ON THE DYNAMICS OF RANDOM BOOLEAN NETWORKS WITH SCALE-FREE OUTGOING CONNECTIONS

In the classical model of Random Boolean Networks (RBN) the number of incoming connectionsis the same for every node, while the distribution of outgoing links is Poissonian. TheseRBN are known to display two major dynamical behaviours, depending upon the value of somemodel parameters: an “ordered” and a “chaotic” regime. We introduce a modi7cation of theclassical way of building a RBN, which maintains the property that all the nodes have the samenumber of incoming links, but which gives rise to a scale-free distribution of outgoing connections.Because of this modi7cation, the dynamical properties are deeply modi7ed: the number ofattractors is much smaller than in classical RBN, their length and the duration of the transientsare shorter. Moreover, the number of di8erent attractors is almost independent of the networksize, over almost three orders of magnitudes (while in classical RBN this number grows with thesize of the network). These results are based upon a detailed study of networks where each nodehas two input connections. A limited study of networks with three input connections per nodeshows that also in this case the number of attractors is almost independent of the network size.