Article

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

  • Qingwen HuAffiliated withDepartment of Mathematics and Statistics, Memorial University of Newfoundland
  • , Jianhong WuAffiliated withDepartment of Mathematics and Statistics, York University Email author 

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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.

Keywords

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

Mathematics Subject Classification (2000)

34K18 46A30