Self-organization to criticality in a system without conservation law

Abstract

We numerically investigate the approach to the stationary state in the non-conservative Olami–Feder–Christensen (OFC) model for earthquakes. Starting from initially random configurations, we monitor the average earthquake size in different portions of the system as a function of time (the time is defined as the input energy per site in the system). We find that the process of self-organization develops from the boundaries of the system and it is controlled by a dynamical critical exponent z ∼ 1.3 that appears to be universal over a range of dissipation levels of the local dynamics. We show moreover that the transient time of the system ttr scales with system size L as ttr ∼ Lz. We argue that the (non-trivial) scaling of the transient time in the OFC model is associated with the establishment of long-range spatial correlations in the steady state.