A periodically forced flow displaying symmetry breaking via a three-tori gluing bifurcation and two-tori resonances

F. Marques, Juan Lopez, J. Shen

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

The dynamics due to a periodic forcing (harmonic axial oscillations) in a Taylor-Couette apparatus of finite length is examined numerically in an axisymmetric subspace. The forcing delays the onset of centrifugal instability and introduces a Z2 symmetry that involves both space and time. This paper examines the influence of this symmetry on the subsequent bifurcations and route to chaos in a one-dimensional path through parameter space as the centrifugal instability is enhanced. We have observed a well-known route to chaos via frequency locking and torus break-up on a two-tori branch once the Z2 symmetry has been broken. However, this branch is not connected in a simple manner to the Z2-invariant primary branch. An intermediate branch of three-tori solutions, exhibiting heteroclinic and homoclinic bifurcations, provides the connection. On this three-tori branch, a new gluing bifurcation of three-tori is seen to play a central role in the symmetry breaking process.

Original languageEnglish (US)
Pages (from-to)81-97
Number of pages17
JournalPhysica D: Nonlinear Phenomena
Volume156
Issue number1-2
DOIs
StatePublished - Aug 1 2001

Keywords

  • Gluing bifurcation
  • Naimark-Sacker bifurcation
  • Periodic forcing
  • Symmetry breaking
  • Taylor-Couette flow

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'A periodically forced flow displaying symmetry breaking via a three-tori gluing bifurcation and two-tori resonances'. Together they form a unique fingerprint.

  • Cite this