  The nonlinear evolution and the saturation mechanism of the magnetorotational
instability (MRI) are investigated using three-dimensional resistive MHD
simulations. A local shearing box is used for our numerical analysis and the
simulations begin with a purely vertical magnetic field. We find that the
magnetic stress in the nonlinear stage of the MRI is strongly fluctuating. The
time evolution shows the quasi-periodic recurrence of spike-shape variations
typically for a few orbits which correspond to the rapid amplification of the
magnetic field by the nonlinear growth of a two-channel solution followed by
the decay through magnetic reconnections. The increase rate of the total energy
in the shearing box system is analytically related to the volume-averaged
torque in the system. We find that at the saturated state this energy gain of
the system is balanced with the increase of the thermal energy mostly due to
the joule heating. The spike-shape time evolution is a general feature of the
nonlinear evolution of the MRI in the disks threaded by vertical fields and can
be seen if the effective magnetic Reynolds number is larger than about unity.
