Self - organized - criticality and synchronization in pulse coupled relaxation oscillator systems: the Olami, Feder and Christensen model and the Feder and Feder model

摘要

We reexamine the dynamics of the Olami, Feder and Christensen (OFC) model. Weshow that, depending on the dissipation, it exhibits two different behaviorsand that it can or cannot show self - organized - criticality (SOC) and/orsynchronization. We also show that while the Feder and Feder model perturbed bya stochastic noise is SOC and has the same exponent for the distribution ofavalanche sizes as the OFC model, it does not show synchronization. We concludethat a relaxation oscillator system can be synchronized and/or SOC and thattherefore synchronization is not necessary for criticality in these models.