A permanence theorem for replicator and Lotka-Volterra systems
type: Item
instance of: scholarly article
title: A permanence theorem for replicator and Lotka-Volterra systems
zbMATH Open document ID: 0647.92021
DOI: 10.1007/BF00277165
author: Wolfgang Jansen
published in: Journal of Mathematical Biology
publication date: 1987-01-01T00:00:00Z
review text: The author obtains sufficient conditions for the boundary of a compact invariant set S of the replicator equations to be a repeller and conditions for it not to be a repeller. These conditions are formulated in terms of the existence of an average Lyapunov function in the form of a power function. He then demonstrates how these sufficiency conditions can be checked by solving an equivalent linear programming problem. These results require the compactness of S, but the author also shows how to extend his results to the flow in the positive quadrant determined by Lotka-Volterra equations.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 34D99
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 4057352
zbMATH Keywords: sufficient criterion for permanence
zbMATH Keywords: compact state space
zbMATH Keywords: dual programming problem
zbMATH Keywords: polyhedral state spaces
zbMATH Keywords: boundary
zbMATH Keywords: compact invariant set
zbMATH Keywords: replicator equations
zbMATH Keywords: repeller
zbMATH Keywords: existence of an average Lyapunov function
zbMATH Keywords: power function
zbMATH Keywords: Lotka-Volterra equations
Wikidata QID: Q113909011
reviewed by: J. M. Cushing
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4057352