Adding any spontaneous activation to a spreading process on networks shifts the critical behavior from directed to undirected percolation, with a derived critical line and a crossover scale of p^{-2/3}.
Ponce-Alvarez, A
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Criticality in spreading processes without time-scale separation and the critical brain hypothesis
Adding any spontaneous activation to a spreading process on networks shifts the critical behavior from directed to undirected percolation, with a derived critical line and a crossover scale of p^{-2/3}.