Multiresonant forcing of the complex Ginzburg-Landau equation: pattern selection.
We study spatial patterns excited by resonant, 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.
Conway
Jessica M
JM
Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA.
Riecke
Hermann
H