Uniqueness of limit cycles in a predator-prey system with Holling-type functional response

Quarterly of Applied Mathematics

Volumn 58, Issue 3, 2000, Pages 577-590

  Sugie, Jitsuro ^a  

^a SHIMANE UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTION EVALUATION; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING; THEOREM PROVING;

FREEDMAN THEOREM; HOLLING TYPE FUNCTIONAL RESPONSE; KUANG THEOREM; LIENARD SYSTEM; PREDATOR PREY SYSTEM;

SYSTEM THEORY;

EID: 0034274197     PISSN: 0033569X     EISSN: None     Source Type: Journal    
DOI: 10.1090/qam/1770656     Document Type: Article

References (13)

1. Jun-Ping Chen and Hong-De Zhang, The qualitative analysis of two species predator-prey model with Holling's type III functional response, Appl. Math. Mech. 7, 77-86 (1986)
2. Kuo-Shung Cheng, Uniqueness of a limit, cycle for a predator-prey system, SIAM J. Math. Anal. 12, 541-548 (1981)
3. Sun-Hong Ding, On a kind of predator-prey system, SIAM J. Math. Anal. 20, 1426-1435 (1989)
4. Xun-Cheng Huang, Uniqueness of limit cycles of generalised Liénard systems and predator-prey systems, J. Phys. A: Math. Gen. 21, L685-L691 (1988)
5. R. E. Kooij and A. Zegeling, Qualitative properties of two-dimensional predator-prey systems, Nonlinear Anal. 29, 693-715 (1997)
6. Yang Kuang and H. I. Freedman, Uniqueness of limit cycles in Cause-type models of predator-prey system, Math. Biosci. 88, 67-84 (1988)
7. H. N. Moreira, On Liénard's equation and the uniqueness of limit cycles in predator-prey systems, J. Math. Biol. 28, 341-354 (1990)
8. J. Sugie and M. Katayama, Global asymptotic stability of a predator-prey system of Holling type, Nonlinear Anal. 38, 105-121 (1999)
9. J. Sugie, R. Kohno, and R. Miyazaki, On a predator-prey system of Hailing type, Proc. Amer. Math. Soc. 125, 2041-2050 (1997)
10. J. Sugie, K. Miyamoto, and K. Morino, Absence of limit cycles of a predator-prey system with a sigmoid functional response, Appl. Math. Lett. 9, 85-90 (1996)
11. Xian-Wu Zeng, Zhi-Fen Zhang, and Su-Zhi Gao, On the uniqueness of the limit cycle of the generalized Liénard equation, Bull. London Math. Soc. 26, 213-247 (1994)
12. Zhi-Fen Zhang, Proof of the uniqueness theorem of limit cycles of generalized Liénard equation, Appl. Anal. 23, 63-74 (1986)
13. Zhi-Fen Zhang and Su-Zhi Gao, On the uniqueness of the limit cycle of Liénard equation, Acta Math. Peking Univ. 22, 1-13 (1986)