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

Authors

  • Qingwen Hu
    • Department of Mathematics and StatisticsMemorial University of Newfoundland
    • Department of Mathematics and StatisticsYork University
Article

DOI: 10.1007/s10884-010-9162-5

Cite this article as:
Hu, Q. & Wu, J. J Dyn Diff Equat (2010) 22: 253. doi:10.1007/s10884-010-9162-5

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 equationsState-dependent delayHopf bifurcationGlobal continuationUpper bound of period

Mathematics Subject Classification (2000)

34K1846A30

Copyright information

© Springer Science+Business Media, LLC 2010