Abstract
The steady-state reflection-breaking bifurcation from a circle of nontrivial equilibria in O(2)-equivariant systems results in a pair of travelling waves. When the continuous part of the group O(2) is weakly broken, the corresponding instability may lead to nonsymmetric but steady states. The transition from this state to the travelling wave state with increasing bifurcation parameter is complex, and typically involves sequences of global bifurcations. The possible scenarios are described in detail and the results are related to the dynamics associated with parity-breaking instabilities of spatially periodic patterns in inhomogeneous systems.
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