Issue
EPL
Volume 84, Number 1, October 2008
Article Number 10004
Number of page(s) 6
Section General
DOI http://dx.doi.org/10.1209/0295-5075/84/10004
Published online 19 September 2008
EPL, 84 (2008) 10004
DOI: 10.1209/0295-5075/84/10004

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

T. Rohlf

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

rohlf@mis.mpg.de

received 22 April 2008; accepted in final form 13 August 2008; published October 2008
published online 19 September 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 1- p the node's threshold is increased, if it is frozen, with probability p it acquires a new link, with probability 1- p the node's threshold is decreased. For any p < 1, we find spontaneous symmetry breaking into a new class of self-organized networks, characterized by a much higher average connectivity $\bar{K}_{evo} $ than networks without threshold adaptation (p = 1). While $\bar{K}_{evo} $ and evolved out-degree distributions are independent from p for p < 1, in-degree distributions become broader when $p\rightarrow 1$, 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.

PACS
05.45.-a - Nonlinear dynamics and chaos.
05.65.+b - Self-organized systems.
89.75.-k - Complex systems.

© EPLA 2008