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.
Mathematics Subject Classification (2010): Primary 34K20, 34K06
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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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Chen, Y., Wu, J. (2013). Threshold Dynamics of Scalar Linear Periodic Delay-Differential Equations. In: Mallet-Paret, J., Wu, J., Yi, Y., Zhu, H. (eds) Infinite Dimensional Dynamical Systems. Fields Institute Communications, vol 64. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4523-4_10
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DOI: https://doi.org/10.1007/978-1-4614-4523-4_10
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