A global attractor in some discrete contest competition models with delay under the effect of periodic stocking
type: Item
instance of: scholarly article
title: A global attractor in some discrete contest competition models with delay under the effect of periodic stocking
zbMATH Open document ID: 1297.39018
DOI: 10.1155/2013/101649
author: Ziyad AlSharawi
published in: Abstract and Applied Analysis
publication date: 2014-06-20T00:00:00Z
review text: Summary: We consider discrete models of the form \(x_{n+1}=x_nf(x_{n-1})+h_n\), where \(h_n\) is a nonnegative \(p\)-periodic sequence representing stocking in the population, and investigate their dynamics. Under certain conditions on the recruitment function \(f(x)\), we give a compact invariant region and use Brouwer fixed point theorem to prove the existence of a \(p\)-periodic solution. Also, we prove the global attractivity of the \(p\)-periodic solution when \(p=2\). In particular, this study gives theoretical results attesting to the belief that stocking (whether it is constant or periodic) preserves the global attractivity of the periodic solution in contest competition models with short delay. Finally, as an illustrative example, we discuss Pielou's model with periodic stocking.
Mathematics Subject Classification ID: 39A30
Mathematics Subject Classification ID: 39A23
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 6306021
zbMATH Keywords: periodic solution
zbMATH Keywords: global attractivity
zbMATH Keywords: contest competition models
zbMATH Keywords: Pielou's model
zbMATH Keywords: periodic stocking
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/101649
OpenAlex ID: W2108790543
Wikidata QID: Q58915276
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description: scientific article; zbMATH DE number 6306021