Complex oscillations in systems subject to periodic perturbation

The principle of antisymmetry that gives rise to closed orbits of limit cycles and quasiperiodic trajectories of stable oscillations is formulated. The conditions of attraction of synchronized limit cycle as a whole are established. A bifurcational phase portrait of a synchronized limit cycle is considered. It is shown that the subharmonic capture of the limit cycle with period multiplication involves loss of symmetry and preservation of attraction