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Global Continua of Rapidly Oscillating Periodic Solutions of State-Dependent Delay Differential Equations

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Abstract

We apply our recently developed global Hopf bifurcation theory to examine global continuation with respect to the parameter for periodic solutions of functional differential equations with state-dependent delay. We give sufficient geometric conditions to ensure the uniform boundedness of periodic solutions, obtain an upper bound of the period of non-constant periodic solutions in a connected component of Hopf bifurcation, and establish the existence of rapidly oscillating periodic solutions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C 5S7, Canada

    Qingwen Hu

  2. Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J 1P3, Canada

    Jianhong Wu

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  1. Qingwen Hu
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  2. Jianhong Wu
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Correspondence to Jianhong Wu.

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Dedicated to the 80th birthday of Professor Jack K. Hale.

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Hu, Q., Wu, J. Global Continua of Rapidly Oscillating Periodic Solutions of State-Dependent Delay Differential Equations. J Dyn Diff Equat 22, 253–284 (2010). https://doi.org/10.1007/s10884-010-9162-5

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  • DOI: https://doi.org/10.1007/s10884-010-9162-5

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