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

  • Qingwen Hu
  • Jianhong WuEmail author


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.


Differential equations State-dependent delay Hopf bifurcation Global continuation Upper bound of period 

Mathematics Subject Classification (2000)

34K18 46A30 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMemorial University of NewfoundlandSt. John’sCanada
  2. 2.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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