Attractor and Basin Entropies of Random Boolean Networks Under Asynchronous Stochastic Update

We introduce a numerical method to study random Boolean networks with asynchronous stochas- tic update. Each node in the network of states starts with equal occupation probability and this probability distribution then evolves to a steady state. Nodes left with finite occupation probability determine the attractors and the sizes of their basins. As for synchronous update, the basin entropy grows with system size only for critical networks, where the distribution of attractor lengths is a power law. We determine analytically the distribution for the number of attractors and basin sizes for frozen networks with connectivity K = 1.