The complex fluctuations of probabilistic Boolean networks

Probabilistic Boolean networks (PBNs) are extensions of Boolean networks (BNs), and both have been widely used to model biological systems. In this paper, we study the long-range correlations of PBNs based on their corresponding Markov chains. PBN states are quantified by the deviation of their steady-state distributions. The results demonstrate that, compared with BNs, PBNs can exhibit these dynamics over a wider and higher noise range. In addition, the constituent BNs significantly impact the generation of 1/f dynamics of PBNs, and PBNs with homogeneous steady-state distributions tend to sustain the 1/f dynamics over a wider noise range.