TY - JOUR
T1 - Time-modulated oscillatory convection
AU - Riecke, Hermann
AU - Crawford, John David
AU - Knobloch, Edgar
PY - 1988
Y1 - 1988
N2 - We investigate the effect of temporal modulation on the spatial patterns produced by a spatially extended system undergoing a Hopf bifurcation. It is shown that physically this modulation can stabilize standing waves, which would otherwise be stable to traveling waves. Mathematically a codimension-3 point is naturally introduced which encompasses a Takens-Bogdanov codimension-2 point with vanishing Hopf frequency. Experimentally this setup is attractive since the three relevant parameters are easily accessible and the steady bifurcation can be made forward as well as backward near a codimension-2 point.
AB - We investigate the effect of temporal modulation on the spatial patterns produced by a spatially extended system undergoing a Hopf bifurcation. It is shown that physically this modulation can stabilize standing waves, which would otherwise be stable to traveling waves. Mathematically a codimension-3 point is naturally introduced which encompasses a Takens-Bogdanov codimension-2 point with vanishing Hopf frequency. Experimentally this setup is attractive since the three relevant parameters are easily accessible and the steady bifurcation can be made forward as well as backward near a codimension-2 point.
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U2 - 10.1103/PhysRevLett.61.1942
DO - 10.1103/PhysRevLett.61.1942
M3 - Article
C2 - 10038938
AN - SCOPUS:0000031507
SN - 0031-9007
VL - 61
SP - 1942
EP - 1945
JO - Physical Review Letters
JF - Physical Review Letters
IS - 17
ER -