  In this work we use the radiation hydrodynamic code TRAMP to perform a
two-dimensional axially symmetric model of the layered disc. Using this model
we follow the accumulation of mass in the dead zone due to the radially varying
accretion rate. We found a new type of instability which causes the dead zone
to split into rings. This "ring instability" works due to the positive feedback
between the thickness of the dead zone and the mass accumulation rate.
  We give an analytical description of this instability, taking into account
non-zero thickness of the dead zone and deviations from the Keplerian
rotational velocity. The analytical model agrees reasonably well with results
of numerical simulations. Finally, we speculate about the possible role of the
ring instability in protoplanetary discs and in the formation of planets.
