Nonuniqueness of Limit Cycles of Gause-Type Predator-Prey Systems

Yang Kuang

doi:10.1080/00036818808839785

Nonuniqueness of Limit Cycles of Gause-Type Predator-Prey Systems

Yang Kuang

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

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.

Original language	English (US)
Pages (from-to)	269-287
Number of pages	19
Journal	Applicable Analysis
Volume	29
Issue number	3-4
DOIs	https://doi.org/10.1080/00036818808839785
State	Published - Jan 1 1988
Externally published	Yes

Keywords

Gause-type predator-prey system
Limit cycle
Lotka–Volterra system
prey isocline

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/00036818808839785

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AB - 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.

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KW - prey isocline

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Nonuniqueness of Limit Cycles of Gause-Type Predator-Prey Systems

Abstract

Keywords

ASJC Scopus subject areas

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