TY - JOUR
T1 - Symmetry breaking via global bifurcations of modulated rotating waves in hydrodynamics
AU - Abshagen, Jan
AU - Lopez, Juan
AU - Marques, Francisco
AU - Pfister, Gerd
PY - 2005/2/25
Y1 - 2005/2/25
N2 - The combined experimental and numerical study finds a complex mechanism of Z2 symmetry breaking involving global bifurcations for the first time in hydrodynamics. In addition to symmetry breaking via pitchfork bifurcation, the Z2 symmetry of a rotating wave that occurs in Taylor-Couette flow is broken by a global saddle-node-infinite-period (SNIP) bifurcation after it has undergone a Neimark-Sacker bifurcation to a Z2-symmetric modulated rotating wave. Unexpected complexity in the bifurcation structure arises as the curves of cyclic pitchfork, Neimark-Sacker, and SNIP bifurcations are traced towards their apparent merging point. Instead of symmetry breaking due to a SNIP bifurcation, we find a more complex mechanism of Z2 symmetry breaking involving nonsymmetric two-tori undergoing saddle-loop homoclinic bifurcations and complex dynamics in the vicinity of this global bifurcation.
AB - The combined experimental and numerical study finds a complex mechanism of Z2 symmetry breaking involving global bifurcations for the first time in hydrodynamics. In addition to symmetry breaking via pitchfork bifurcation, the Z2 symmetry of a rotating wave that occurs in Taylor-Couette flow is broken by a global saddle-node-infinite-period (SNIP) bifurcation after it has undergone a Neimark-Sacker bifurcation to a Z2-symmetric modulated rotating wave. Unexpected complexity in the bifurcation structure arises as the curves of cyclic pitchfork, Neimark-Sacker, and SNIP bifurcations are traced towards their apparent merging point. Instead of symmetry breaking due to a SNIP bifurcation, we find a more complex mechanism of Z2 symmetry breaking involving nonsymmetric two-tori undergoing saddle-loop homoclinic bifurcations and complex dynamics in the vicinity of this global bifurcation.
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U2 - 10.1103/PhysRevLett.94.074501
DO - 10.1103/PhysRevLett.94.074501
M3 - Article
AN - SCOPUS:18144422069
SN - 0031-9007
VL - 94
JO - Physical Review Letters
JF - Physical Review Letters
IS - 7
M1 - 074501
ER -