Global Continua of Rapidly Oscillating Periodic Solutions of State-Dependent Delay Differential Equations |
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Authors: | Qingwen Hu Jianhong Wu |
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Affiliation: | 1.Department of Mathematics and Statistics,Memorial University of Newfoundland,St. John’s,Canada;2.Department of Mathematics and Statistics,York University,Toronto,Canada |
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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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