Symmetry breaking via global bifurcations of modulated rotating waves in hydrodynamics

Jan Abshagen, Juan Lopez, Francisco Marques, Gerd Pfister

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Abstract

The combined experimental and numerical study finds a complex mechanism of Z2 symmetry breaking involving global bifurcations for the first time in hydrodynamics. In addition to symmetry breaking via pitchfork bifurcation, the Z2 symmetry of a rotating wave that occurs in Taylor-Couette flow is broken by a global saddle-node-infinite-period (SNIP) bifurcation after it has undergone a Neimark-Sacker bifurcation to a Z2-symmetric modulated rotating wave. Unexpected complexity in the bifurcation structure arises as the curves of cyclic pitchfork, Neimark-Sacker, and SNIP bifurcations are traced towards their apparent merging point. Instead of symmetry breaking due to a SNIP bifurcation, we find a more complex mechanism of Z2 symmetry breaking involving nonsymmetric two-tori undergoing saddle-loop homoclinic bifurcations and complex dynamics in the vicinity of this global bifurcation.

Original languageEnglish (US)
Article number074501
JournalPhysical Review Letters
Volume94
Issue number7
DOIs
Publication statusPublished - Feb 25 2005

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

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