Fixed points of Boolean networks with sparse connections (opens in new tab)

We study fixed points (FPs) of cellular automata with sites on random sparse graphs. In the large limit such models are known to exhibit phase transitions, from a ‘frozen’ phase, where at most a finite number of sites fluctuate at long times, to a ‘fluctuating’ phase where a finite fraction of sites fluctuate. We consider several models, calculating the first and second moments of the number of FPs, and find that these moments remain finite in the large limit, except at the transitions where ...