  Cosmic rays produced by young stellar objects can potentially alter the
ionization structure, heating budget, chemical composition, and accretion
activity in circumstellar disks. The inner edges of these disks are truncated
by strong magnetic fields, which can reconnect and produce flaring activity
that accelerates cosmic radiation. The resulting cosmic rays can provide a
source of ionization and produce spallation reactions that alter the
composition of planetesimals. This reconnection and particle acceleration are
analogous to the physical processes that produce flaring in and heating of
stellar coronae. Flaring events on the surface of the Sun exhibit a power-law
distribution of energy, reminiscent of those measured for Earthquakes and
avalanches. Numerical lattice-reconnection models are capable of reproducing
the observed power-law behavior of solar flares under the paradigm of
self-organized criticality. One interpretation of these experiments is that the
solar corona maintains a nonlinear attractor -- or ``critical'' -- state by
balancing energy input via braided magnetic fields and output via reconnection
events. Motivated by these results, we generalize the lattice-reconnection
formalism for applications in the truncation region of magnetized disks. Our
numerical experiments demonstrate that these nonlinear dynamical systems are
capable of both attaining and maintaining criticality in the presence of
Keplerian shear and other complications. The resulting power-law spectrum of
flare energies in the equilibrium attractor state is found to be nearly
universal in magnetized disks. This finding indicates that magnetic
reconnection and flaring in the inner regions of circumstellar disks occur in a
manner similar to activity on stellar surfaces.
