Self-organised criticality in some dissipative sandpile models

We investigate here self-organised criticality (SOC) in two-dimensional dissipative sandpile models without the local conservation law. Both dissipative cellular automata and dissipative coupled map lattice models with open boundary conditions are considered. There appears to be no evidence for the existence of SOC in the former models. In 2he CML models, scale-invariant avalanches are observed to occur for some specific local dynamical rules. This suggests that the occurrence of SOC depends, at least in part, on the nature of the dissipative dynamics.