Dynamical stability in random Boolean Networks

In this work we propose a new approach to the stability analysis ofRandom Boolean Networks (RBNs). In particular, we focus on two families ofRBNs with k=2, in which only two subsets of canalizing Boolean function areallowed, and we show that the usual measure of RBNs stability - sometimesknown as the Derrida parameter (DP) - is similar in the two cases, while theirdynamics (e.g. number of attractors, length of cycles, number of frozen nodes) aredifferent. For this reason we have introduced a new measure, that we have calledattractor sensitivity (AS), computed in a way similar to DP, but perturbing only theattractors of the networks. It is proven that AS turns out to be different in the twocases analyzed. Finally, we investigate Boolean networks with k=3, tailored tosolve the Density Classification Problem, and we show that also in this case theAS describes the system dynamical stability.