, Volume 22, Issue 2, pp 253-284

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.

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