Median attractor and transients in random boolean nets

Variants of a random boolean network of binary gates called the Kauffman net are studied. Each gate receives two random inputs from the other gates in the network and is assigned a transition function from a non-uniform distribution. Fine upper bounds on the attractor and transient lengths as the behavioral characteristics of the network are determined for large net size, N, and different transition function distributions. The effects of these distributions on the localization property of the net is shown. Analysis of nets with N > 1000 was shown to be very difficult. We also determine the scaling properties of attractors and transients with the net size. Our results exhibit strong ''antichaos'' behavior even for very large N for some of the networks.