Volume 84, Number 1, October 2008
|Number of page(s)||6|
|Published online||19 September 2008|
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: firstname.lastname@example.org
Accepted: 13 August 2008
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.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 05.65.+b – Self-organized systems / 89.75.-k – Complex systems
© EPLA, 2008
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