Permanence and viability
type: Item
instance of: scholarly article
title: Permanence and viability
zbMATH Open document ID: 0659.93059
DOI: 10.1016/0377-0427(88)90400-1
author: Jean-Pierre Aubin
author: Karl Sigmund
published in: Journal of Computational and Applied Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Two concepts from the nonequilibrium theory in systems analysis are discussed. These are permanence and viability. Permanence is a property of a system of ordinary differential equations in \(R^ n\) or in the simplex \(S_ n\subset R^ n\) for which the state space is an unreachable repellor. A sufficient condition for permanence in form of an average Lyapunov function method is proposed. Viability is a property of differential inclusions (or control systems) which means that the trajectories lie in the interior of a prescribed compact set. Some possibilities for applications of these two concepts in ecology, biological evolution, economy, biomathematics and so on are presented.
reviewed by: Z.Wyderka
Mathematics Subject Classification ID: 93D99
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 92B05
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 91B62
zbMATH DE Number: 4079292
zbMATH Keywords: replicator equations
zbMATH Keywords: heavy trajectories
zbMATH Keywords: nonequilibrium theory
zbMATH Keywords: permanence
zbMATH Keywords: viability
zbMATH Keywords: biomathematics
MaRDI profile type: Publication
full work available at URL: 0377-0427(88)90400-1
OpenAlex ID: W2147914522
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description: scientific article; zbMATH DE number 4079292