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A Global Attractor in Some Discrete Contest Competition Models with Delay under the Effect of Periodic Stocking
Al-Sharawi, Ziyad
Al-Sharawi, Ziyad
Date
2013
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Type
Peer-Reviewed
Article
Published version
Article
Published version
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Abstract
We consider discrete models of the form ๐ณโโโ= ๐ณโ๐(๐ณโโโ) + ๐โ , where ๐โ is a nonnegative ๐-periodic sequence representing stocking in the population, and investigate their dynamics. Under certain conditions on the recruitment function ๐(๐ณ), 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 ๐-periodic solution when ๐ = 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 Pielouโs model with periodic stocking.