TY - JOUR
T1 - Multiresonant forcing of the complex Ginzburg-Landau equation
T2 - Pattern selection
AU - Conway, Jessica M.
AU - Riecke, Hermann E
PY - 2007/11/9
Y1 - 2007/11/9
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevE.76.057202
DO - 10.1103/PhysRevE.76.057202
M3 - Article
C2 - 18233797
AN - SCOPUS:36049031126
SN - 1539-3755
VL - 76
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 5
M1 - 057202
ER -