Many complex systems respond to a continuous input of energy by an accumulation of stress over time, and sudden energy releases, called avalanches. Recently, it has been pointed out that several basic features of avalanche dynamics are induced at the microscopic level by relaxation processes, usually neglected by conventional models. I will present a minimal model with relaxation and its mean field treatment, and give an outline of the finite dimensional results.
In mean-field, our model yields a periodic behavior (with a new, emerging time scale), with events that span the whole system. In finite dimension (2D), the mean-field system-sized events become local, and numerical simulations give qualitative and quantitative results similar to the earthquakes observed in reality.
