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 language||English (US)|
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|State||Published - Nov 9 2007|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics