Symmetry and Dynamics of a Magnetic Oscillator

Symmetry and Dynamics of a Magnetic Oscillator

We consider a permanent magnetic dipole in an oscillating magnetic field. This magnetic oscillator has two dynamical symmetries. The breakdown and the restoration of these symmetries are investigated by varying the amplitude A of the magnetic field. For small A, symmetric states exist with respect to one of the two symmetries. However, such symmetric states lose their symmetries via symmetry-breaking pitchfork bifurcations, and then the symmetry-broken states exhibit period-doubling transitions to chaos. Consequently, small chaotic attractors with broken symmetries appear. However, as A is further increased they merge into a large symmetric chaotic attractor via symmetry-restoring attractor-merging crisis.