Dynamics in the 1:2 spatial resonance with broken reflection symmetry

The dynamics near the 1:2 spatial resonance in systems with broken O(2) symmetry are described. The system is assumed to remain SO(2) invariant, and attention is focused on the behavior that replaces the structurally stable heteroclinic cycles present in the O(2)-symmetric system. The symmetry-breaking destroys these cycles, and introduces a variety of new bifurcations into the system, some which are associated with complex behavior. The possible scenarios with increasing symmetry-breaking are described and possible applications of the results are discussed.