Viscoelastic Effects in Avalanche Dynamics: A Key to Earthquake Statistics

In many complex systems a continuous input of energy over time can be suddenly relaxed in the form of avalanches. Conventional avalanche models disregard the possibility of internal dynamical effects in the inter-avalanche periods, and thus miss basic features observed in some real systems. We address this issue by studying a model with viscoelastic relaxation, showing how coherent oscillations of the stress field can emerge spontaneously. Remarkably, these oscillations generate avalanche patterns that are similar to those observed in seismic phenomena.