Algebraic approach to asynchronous Boolean networks

Using the structural matrix, we give a new frame work to study asynchronous random Boolean networks under different update schemes, which contain asynchronous random networks (ARBNs), deterministic asynchronous random networks (DARBNs), generalized asynchronous random networks (GARBNs), deterministic generalized asynchronous random networks (DGARBNs). The ARBNs and GARBNs are converted to probabilistic Boolean transition matrices, while DARBNs and DGARBNs are converted to time-variant Boolean transition matrixes. It paves the way to study the properties of RBNs.