
Physics 2002
Dynamics of Boolean Networks with ScaleFree TopologyAbstract: The dynamics of Boolean networks (the NK model) with scalefree topology are studied here. The existence of a phase transition governed by the value of the scalefree exponent of the network is shown analytically by analyzing the overlap between two distinct trajectories. The phase diagram shows that the phase transition occurs for values of the scalefree exponent in the open interval (2,2.5). Since the Boolean networks under study are directed graphs, the scalefree topology of the input connections and that of the output connections are studied separately. Ultimately these two topologies are shown to be equivalent. An important result of this work is that the finetuning usually required to achieve stability in Boolean networks with a totally random topology is no longer necessary when the network topology is scalefree.
