Robustness and information propagation in attractors of random boolean networks

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 (Formula: see text]), relates to the robustness of the attractor to perturbations (Formula: see text]). We find that the dynamical regime of the network affects the relationship between Formula: see text] and Formula: see text]. In the ordered and chaotic regimes, Formula: see text] is anti-correlated with Formula: see text], 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 Formula: see text] 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.