Dynamics in the 1:2 spatial resonance with broken reflection symmetry
This paper is devoted to the study of effects of small symmetry-breaking perturbations on dynamics near heteroclinic cycles. The authors consider generic effects of breaking \(O(2)\) symmetry down to \(SO(2)\). They show that new types of dynamics are introduced into the system above and beyond the quasiperiodic orbit. Specifically, the authors find secondary Takens-Bogdanov bifurcations, so-called \(T\)-points, and degenerate heteroclinic cycles are responsible for the appearance of new types of global bifurcations, and with them of complex dynamics. Moreover, possible scenarios with increasing symmetry breaking are described.
scientific article; zbMATH DE number 2167904
scientific article