FORCED SYMMETRY-BREAKING OF HOMOCLINIC CYCLES

We consider two equivariant equations admitting structurally stable he teroclinic cycles. These equations stem from mode equations for the Ra yleigh-Benard convection and a model for turbulent layers in wall regi ons with riblets. Breaking the symmetry causes several different bifur cations to occur which can be explained by bifurcations of codimension two of homoclinic orbits for non-symmetric systems. In particular, st able periodic solutions of different symmetry type, other complicated heteroclinic cycles or geometric Lorenz attractors may emanate. Moreov er, we delevop stability criteria for the bifurcating periodic solutio ns. In general, their stability type differs from the stability proper ties of the original heteroclinic cycle.