Critical percolation in self-organized media: A case study on random directed networks

A minimal model for self-organized critical percolation on directed graphs with activating and de-activating links is studied. Unlike classical self-organized criticality, the variables that determine criticality are separated from the dynamical variables of the system and evolve on a slower timescale, resulting in robust criticality. While activity of nodes percolates across the network, the network self-organizes through local adjustment of links according to the criterion that a link's adjacent nodes' average activities become similar. As a result, the network self-organizes to the percolation transition with activity avalanches propagating marginally across the graph. No fine-tuning of parameters is needed.