Dynamical interplay between random Boolean networks and awareness propagation

The stability of random Boolean networks (RBNs) has aroused continuous attention due to its profound applications in genetic regulatory. With extensive research on the joint influence of network topology and update rules, the interaction between RBN stability and other dynamic processes remains to be investigated. In this paper we propose an interactive multiplex model and study the dynamical interplay between RBN stability and awareness propagation. Theoretical analysis reveals that the stability of RBN is enhanced by awareness propagation. Specifically, its transition point between stable and unstable phases is determined by the main eigenvalue of H, which is closely related to the prevalence of awareness propagation and coupling strength between two layers. In addition, we illustrate the existence of a meta-critical point, from which awareness propagates and thus inhibits chaotic behaviors in RBN. Our work sheds light on the interaction between RBN stability and awareness propagation, and provides theoretical guidance to intervention of real Boolean systems.