Dynamics of a predator-prey system with Beddington-DeAngelis functional response and delays
type: Item
instance of: scholarly article
title: Dynamics of a predator-prey system with Beddington-DeAngelis functional response and delays
zbMATH Open document ID: 1474.92082
DOI: 10.1155/2014/930762
author: Nai-Wei Liu
author: Ting-Ting Kong
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We consider a predator-prey system with Beddington-DeAngelis functional response and delays, in which not only the stage structure on prey but also the delay due to digestion is considered. First, we give a sufficient and necessary condition for the existence of a unique positive equilibrium by analyzing the corresponding locations of a hyperbolic curve and a line. Then, by constructing an appropriate Lyapunov function, we prove that the positive equilibrium is locally asymptotically stable under a sufficient condition. Finally, by using comparison theorem and the \(\omega\)-limit set theory, we study the global asymptotic stability of the boundary equilibrium and the positive equilibrium, respectively. Also, we obtain a sufficient condition to assure the global asymptotic stability.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K60
zbMATH DE Number: 7023333
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/930762
OpenAlex ID: W2155675216
Wikidata QID: Q59042910
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description: scientific article; zbMATH DE number 7023333