Evaluation of attractors and basins of asynchronous random Boolean networks

We present an algebraic approach for determining the attractors and their basins of random Boolean networks under an asynchronous stochastic update based on the recently developed matrix semitensor product theory, which allows for converting the logical dynamics of a Boolean network into a standard iterative dynamics. In this setting, all attractors and basins are specified by the network transition matrices. We then devise procedures that can find all attractors and their basins exactly. We also discuss the issue of overlapping basins in asynchronous random Boolean networks, and we propose methods to compute the weight of each attractor and the basin entropy of the systems.