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.
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