  It was discovered recently that frictional granular materials can exhibit an
important mechanism for instabilities, i.e the appearance of pairs of complex
eigenvalues in their stability matrix. The consequence is an oscillatory
exponential growth of small perturbations which are tamed by dynamical
nonlinearities. The amplification can be giant, many orders of magnitude, and
it ends with a catastrophic system-spanning plastic event. Here we follow up on
this discovery, explore the scaling laws characterizing the onset of the
instability, the scenarios of the development of the instability with and
without damping, and the nature of the eventual system spanning events. The
possible relevance to earthquake physics and to the transition from static to
dynamic friction is discussed.
