Limiting the complexity of limit sets in self-regulating systems
type: Item
instance of: scholarly article
title: Limiting the complexity of limit sets in self-regulating systems
zbMATH Open document ID: 0707.92001
DOI: 10.1016/0022-247X(90)90384-R
author: Geoffrey Butler
author: R. Schmid
author: Paul Waltman
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: A theorem is proved which is very useful in limiting the complexity of limit sets for a class of biologically important equations: \[ x_ i'(t)=x_ if_ i(x_ 1,...,x_ n),\quad x_ i(0)\geq 0,\quad i=1,...,n, \] where the \(f_ i\) are continuously differentiable scalar functions. The proof is based on methods from differential geometry.
Mathematics Subject Classification ID: 92B05
Mathematics Subject Classification ID: 37C80
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 4162697
zbMATH Keywords: self-regulating systems
zbMATH Keywords: invariant sets
zbMATH Keywords: Dulac criterion
zbMATH Keywords: Lebesgue measure
zbMATH Keywords: manifold
zbMATH Keywords: Lie derivative
zbMATH Keywords: ecosystems
zbMATH Keywords: complexity of limit sets
reviewed by: Sebastian Aniţa
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4162697