On the fate of perturbations in critical random Boolean networks

Abstract Random Boolean models of genetic regulatory networks, when subject tosmall noise, may either forget past distinctions or yield divergence in state space trajectoriesprecluding reliable action. With a specic choice of the model parameters, suchnetworks are in a critical regime and optimize capacity to bind past and future. Anin-depth study of the response to perturbation of critical random Boolean networks ishere presented. It is shown that networks built with critical values of the parametersmay, however, frequently show behaviours that are more typical of the ordered or of thedisordered regime. A further classication of critical networks is thus proposed withthe objective of isolating those networks that exhibit really critical dynamic