Sufficient and necessary conditions for the permanence of a discrete model with Beddington-DeAngelis functional response
type: Item
instance of: scholarly article
title: Sufficient and necessary conditions for the permanence of a discrete model with Beddington-DeAngelis functional response
zbMATH Open document ID: 1474.92074
DOI: 10.1155/2014/740895
author: Yong-Hong Fan
author: Linlin Wang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We give a sufficient and necessary condition for the permanence of a discrete model with Beddington-DeAngelis functional response with the form \(x(n+1)=x(n)\exp\{a(n)-b(n)x(n)-c(n)y(n)/(\alpha(n)+\beta(n)x(n)+\gamma(n)y(n))\}\), \(y(n+1)=y(n)\exp\{-d(n)+f(n)x(n)/(\alpha(n)+\beta(n)x(n)+\gamma(n)y(n))\}\), where \(a(n)\), \(b(n)\), \(c(n)\), \(d(n)\), \(f(n)\), \(\alpha(n)\), \(\beta(n)\), and \(\gamma(n)\) are periodic sequences with the common period \(\omega\); \(b(n)\) is nonnegative; \(c(n)\), \(d(n)\), \(f(n)\), \(\alpha(n)\), \(\beta(n)\), and \(\gamma(n)\) are positive. It is because of the difference between the comparison theorem for discrete system and its corresponding continuous system that an additional condition should be considered. In addition, through some analysis on the limit case of this system, we find that the sequence \(\alpha(n)\) has great influence on the permanence.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 39A23
Mathematics Subject Classification ID: 34K13
zbMATH DE Number: 7022991
Wikidata QID: Q59041115
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/740895
OpenAlex ID: W2070618419
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description: scientific article; zbMATH DE number 7022991