Harmless delays for uniform persistence
type: Item
instance of: scholarly article
title: Harmless delays for uniform persistence
zbMATH Open document ID: 0731.34085
DOI: 10.1016/0022-247X(91)90281-4
author: Wang Wendi
author: Ma Zhien
published in: Journal of Mathematical Analysis and Applications
publication date: 1991-01-01T00:00:00Z
review text: The authors consider a predator-prey system of Lotka-Volterra type with a finite number of discrete delays. They give sufficient conditions that the system either be uniformly persistent or not persistent. These conditions are the same as the corresponding conditions for the system with all delays set equal to zero and are independent of the magnitude of the delays. Hence uniform persistence of a system is not affected by the time delays. The results are obtained by construction of suitable Lyapunov functionals. If the condition for persistence is satisfied, the system possesses an equilibrium. In this case, the average of the solution approaches the equilibrium. Finally, the authors give an example of a system in which the stability of the equilibrium changes as the delay varies, but the persistence of the system is unaffected.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 4208601
zbMATH Keywords: harmless delays
zbMATH Keywords: predator-prey system
zbMATH Keywords: Lotka-Volterra type
zbMATH Keywords: uniform persistence
zbMATH Keywords: Lyapunov functionals
reviewed by: Alan R. Hausrath
MaRDI profile type: Publication
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full work available at URL: 0022-247x(91)90281-4
OpenAlex ID: W2056399615
description: scientific article; zbMATH DE number 4208601