A global attractor in some discrete contest competition models with delay under the effect of periodic stocking

Ziyad Alsharawi

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We consider discrete models of the form xn+1=xnf(xn-1)+hn, where hn 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.

Original languageEnglish
Article number101649
JournalAbstract and Applied Analysis
Volume2013
DOIs
Publication statusPublished - 2013

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Competition Model
Global Attractor
Discrete Model
Periodic Solution
Global Attractivity
Invariant Region
Brouwer Fixed Point Theorem
Periodic Sequence
Non-negative
Model

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

A global attractor in some discrete contest competition models with delay under the effect of periodic stocking. / Alsharawi, Ziyad.

In: Abstract and Applied Analysis, Vol. 2013, 101649, 2013.

Research output: Contribution to journalArticle

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