A Lotka--Volterra type food chain model with stage structure and time delays
type: Item
instance of: scholarly article
title: A Lotka--Volterra type food chain model with stage structure and time delays
zbMATH Open document ID: 1096.34055
author: Rui Xu
author: M. A. J. Chaplain
author: Fordyce A. Davidson
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-03-22T00:00:00Z
review text: A three species Lotka-Volterra-type food chain model with mature and immature species and delay is investigated. First, the positivity of the solutions is proved. Then, sufficient conditions for the permanence of the solutions are given. Equilibrium solutions of the system are found. They represent the total annihilation of the system (E0), the annihilation of predators (E1), the annihilation of the top prey only (E2) and the coexistence of all species (E*). Sufficient conditions for the global stability of E1, E2, E* are derived. A related paper is given by \textit{J. F. M. Al-Omari} and \textit{S. A. Gourley} [Nonlinear Anal., Real World Appl. 6, 13--33 (2005; Zbl 1088.34070)].
reviewed by: E. Ahmed
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 5014227
zbMATH Keywords: global stability
zbMATH Keywords: permanence
zbMATH Keywords: delay
zbMATH Keywords: stage structured
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.09.090
OpenAlex ID: W1998159738
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DOI: 10.1016/J.JMAA.2005.09.090
description: scientific article; zbMATH DE number 5014227