The existence of an equilibrium for permanent systems
type: Item
instance of: scholarly article
title: The existence of an equilibrium for permanent systems
zbMATH Open document ID: 0722.92012
author: D. Kharzeev
published in: Rocky Mountain Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: The property of permanence in biological populations described by the ODE \(\dot x_ i=x_ i\cdot f_ i(^{\rightharpoonup})\), \(i=1,...,n\) (or by a corresponding difference equation) implies the existence of an equilibrium point in the interior of \({\mathbb{R}}^ n_+\). This known fact is proved in a simple way by application of Schauder's fixed point theorem. Analogous results are derived for a class of differential-delay equations by means of Horn's theorem.
reviewed by: Michael Baake
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 4191455
zbMATH Keywords: compact attractor
zbMATH Keywords: stationary coexistence state
zbMATH Keywords: permanence
zbMATH Keywords: equilibrium point
zbMATH Keywords: Schauder's fixed point theorem
zbMATH Keywords: differential-delay equations
zbMATH Keywords: Horn's theorem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181073060
OpenAlex ID: W2043329880
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DOI: 10.1216/RMJM/1181073060
description: scientific article; zbMATH DE number 4191455