Self-organization of heterogeneous topology and symmetry breaking in networks with adaptive thresholds and rewiring

Max-Planck-Institute for Mathematics in the Sciences - Inselstr. 22, D-04103 Leipzig, Germany, EU

Corresponding author: rohlf@mis.mpg.de

Received: 22 April 2008
Accepted: 13 August 2008

Abstract

We study an evolutionary algorithm that locally adapts thresholds and wiring in Random Threshold Networks, based on measurements of a dynamical order parameter. If a node is active, with probability p an existing link is deleted, with probability the node's threshold is increased, if it is frozen, with probability p it acquires a new link, with probability the node's threshold is decreased. For any , we find spontaneous symmetry breaking into a new class of self-organized networks, characterized by a much higher average connectivity than networks without threshold adaptation (). While and evolved out-degree distributions are independent from p for , in-degree distributions become broader when , indicating crossover to a power law. In this limit, time scale separation between threshold adaptions and rewiring also leads to strong correlations between thresholds and in-degree. Finally, evidence is presented that networks converge to self-organized criticality for large N, and possible applications to problems in the context of the evolution of gene regulatory networks and development of neuronal networks are discussed.