An order parameter for networks of automata

Abstract

An exact polynomial equation is given for the size of the stable core of networks of automata with random connections. When the connectivity K of a network equals 1, 2, 3, 4 or 5 this equation is exactly solvable. It is found that the size of the stable core is an order parameter for a phase transition well known from Kauffman's model. A new derivation of critical parameter values follows. The phase structure is found to be independent of the updating scheme used in the dynamical law for the network.