Persistence in three-dimensional Lotka-Volterra systems
type: Item
instance of: scholarly article
title: Persistence in three-dimensional Lotka-Volterra systems
zbMATH Open document ID: 0632.92019
DOI: 10.1016/0895-7177(88)90117-3
author: Paul Waltman
author: Geoffrey Butler
published in: Mathematical and Computer Modelling
publication date: 1988-01-01T00:00:00Z
review text: An ecosystem is persistent if for any initial configuration, each component population which is initially present in the system is bounded away from zero in the long run. Using a recent dynamical system approach developed by the authors, J. Differ. Equations 63, 255-263 (1986; Zbl 0603.58033), we obtain a criterion for the persistence of three- dimensional Lotka-Volterra systems. Except for the case of ``intransitive'' competition, the criterion is easily computable.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 37N99
zbMATH DE Number: 4029342
zbMATH Keywords: limit cycles
zbMATH Keywords: critical points
zbMATH Keywords: hyperbolic
zbMATH Keywords: persistence of three- dimensional Lotka-Volterra systems
MaRDI profile type: Publication
full work available at URL: 0895-7177(88)90117-3
OpenAlex ID: W2054755064
cites work: Persistence in dynamical systems
cites work: Mathematical analysis of some three-species food-chain models
cites work: Persistence in models of three interacting predator-prey populations
cites work: Persistence in a model of three competitive populations
cites work: Persistence in food webs: Holling-type food chains
cites work: Persistence and extinction in three species Lotka-Volterra competitive systems
cites work: Nonlinear Aspects of Competition Between Three Species
cites work: Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets
cites work: Q4768040
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description: scientific article; zbMATH DE number 4029342