Nonuniqueness of limit cycles of gause-type predator-prey systems
- 1 January 1988
- journal article
- research article
- Published by Taylor & Francis in Applicable Analysis
- Vol. 29 (3-4) , 269-287
- https://doi.org/10.1080/00036818808839785
Abstract
By comparison with the Lotka-Volterra system, we obtain a theorem concerning the nonuniqueness of limit cycles of a Gause-type predator-prey system The method we develope here can be generalized. Moreover, we disprove a conjecture posed by H.I. Freedman by constructing an example of a system with a strictly concave down prey isocline which has at least three limit cycles.Keywords
This publication has 13 references indexed in Scilit:
- Proof of the uniqueness theorem of limit cycles of generalized liénard equationsApplicable Analysis, 1986
- Global Analysis of a System of Predator–Prey EquationsSIAM Journal on Applied Mathematics, 1986
- Competition Models in Population BiologyPublished by Society for Industrial & Applied Mathematics (SIAM) ,1983
- Some results on global stability of a predator-prey systemJournal of Mathematical Biology, 1982
- Uniqueness of a Limit Cycle for a Predator-Prey SystemSIAM Journal on Mathematical Analysis, 1981
- On global stability of a predator-prey systemMathematical Biosciences, 1978
- The Hopf Bifurcation and Its ApplicationsPublished by Springer Nature ,1976
- The dynamics of two interacting populationsJournal of Mathematical Analysis and Applications, 1974
- Stable Limit Cycles in Prey-Predator PopulationsScience, 1973
- Limit Cycles in Predator-Prey CommunitiesScience, 1972