Self-Organized Criticality in Nonconserved Systems

The origin of self-organized criticality in a model without conservation law [Z. Olami, H. Feder, and K. Christensen, Phys. Rev. Lett. 68, 1244 (1992)] is studied. The initially periodic and neutrally stable interior of the system is invaded by a "self-organized" region. This self-organization is due to the synchronization of the individual elements with each other. A simplified model of marginal oscillator locking on a directed lattice explains many of the features in the nonconserved model: in particular, the dependence of the avalanche-distribution exponent on the conservation parameter $\alpha$ is examined.