Global attractivity of a circadian pacemaker model in a periodic environment

Y. Chen; L. Wang

doi:10.3934/dcdsb.2005.5.277

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2005, Volume 5, Issue 2: 277-288. Doi: 10.3934/dcdsb.2005.5.277

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Global attractivity of a circadian pacemaker model in a periodic environment

Y. Chen^1, and
L. Wang^2,

1.
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5
2.
Department of Mathematics & Statistics, McMaster University, Hamilton, Ontario Canada L8S 4K1

Received: November 30, 2003

Revised: June 30, 2004

Published: April 2008

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Abstract

In this paper, we propose a delay differential equation with continuous periodic parameters to model the circadian pacemaker in a periodic environment. First, we show the existence of a positive periodic solution by using the theory of coincidence degree. Then we establish the global attractivity of the periodic solution under two sufficient conditions. These conditions are easily verifiable and are independent of each other. Some numerical simulations are also performed to demonstrate the main results.

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Mathematics Subject Classification: 34K13, 34K20.

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