Persistence and attractivity in an \(N\)-species ratio-dependent predator-prey system with distributed time delays.
type: Item
instance of: scholarly article
title: Persistence and attractivity in an \(N\)-species ratio-dependent predator-prey system with distributed time delays.
zbMATH Open document ID: 1043.34088
DOI: 10.1016/S0096-3003(01)00127-8
author: Rui Xu
author: M. A. J. Chaplain
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The paper investigates a linear food chain with \(n\) species, in which the Michaelis-Menten predator-prey interaction is altered to include ratio-dependent predation and distributed time delays. The authors give conditions for boundedness and uniform persistence of the solutions. They further provide necessary and sufficient conditions for the existence of a unique positive equilibrium and provide conditions for its global attractivity. The latter proof is based on the construction of a suitable Lyapunov functional.
reviewed by: David S. Boukal
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1861151
zbMATH Keywords: linear food chain
zbMATH Keywords: distributed time delay
zbMATH Keywords: uniform persistence
zbMATH Keywords: global attractivity
Wikidata QID: Q114656478
MaRDI profile type: Publication
cites work: Delay differential equations: with applications in population dynamics
cites work: The trade-off between mutual interference and time lags in predator-prey systems
cites work: Coexistence in a Model of Competition in the Chemostat Incorporating Discrete Delays
cites work: Harmless delays for uniform persistence
cites work: Global analyses in some delayed ratio-dependent predator-prey systems
cites work: Q4003237
full work available at URL: s0096-3003(01)00127-8
OpenAlex ID: W1969531076
description: scientific article; zbMATH DE number 1861151