Influence and dynamic behavior in random Boolean networks

We present a rigorous mathematical framework for analyzing dynamics of a broad class of Boolean network models. We use this framework to provide the first formal proof of many of the standard critical transition results in Boolean network analysis, and offer analogous characterizations for novel classes of random Boolean networks. We show that some of the assumptions traditionally made in the more common mean-field analysis of Boolean networks do not hold in general. For example, we offer evidence that imbalance (internal inhomogeneity) of transfer functions is a crucial feature that tends to drive quiescent behavior far more strongly than previously observed.