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May  2005, 5(2): 277-288. doi: 10.3934/dcdsb.2005.5.277

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, Canada
2. 

Department of Mathematics & Statistics, McMaster University, Hamilton, Ontario Canada L8S 4K1, Canada

Received  December 2003 Revised  July 2004 Published  February 2005

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.
Keywords: global attractivity, delay differential equations, Circadian pacemaker, coincidence degree, periodic solution..
Mathematics Subject Classification: 34K13, 34K2.
Citation: Y. Chen, L. Wang. Global attractivity of a circadian pacemaker model in a periodic environment. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 277-288. doi: 10.3934/dcdsb.2005.5.277
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