  Differentially rotating disks under the effect of axial magnetic field are
prone to a nonlinear explosive magnetorotational instability (EMRI).
  The dynamic equations that govern the temporal evolution of the amplitudes of
three weakly-detuned resonantly interacting modes are derived. As distinct from
exponential growth in the strict resonance triads EMRI occurs due to the
resonant interactions of a MRI mode with stable Alfv\'en-Coriolis and
magnetosonic modes. Numerical solutions of the dynamic equations for amplitudes
of a triad indicate that two types of perturbations behavior can be excited for
resonance conditions: (i) EMRI which leads to infinite values of the three
amplitudes within a finite time, and (ii) bounded irregular oscillations of all
three amplitudes.
  Asymptotic explicit solutions of the dynamic equations are obtained for EMRI
regimes and are shown to match the numerical solutions near the explosion time.
