  Recent experiments with strongly interacting, driven Rydberg ensembles have
introduced a promising setup for the study of self-organized criticality (SOC)
in cold atom systems. Based on this setup, we theoretically propose a control
mechanism for the paradigmatic avalanche dynamics of SOC in terms of a
time-dependent drive amplitude. This gives access to a variety of avalanche
dominated, self-organization scenarios, prominently including self-organized
criticality, as well as sub- and supercritical dynamics. We analyze the
dependence of the dynamics on external scales and spatial dimensionality. It
demonstrates the potential of driven Rydberg systems as a playground for the
exploration of an extended SOC phenomenology and their relation to other common
scenarios of SOC, such as e.g. in neural networks and on graphs.
