Topological Evolution of Dynamical Networks: Global Criticality from Local Dynamics

Abstract

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 leads to convergence of the average connectivity of the network towards the critical value $K_c=2\mathrm{}$ in the limit of large system size $N$. How this principle could generate self-organization in natural complex systems is discussed for two examples: neural networks and regulatory networks in the genome.