Bendixson's criterion for autonomous systems with an invariant linear subspace
type: Item
instance of: scholarly article
title: Bendixson's criterion for autonomous systems with an invariant linear subspace
zbMATH Open document ID: 0841.34029
author: Michael Y. Li
published in: Rocky Mountain Journal of Mathematics
publication date: 1996-07-21T00:00:00Z
review text: The author studies the autonomous system \(x'= f(x)\) in \(\mathbb{R}^n\), with the hypothesis that the Jacobian matrix has the form \(- \nu I+ A(x)\). In addition, he assumes that there exists a constant matrix \(B\) such that \(BA(x)= 0\) for all \(x\) in the domain of the differential equation. He characterizes an invariant manifold of the system in terms of \(B\) and gives sufficient conditions for the nonexistence of invariant closed curves in the invariant manifold. An application to SEIS epidemic model is given.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C30
zbMATH DE Number: 796926
zbMATH Keywords: center manifold
zbMATH Keywords: Bendixson criterion
zbMATH Keywords: invariant manifold
zbMATH Keywords: SEIS epidemic model
reviewed by: Alan R. Hausrath
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072288
OpenAlex ID: W1975814370
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DOI: 10.1216/RMJM/1181072288
description: scientific article; zbMATH DE number 796926