Symmetry-breaking bifurcation with on-off intermittency in chaotic dynamical systems

When a dynamical system possesses certain symmetry, there can be an invariant subspace in the phase space. In the invariant subspace there can be a chaotic attractor. As a parameter changes through a critical value, the chaotic attractor can lose stability with respect to perturbations transverse to the invariant subspace. We show that the loss of the transverse stability can lead to a symmetry-breaking bifurcation characterized by lack of the system symmetry in the asymptotic attractor. An accompanying physical phenomenon is an extreme type of temporally intermittent bursting behavior. The mechanism for this type of symmetry-breaking bifurcation is elucidated.