Uniqueness of the limit cycle for Gause-type predator-prey systems
type: Item
instance of: scholarly article
title: Uniqueness of the limit cycle for Gause-type predator-prey systems
zbMATH Open document ID: 0935.34023
author: Tzy-Wei Hwang
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-02-08T00:00:00Z
review text: The author gives two theorems ensuring that a generalized Gause-type predator-prey system possesses no and at most one (and then stable) limit cycle, respectively. The latter theorem covers the criterion for the uniqueness of limit cycles given by \textit{S. H. Ding} [SIAM J. Math. Anal. 20, No. 6, 1426-1435 (1989; Zbl 0678.92013)] and \textit{X.-C. Huang} and \textit{S. J. Merrill} [Math. Biosci. 96, No. 1, 47-60 (1989, Zbl 0676.92008)] as a special case. Two examples of predator-prey dynamics are presented as illustrations.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1354757
zbMATH Keywords: predator-prey system
zbMATH Keywords: limit cycle uniqueness
zbMATH Keywords: Dulac criterion
Wikidata QID: Q115611184
reviewed by: David S. Boukal
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6520
OpenAlex ID: W1990714852
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DOI: 10.1006/JMAA.1999.6520
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description: scientific article; zbMATH DE number 1354757