A qualitative analysis of \(\dot x=Ax+b\)
type: Item
instance of: scholarly article
title: A qualitative analysis of \(\dot x=Ax+b\)
zbMATH Open document ID: 0646.34057
DOI: 10.1016/0166-218X(88)90038-8
author: Terrence Bone
author: Clark Jeffries
author: Victor Klee
published in: Discrete Applied Mathematics
publication date: 1988-01-01T00:00:00Z
review text: For a dynamical system \(\dot x=Ax+b\), where A is a constant real \(n\times n\) matrix and b is an n-vector, there is special interest in the existence of a constant asymptotically stable attractor trajectory in the positive orthant of \({\mathbb{R}}^ n\). For certain patterns of signs of entries \((+,-,\)or 0) in A and b, such a trajectory always must exist, regardless of the magnitudes of those entries. This paper describes all such patterns in terms of digraphs. Applications to nonlinear systems and ecosystem models are also mentioned.
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 4054107
zbMATH Keywords: Lotka-Volterra
zbMATH Keywords: constant asymptotically stable attractor trajectory
zbMATH Keywords: digraphs
zbMATH Keywords: ecosystem models
MaRDI profile type: Publication
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full work available at URL: 0166-218x(88)90038-8
OpenAlex ID: W869682205
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description: scientific article; zbMATH DE number 4054107