Single-input Boolean networks

The critical Kauffman model with connectivity one is the simplest class of critical Boolean networks. Nevertheless, it exhibits intricate behavior at the boundary of order and chaos. We prove that the number of attractors is at least 2m−o(m), where m is the number of nodes in loops—considerably larger than previously believed. We also find the mean attractor length is at most 2o(m), the first proof that it is sub-exponential in m.