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

TL;DR

This paper investigates how adaptive thresholds and rewiring in Random Threshold Networks lead to self-organization, symmetry breaking, and criticality, with the dynamics depending on a control parameter that influences network connectivity and degree distributions.

Contribution

It introduces an evolutionary algorithm for local adaptation in networks, revealing new self-organized structures and critical behavior depending on the threshold-rewiring probability.

Findings

Networks exhibit symmetry breaking with higher connectivity when thresholds are adaptive.

In-degree distributions become broader and approach a power-law as the threshold adaptation probability approaches 1.

Networks tend to self-organize into critical states for large network sizes.

Abstract

We study an evolutionary algorithm that locally adapts thresholds and wiring in Random Threshold Networks, based on measurements of a dynamical order parameter. A control parameter $p$ determines the probability of threshold adaptations vs. link rewiring. 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 $p \to 1$, approaching 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 $N$.