Uniform persistence and flows near a closed positively invariant set
type: Item
instance of: scholarly article
title: Uniform persistence and flows near a closed positively invariant set
zbMATH Open document ID: 0811.34033
DOI: 10.1007/BF02218848
author: Shigui Ruan
author: Moxun Tang
author: H. I. Freedman
published in: Journal of Dynamics and Differential Equations
publication date: 1994-12-19T00:00:00Z
review text: The behavior of a continuous flow in the vicinity of a closed positively invariant set in a metric space is studied. The obtained results generalize results of Ura-Kimura and Bhatia on classification of a flow near a compact invariant set in a locally compact metric space. Applying the obtained results, the authors prove two persistence theorems. One of the theorems unifies and generalizes earlier persistence results based on Lyapunov-like functions and those about the equivalence of weak uniform persistence and uniform persistence. The second theorem generalizes persistence results based on analysis of a flow on the boundary by relaxing point dissipativity and invariance of the boundary. The obtained results are illustrated by considering several ecological systems.
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 703258
zbMATH Keywords: persistence theorems
zbMATH Keywords: ecological systems
reviewed by: Eugene Ershov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02218848
OpenAlex ID: W2055605553
description: scientific article; zbMATH DE number 703258