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

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 $N$.

4 pages revtex, 6 figures

References in corpus (4)

• Adaptive Coevolutionary Networks: A Review
• Emergent Criticality from Co-evolution in Random Boolean Networks
• Damage Spreading and Criticality in Finite Random Dynamical Networks
• Canalization and Symmetry in Boolean Models for Genetic Regulatory Networks

Cited by in corpus (3)

• Adaptive Coevolutionary Networks: A Review
• Critical Line in Random Threshold Networks with Inhomogeneous Thresholds
• Evolution of regulatory networks towards adaptability and stability in a changing environment