Stability of Attractor Cycles in Random Boolean Networks

Random Boolean networks (RBNs) were proposed as a model of genetic regulatory networks by Kauffman in 1969. This paper addresses the stability of cycles of RBNs and Boolean networks. In particular we define the error probabilities of cycle states as the probability of leaving a cycle after a randomly occurring error. Therefore, we introduce the weight distributions, which are usually used to analyse error probabilities of error-correction codes, and show that these completely determine the error probabilities of the cycles. By simulations of RBNs with 20, 17 and 15 state bits and bias of 0.5 we found that networks with connectivity 2 show less stable attractor cycles compared to RBNs with higher K, namely K ∈ {3,4,5,6}.