POWER-LAW DISTRIBUTIONS IN SOME RANDOM BOOLEAN NETWORKS

The Kauffman net is a dynamical system of logical variables receiving two random inputs and each randomly assigned a Boolean function. We sh ow that the attractor and transient lengths exhibit scaleless behavior with power-law distributions over up to 10 orders of magnitude in pro bability. Our results provide evidence for the existence of the ''edge of chaos'' as a distinct regime between the ordered and chaotic phase s analogous to a critical point in statistical mechanics. The power-la w distributions are robust to the changes in the composition of the tr ansition rules and network dynamics.