Asymptotically autonomous differential equations in the plane
type: Item
instance of: scholarly article
title: Asymptotically autonomous differential equations in the plane
zbMATH Open document ID: 0811.34036
author: Horst R. Thieme
published in: Rocky Mountain Journal of Mathematics
publication date: 1994-09-27T00:00:00Z
review text: The author studies the following questions: Assume that the equilibria of the limit equation of an asymptotically autonomous ordinary differential equation are isolated and that any solution of the limit equation converges to one of them. Does any solution of the asymptotically stable equation converge to an equilibrium of the limit equation as well? The results and several examples show that the question cannot be positively answered without further conditions, even in the plane. The answer is positive whenever the equilibria of the limit equation are isolated compact invariant sets and are cyclically chained to each other. This question has implications for studies of certain chemostat/gradostat and epidemic models.
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 645256
zbMATH Keywords: limit equation
zbMATH Keywords: asymptotically autonomous ordinary differential equation
zbMATH Keywords: chemostat/gradostat and epidemic models
reviewed by: Ubiratan D'Ambrosio
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072470
OpenAlex ID: W2057460393
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DOI: 10.1216/RMJM/1181072470
description: scientific article; zbMATH DE number 645256