Extended notion of attractors in noisy random Boolean networks

Since real networks are noisy systems, in this work we investigate thedynamics of the random Boolean networks affected by different size of smallrandom fluctuations. In this case jumps among different attractors are possible,thereby leading to an asymptotic dynamics different from that of the underlyingdeterministic model. The significance of the jumps among attractors is investigated.The notion of “ergodic set” is discussed and generalized in terms of“threshold ergodic set”, a concept that take into account the system lifetime. Inorder to evaluate possible differences due to the topology of the nets the experimentsare effectuated on Erdos-Renyi and scale-free topologies, showing similarbehaviours