The Olami-Feder-Christensen earthquake model in one dimension
  We study the earthquake model by Olami, Feder and Christensen in one dimension. While the size distribution of earthquakes resembles a power law for small system sizes, it splits for larger system sizes into two parts, one comprising small avalanches and showing a size independent cutoff, and the other comprising avalanches of the order of the system size. We identify four different types of attractors of the dynamics of the system which already exist for very small systems. For larger system sizes, these attractors contain large synchronized regions. 
Felix Wissel and Barbara Drossel