Topological evolution of dynamical networks: Global criticality from localdynamics

We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This lends to convergence of the average connectivity of the networ k towards the critical value K-c = 2 in the limit of large system size N. H ow this principle could generate self-organization in natural complex syste ms is discussed for two examples: neural networks and regulatory networks i n the genome.