MiS Preprint Repository

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 ${\overline{K}}_{evo}$ than networks without threshold adaptation ($p=1$). While ${\overline{K}}_{evo}$ and evolved out-degree distributions are independent from $p$ for $p<1$, in-degree distributions become broader when $p\to 1$, 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.