Multiresonant forcing of the complex Ginzburg-Landau equation: Pattern selection

Jessica M. Conway*, Hermann E Riecke

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

We study spatial patterns excited byresonant, multifrequency forcing of systems near a Hopf bifurcation to spatially homogeneous oscillations. Our third-order, weakly nonlinear analysis shows that for small amplitudes only stripe patterns or hexagons (up and down) are linearly stable; for larger amplitudes rectangles and super-hexagons may become stable. Numerical simulations show, however, that in the latter regime the third-order analysis is insufficient: superhexagons are unstable. Instead large-amplitude hexagons can arise and be bistable with the weakly nonlinear hexagons.

Original languageEnglish (US)
Article number057202
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume76
Issue number5
DOIs
StatePublished - Nov 9 2007

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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