Continuation of quasi-periodic invariant tori

F Schilder, HM Osinga, W Vogt

Research output: Contribution to journalArticle (Academic Journal)peer-review

79 Citations (Scopus)

Abstract

Many systems in science and engineering can be modeled as coupled or forced nonlinear oscillators, which may possess quasi- periodic or phase- locked invariant tori. Since there exist routes to chaos involving the break- down of invariant tori, these phenomena attract considerable attention. This paper presents a new algorithm for the computation and continuation of quasi- periodic invariant tori of ODEs that is based on a natural parametrization of such tori. Since this parametrization is uniquely defined, the proposed method requires neither the computation of a base of a transversal bundle nor remeshing during continuation. It is independent of the stability type of the torus, and examples of attracting and saddle- type tori are given. The algorithm is robust in the sense that it can compute approximations to weakly resonant tori. The performance of the method is demonstrated with examples.
Translated title of the contributionContinuation of quasi-periodic invariant tori
Original languageEnglish
Pages (from-to)459 - 488
Number of pages30
JournalSIAM Journal on Applied Dynamical Systems
Volume4 (3)
DOIs
Publication statusPublished - Jan 2005

Bibliographical note

Publisher: Society for Industrial and Applied Mathematics

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