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

Thimo Rohlf

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Submission date: 18. Aug. 2008
Pages: 8
published in: epl, 84 (2008) 1, art-no. 10004 
DOI number (of the published article): 10.1209/0295-5075/84/10004
Bibtex
PACS-Numbers: 05.45.-a, 05.65.+b, 89.75.-k
Keywords and phrases: dynamical network, self-organized criticality, adaptation
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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 than networks without threshold adaptation (p =1). While and evolved out-degree distributions are independent from p for p <1, 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.