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Forced symmetry breaking of homoclinic cycles

B Sandstede, A Scheel
1995 Nonlinearity  
We consider two equivariant equations admitting s v u c t d l y stable heteroclinic cycles. These equations stem from mode equations for the Rayleigh-Benard convection and a model for turbulent layen in wall rrgions with riblets. Breaking'the symmetry causes several different bifurcations to occur which a n be explained by bifurcations of codimension two of homoclinic orbits for non-symmetric syitems. In particular, stable periodic solutions of different symmetry type. other complicated
more » ... complicated heteroclinic cycles or geometric Lorenr amactors may emanate. Moreover, we delevop stability criteria for the bifurcating periodic solutions. In genenl, their stability type differs from the stability properties of the original heteraclinic cycle.
doi:10.1088/0951-7715/8/3/003 fatcat:rcr67psxljdy5foiay6noesspy