How critical random boolean networks may be affected by the interaction with others

In previous articles we have introduced Multi Random Boolean Networks (MRBNs) as a possible model for the interaction among cells within multicellular organisms or within bacteria colonies. MR.BNs are sets of Random Boolean Networks (RBNs), placed on a Cellular Automaton, whose nodes may be affected by the activation of some nodes in neighbouring networks. In this paper we study the effects induced by interaction on the dynamics of those RBNs that - if isolated - lay in the critical region. It is shown that the influence of interaction is not univocal; nevertheless it is possible to identify three classes of representative behaviours. RBNs belonging to each class seem to have different dynamical peculiarities even in isolation: although sharing the parameters proper of critical networks, they substantially differ in their typical response to perturbations.