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