Uniqueness of limit cycles in Gause-type models of predator-prey systems

This paper deals with the question of uniqueness of limit cycles in predator-prey systems of Gause type. By utilizing several transformations, these systems are reduced to a generalized Lienard system as discussed by Cherkas and Zhilevich and by Zhang. As a consequence, criteria for the uniqueness o...

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Bibliographic Details
Published inMathematical biosciences Vol. 88; no. 1; pp. 67 - 84
Main Authors Kuang, Yang, Freedman, H.I.
Format Journal Article
LanguageEnglish
Published New York, NY Elsevier Inc 1988
Elsevier Science
Subjects
Animal and plant ecology
Animal, plant and microbial ecology
Biological and medical sciences
ecology
Fundamental and applied biological sciences. Psychology
General aspects
mathematical models
population dynamics
predator-prey interactions
Predator prey relation
Theory
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Summary:This paper deals with the question of uniqueness of limit cycles in predator-prey systems of Gause type. By utilizing several transformations, these systems are reduced to a generalized Lienard system as discussed by Cherkas and Zhilevich and by Zhang. As a consequence, criteria for the uniqueness of limit cycles are derived, which include results of Cheng and is related to results in Liou and Cheng. Several examples are given to illustrate our results.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0025-5564
1879-3134
DOI:10.1016/0025-5564(88)90049-1