Attractors represent the long-term behaviors of Random Boolean Networks. We study how the amount of information propagated between the nodes when on an attractor, as quantified by the average pairwise mutual information (I_A), relates to the robustness of the attractor to perturbations (R_A). We find that the dynamical regime of the network affects the relationship between I_A and R_A. In the ordered and chaotic regimes, I_A is anti-correlated with R_A, implying that attractors that are highly robust to perturbations have necessarily limited information propagation. Between order and chaos (for so-called “critical” networks) these quantities are uncorrelated. Finite size effects cause this behavior to be visible for a range of networks, from having a sensitivity of 1 to the point where I_A is maximized. In this region, the two quantities are weakly correlated and attractors can be almost arbitrarily robust to perturbations without restricting the propagation of information in the network.
Lloyd-Price J, Gupta A, Ribeiro AS (2012) Robustness and Information Propagation in Attractors of Random Boolean Networks. PLoS ONE 7(7): e42018. doi:10.1371/journal.pone.0042018