| Random Boolean networks are conceptual models for systems of interacting elements. The dynamics of these models can be represented by a directed state space network by linking each dynamical state, represented as a node, to its temporal successor. Like all finite discrete deterministic systems the dynamics must eventually settle into a periodic attractor cycle. In this thesis we clarify how different weighting schemes and sampling methods affect the estimates for attractor length distributions in random Boolean networks. We find that the unbiased distribution of attractor lengths decays as a power-law for all K > 1, thus power-law behaviour in this distribution is not an indicator of criticality. However, we observe a power-law in the distribution of the sizes of "avalanches" in critical random Boolean networks only. Finally, we find that dynamical criticality manifests itself as multi-scale heterogeneity in the state space networks. |
