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

Jessica Maral Conway, Hermann Riecke

Research output: Contribution to journalArticle

4 Citations (Scopus)

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

Fingerprint

Complex Ginzburg-Landau Equation
hexagons
Landau-Ginzburg equations
Hexagon
Forcing
rectangles
Spatial Pattern
Nonlinear Analysis
Rectangle
Hopf Bifurcation
Linearly
Unstable
Oscillation
Numerical Simulation
oscillations
simulation

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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Multiresonant forcing of the complex Ginzburg-Landau equation : Pattern selection. / Conway, Jessica Maral; Riecke, Hermann.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 76, No. 5, 057202, 09.11.2007.

Research output: Contribution to journalArticle

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