A simple dynamical system is presented which is analogous in many ways to a solar coronal loop. When this system is subject to slow, external driving, representing photospheric motion, it undergoes occasional impulsive relaxations. These relaxations release some fraction of the magnetic energy as Alfven waves in the loop. When the model system is integrated for long times it reaches a statistical steady state in which relaxation events occur at random times with random amplitudes. The distributions of these quantities is compared to similar distributions for microflares occurring in the solar corona.