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

• Published in: Europhysics letters 2008-10, Vol.84 (1), p.10004-10004(6 )
• Main Author: Rohlf, T
• Format: Article
• Language: English
• Subjects: 05.45.-a; 05.65.+b; 89.75.-k
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/0295-5075/84/10004

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.