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Threshold Dynamics of Scalar Linear Periodic Delay-Differential Equations

  • Yuming Chen
  • Jianhong Wu
Chapter
Part of the Fields Institute Communications book series (FIC, volume 64)

Abstract

We consider the scalar linear periodic delay-differential equation \(\dot{x}(t) = -x(t) + ag(t)x(t - 1)\), where \(g : [0,\infty ) \rightarrow (0,\infty )\) is continuous and periodic with the minimal period ω>0. We show that there exists a positive a+ such that the zero solution is stable if \(a \in (0,{a}^{+})\) and unstable if a>a+. Examples and preliminary analysis suggest the challenge in obtaining analogous results when a<0.

Notes

Acknowledgements

Yuming Chen was supported in part by NSERC and the Early Researcher Award program of Ontario. Jianhong Wu was supported in part by CRC, MITACS and NSERC.

Received 4/4/2009; Accepted 2/10/2010

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsWilfrid Laurier UniversityWaterlooCanada
  2. 2.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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