A GENERAL FRAMEWORK FOR VALIDATED CONTINUATION OF PERIODIC ORBITS IN SYSTEMS OF POLYNOMIAL ODES

Jan Bouwe van den Berg*, Elena Queirolo

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

In this paper a parametrized Newton-Kantorovich approach is applied to continuation of periodic orbits in arbitrary polynomial vector fields. This allows us to rigorously validate numerically computed branches of periodic solutions. We derive the estimates in full generality and present sample continuation proofs obtained using an implementation in Matlab. The presented approach is applicable to any polynomial vector field of any order and dimension. A variety of examples is presented to illustrate the efficacy of the method.

Original languageEnglish
Pages (from-to)59-97
Number of pages39
JournalJournal of Computational Dynamics
Volume8
Issue number1
DOIs
Publication statusPublished - Jan 2021

Keywords

  • continuation
  • periodic orbits
  • polynomial ODEs
  • solution branch
  • Validated numerics

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