  The magnetised spherical Couette (MSC) problem, a three dimensional
magnetohydrodynamic paradigmatic model in geo- and astrophysics, is considered
to investigate bifurcations to high-dimensional invariant tori and chaotic
flows in large scale dissipative dynamical systems with symmetry. The main goal
of the present study is to elucidate the origin of chaotic transients and
intermittent behaviour from two different sequences of Hopf bifurcations
involving invariant tori with four fundamental frequencies, which may be
resonant. Numerical evidence of the existence of a crisis event destroying
chaotic attractors and giving rise to the chaotic transients is provided. It is
also shown that unstable invariant tori take part in the time evolution of
these chaotic transients. For one sequence of bifurcations, the study
demonstrates that chaotic transients display on-off intermittent behaviour. A
possible explanatory mechanism is discussed.
