Discrete infinite-dimensional type-\(K\) monotone dynamical systems and time-periodic reaction--diffusion systems.
type: Item
instance of: scholarly article
title: Discrete infinite-dimensional type-\(K\) monotone dynamical systems and time-periodic reaction--diffusion systems.
zbMATH Open document ID: 1036.35091
DOI: 10.1016/S0022-0396(02)00062-1
author: Xing Liang
author: Jifa Jiang
published in: Journal of Differential Equations
publication date: 2003-04-28T00:00:00Z
review text: The authors study the asymptotic behavior of discrete type-\(K\) monotone dynamical systems and time-periodic reaction-diffusion systems, by using the index theory for fixed points, permanence, global stability, convergence everywhere and coexistence. The results can be used to establish the sufficient conditions for the systems to persist uniformly and the convergence results for all orbits. As applications, time-periodic Lotka-Volterra systems with diffusion are considered and sufficient conditions for such systems to have a unique positive solution are given. So the main results of this paper are interesting and nice.
reviewed by: J. K. Kim
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1901951
zbMATH Keywords: Lotka-Volterra system
zbMATH Keywords: global stability
zbMATH Keywords: index theory for fixed points
zbMATH Keywords: permanence
zbMATH Keywords: coexistence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1901951