TY - JOUR
T1 - Competing parametric instabilities with circular symmetry
AU - Crawford, John David
AU - Knobloch, Edgar
AU - Riecke, Hermann
PY - 1989/2/6
Y1 - 1989/2/6
N2 - Recent experiments in circular geometry have studied the dynamics produced by two parametrically excited surface waves. There is a natural theoretical context for experiments of this type, the mode interaction between two period-doubling bifurcations in the presence of O(2) symmetry. We formulate this interaction as a map in four dimensions, and classify the primary, secondary, and tertiary bifurcations. We find that the observed amplitude oscillations can arise as a tertiary Hopf bifurcation from a mixed mode pattern provided exactly one of the primary instabilities is subcritical.
AB - Recent experiments in circular geometry have studied the dynamics produced by two parametrically excited surface waves. There is a natural theoretical context for experiments of this type, the mode interaction between two period-doubling bifurcations in the presence of O(2) symmetry. We formulate this interaction as a map in four dimensions, and classify the primary, secondary, and tertiary bifurcations. We find that the observed amplitude oscillations can arise as a tertiary Hopf bifurcation from a mixed mode pattern provided exactly one of the primary instabilities is subcritical.
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U2 - 10.1016/0375-9601(89)90718-4
DO - 10.1016/0375-9601(89)90718-4
M3 - Article
AN - SCOPUS:45249130017
SN - 0375-9601
VL - 135
SP - 20
EP - 24
JO - Physics Letters A
JF - Physics Letters A
IS - 1
ER -