A second order analysis of the periodic solutions for nonlinear periodic differential systems with a small parameter

Adriana Buic, Jaume Giné, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

18 Citations (Scopus)

Abstract

We deal with nonlinear T-periodic differential systems depending on a small parameter. The unperturbed system has an invariant manifold of periodic solutions. We provide the expressions of the bifurcation functions up to second order in the small parameter in order that their simple zeros are initial values of the periodic solutions that persist after the perturbation. In the end two applications are done. The key tool for proving the main result is the LyapunovSchmidt reduction method applied to the T-PoincaréAndronov mapping. © 2011 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)528-533
JournalPhysica D: Nonlinear Phenomena
Volume241
Issue number5
DOIs
Publication statusPublished - 1 Mar 2012

Keywords

  • Averaging method
  • Lyapunov-Schmidt reduction
  • Periodic solution

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