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 multi- cellular organisms or within bacteria colonies. MRBNs are sets of Random Boolean Networks (RBNs), placed on a Cellular Automaton, whose gene ex- pressions may be affected by the activation of some genes in neighbouring networks. In this paper we study the effects induced by interaction on the dy- namics of those RBNs that - if isolated - lay in the critical region. It is shown that the influence of interaction is not univocal; nevertheless its 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 differ substantially in their typical response to perturbations