Persistence and stability for a two-species ratio-dependent predator-prey system with distributed time delay
type: Item
instance of: scholarly article
title: Persistence and stability for a two-species ratio-dependent predator-prey system with distributed time delay
zbMATH Open document ID: 1008.34065
DOI: 10.1016/S0022-247X(02)00020-3
author: Rui Xu
author: Fordyce A. Davidson
author: M. A. J. Chaplain
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-07-08T00:00:00Z
review text: The family of models introduced here and the results achieved are generalisations to a wider class of delays of the ones obtained in [\textit{E. Beretta} and \textit{Y. Kuang}, Nonlinear Anal., Theory Methods Appl. 32, No. 3, 381-408 (1998; Zbl 0946.34061)]. The reference system without delays is the Michaelis-Menten predator-prey model which is very similar to the better known Michaelis-Menten-Holling predator-prey model. For this family of models, the uniform persistence of positive solutions is proven under certain conditions. The unique positive equilibrium of this system is then considered and results on its local and global stability properties are presented. An example of this generalised family of models is then introduced and explored numerically with MATLAB.
reviewed by: Domingo Salazar
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1764682
zbMATH Keywords: time delay
zbMATH Keywords: uniform persistence
zbMATH Keywords: local stability
zbMATH Keywords: global stability
zbMATH Keywords: Michaelis-Menten predator-prey model
Wikidata QID: Q115565774
describes a project that uses: Matlab
MaRDI profile type: Publication
cites work: Global analyses in some delayed ratio-dependent predator-prey systems
cites work: Q4138551
cites work: Delay differential equations: with applications in population dynamics
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cites work: Coexistence in a Model of Competition in the Chemostat Incorporating Discrete Delays
cites work: Harmless delays for uniform persistence
cites work: Q4003237
full work available at URL: s0022-247x(02)00020-3
OpenAlex ID: W2077831060
description: scientific article; zbMATH DE number 1764682