Attractors and basins of asynchronous random Boolean networks

We present a method for studying the attractors and their basins of random Boolean networks under asynchronous stochastic update, based on the recently developed Matrix Semi-tensor Product theory. By the method, all attractors are determined by the network transition matrices. We devise procedures that are effective in finding all attractors and their basins. Compared with existing results, our approach has the advantage of obtaining the exact basins of all attractors despite the difficulty of possible overlapping of different basins in ARBNs. In addition, we also propose a procedure for computing the weight of an attractor and the basin entropy for ARBNs. The results show that the basin entropy of ARBNs increases with the system size only for critical networks.