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

T. Rohlf
Europhysics Letters, 84(1),10004, 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 $1 - p$ 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.

This paper in Europhysics Letters

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