The classification on the global phase portraits of two-dimensional Lotka-Volterra system
type: Item
instance of: scholarly article
title: The classification on the global phase portraits of two-dimensional Lotka-Volterra system
zbMATH Open document ID: 1168.34035
author: Feng Cao
author: Jifa Jiang
published in: Journal of Dynamics and Differential Equations
publication date: 2008-12-01T00:00:00Z
review text: The authors present a complete classification of all quadratic planar Lotka-Volterra systems. By a very detailed investigation, they find 143 topologically inequivalent global phase portraits for these systems, up to time reversal. First, all systems with nontrivial closed orbits are examined separately. Then, using rescaling and normal forms, they generally classify the inhomogeneous quadratic systems under discussion, thus obtaining classes with up to three real parameters. These classes are treated separately, while the remaining homogeneous systems had already been analyzed in the literature. The main tool of investigation is the Poincaré compactification. All the global phase portraits are shown in the Poincaré disc.
reviewed by: Josef Hainzl
Mathematics Subject Classification ID: 34C99
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 5375867
zbMATH Keywords: Lotka-Volterra system
zbMATH Keywords: global phase portrait
zbMATH Keywords: Poincaré disc
MaRDI profile type: Publication
full work available at URL: s10884-008-9122-5
OpenAlex ID: W2009968757
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DOI: 10.1007/S10884-008-9122-5
description: scientific article; zbMATH DE number 5375867