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

Yang Kuang; H. I. Freedman

doi:10.1016/0025-5564(88)90049-1

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

Yang Kuang, H. I. Freedman

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

274 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	67-84
Number of pages	18
Journal	Mathematical Biosciences
Volume	88
Issue number	1
DOIs	https://doi.org/10.1016/0025-5564(88)90049-1
State	Published - Mar 1988
Externally published	Yes

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
General Biochemistry, Genetics and Molecular Biology
General Immunology and Microbiology
General Agricultural and Biological Sciences
Applied Mathematics

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title = "Uniqueness of limit cycles in Gause-type models of predator-prey systems",

abstract = "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.",

author = "Yang Kuang and Freedman, {H. I.}",

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PY - 1988/3

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N2 - 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.

AB - 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.

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

Abstract

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