Critical values in asynchronous Random Boolean Networks

Abstract

Wherever we see life, we see different kinds of complex networks, reason why they are studied across various fields of science. Random Boolean Networks (RBNs) form a special class in which the links between the nodes and the boolean functions are specified at random. Whereas synchronous RBNs were investigated in detail, there has little been done around their asynchronous counterpart, although there is evidence that most living systems are governed by asynchronous updating. Derrida's annealed approximation predicts a critical connectivity value of K = 2 for synchronous RBNs. We present a similar and original approach for asynchronous RBNs and show that they do not possess such a critical connectivity value. The asynchronous and nondeterministic updating scheme introduces perturbations that reach about 25% of the nodes and thus prevents the networks to become stable. Further, our numerical simulations show that asynchronous RBN tend to amplify small and to reduce big perturbations.