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Permanence And Existence Of A Positive Periodic Solution To A Periodic Stage-Structured System With In Infinite Delay

Kouche, M and Tatar, NE and Liu, SQ (2008) Permanence And Existence Of A Positive Periodic Solution To A Periodic Stage-Structured System With In Infinite Delay. ELSEVIER SCIENCE INC, APPLIED MATHEMATICS AND COMPUTATION, 202.

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Abstract

In this paper we consider a periodic non-autonomous competitive stage-structured system with infinite delay for the interaction between n species, the adult members of which are in competition. For each of the n species the model incorporates a time delay which represents the time from birth to maturity of that species. Infinite delay is introduced which denotes the influential effect of the entire past history of the system on the current competition interactions. We first prove by using the comparison principle that if the growth rates are sufficiently large then the solutions are uniformly permanent. Then by using Horn's fixed point Theorem, we show that the system with finite delay has a positive periodic solution. As a consequence of this result, we prove that even the system with infinite delay admits a positive periodic solution.



Item Type:Article
Date:2008
Date Type:Publication
Subjects:General
Divisions:General
Creators:Kouche, M and Tatar, NE and Liu, SQ
Email:kouchebone@yahoo.fr, tatarn@kfupm.edu.sa, sheliu@utu.fi
ID Code:16123
Deposited By:Morshed Alam Bhuiyan
Deposited On:19 Aug 2008 09:15
Last Modified:12 Apr 2011 13:16

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