S. H. On a kind of predator-prey system. SIAM J. Math. Anal. 20:1989;1426-1435.
5. Duff G. F. D. Limit cycle and rotated vector fields. Ann. Math. (2). 57:1953;15-31.
6. Freedman H. I. Deterministic Mathematical Models in Population Ecology. 1980;Marcel Dekker, New York.
7. Goh B. S. Global stability in two species interactions. Math. Biosci. 3:1976;313-318.
8. Hsu S. B. On global stability of a predator-prey system. Math. Biosci. 39:1978;1-10.
9. Hsu S. B., Hwang T. W. Global stability for a class of predator-prey system. SIAM J. Appl. Math. 55:1995;763-783.
10. Hsu S. B., Hwang T. W. Uniqueness of limit cycles for a predator-prey system of Holling and Leslie type. Canad. Appl. Math. Quart. 6:1997;91-117.
11. Huang X. C., Merrill S. Condition for uniqueness of limit cycles in general predator-prey system. Math. Biosci. 96:1989;47-60.
12. Kuang Y. Global stability of Gause-type predator-prey system. J. Math. Biol. 28:1990;463-474.
13. Kuang Y., Freedman H. I. Uniqueness of limit cycles in Gause-type models of predator-prey system. Math. Biosci. 88:1988;67-84.
14. Liou L. P., Cheng K. S. On the uniqueness of a limit cycle for a predator-prey system. SIAM J. Math. Anal. 19:1988;867-878.
15. Liou L. P., Cheng K. S. Global stability of a predator-prey system. J. Math. Biol. 26:1988;65-71.
16. Labine P. A., Wilson D. H. A teaching model of population interactions: an algaedaphnia-predator system. Bioscience. 23:1973;162-167.
17. May R. M. Complexity and Stability in Model Ecosystems. 1973;Princeton Univ. Press, Princeton.
18. May R. M. Theoretical Ecology: Principles and Applications. 1976;Blackwell Sci. Oxford/London.
19. Murray J. D. Mathematical Biology. 1989;Springer-Verlag, Berlin/Heidelberg/New York.
20. Real L. A. The kinetics of functional response. Amer. Natur. 111:1978;289-300.