Journal of Dynamics and Differential Equations

, Volume 22, Issue 2, pp 253–284

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

Article

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.

Keywords

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

Mathematics Subject Classification (2000)

34K18 46A30 

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Copyright information

© 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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