  We study effects of tunnel coupling on a pair of parallel disk-shaped
Bose-Einstein condensates with the self-attractive intrinsic nonlinearity. Each
condensate is trapped in a combination of in-plane and transverse
harmonic-oscillator potentials. It is shown that, depending on the
self-interaction strength and tunneling coupling, the ground state of the
system exhibits a phase transition which links three configurations: a
symmetric one with equal numbers of atoms in the coupled condensates, an
asymmetric configuration with a population imbalance (a manifestation of the
macroscopic quantum self-trapping), and the collapsing state. A modification of
the phase diagram of the system in the presence of vortices in the disk-shaped
condensates is reported too. The study of dynamics around the stationary
configurations reveals properties which strongly depend on the symmetry of the
configuration.
