Fixed points of Boolean networks on sparse random graphs have finite moments away from frozen-to-fluctuating transitions and organize into clusters whose number and separation change across the transition.
The dynamical update rule reads ψt+1 = ∞∑ k=0 Pk [ 1−(1−ψt)k−kψt (1−ψt)k−1 ] , whereP k is the probability forkincoming edges
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Fixed points of Boolean networks with sparse connections
Fixed points of Boolean networks on sparse random graphs have finite moments away from frozen-to-fluctuating transitions and organize into clusters whose number and separation change across the transition.