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

摘要

We introduce a numerical method to study random Boolean networks withasynchronous stochas- tic update. Each node in the network of states startswith equal occupation probability and this probability distribution thenevolves to a steady state. Nodes left with finite occupation probabilitydetermine the attractors and the sizes of their basins. As for synchronousupdate, the basin entropy grows with system size only for critical networks,where the distribution of attractor lengths is a power law. We determineanalytically the distribution for the number of attractors and basin sizes forfrozen networks with connectivity K = 1.