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

31 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

Access to Document

10.1080/00036818808839785

Cite this

@article{88d04c701a0b41d6a30fedcb7d9950f4,

title = "Nonuniqueness of Limit Cycles of Gause-Type Predator-Prey Systems",

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

author = "Yang Kuang",

year = "1988",

month = jan,

day = "1",

doi = "10.1080/00036818808839785",

language = "English (US)",

volume = "29",

pages = "269--287",

journal = "Applicable Analysis",

issn = "0003-6811",

publisher = "Taylor and Francis Ltd.",

number = "3-4",

}

TY - JOUR

T1 - Nonuniqueness of Limit Cycles of Gause-Type Predator-Prey Systems

AU - Kuang, Yang

PY - 1988/1/1

Y1 - 1988/1/1

N2 - 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.

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.

KW - Gause-type predator-prey system

KW - Limit cycle

KW - Lotka–Volterra system

KW - prey isocline

UR - http://www.scopus.com/inward/record.url?scp=84972834610&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972834610&partnerID=8YFLogxK

U2 - 10.1080/00036818808839785

DO - 10.1080/00036818808839785

M3 - Article

AN - SCOPUS:84972834610

VL - 29

SP - 269

EP - 287

JO - Applicable Analysis

JF - Applicable Analysis

SN - 0003-6811

IS - 3-4

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this