SELF-ORGANIZED-CRITICALITY AND SYNCHRONIZATION IN PULSE COUPLED RELAXATION-OSCILLATOR SYSTEMS - THE OLAMI-FEDER-AND-CHRISTENSEN-MODEL AND THE FEDER-AND-FEDER-MODEL

We re-examine the dynamics of the Olami, Feder and Christensen (OFC) m odel. We show that, depending on the dissipation, it exhibits two diff erent behaviors and that it can or cannot show self-organized-critical ity (SOC) and/or synchronization. We also show that while the Feder an d Feder model perturbed by a stochastic noise is SOC and has the same exponent for the distribution of avalanche sizes as the OFC model, it does not show synchronization. We conclude that a relaxation oscillato r system can be synchronized and/or SOC and that synchronization is th erefore not necessary for criticality in these models.