Stability Analysis of Boolean Networks With Stochastic Function Perturbations

Using the semi-tensor product method, this paper studies the set stability of Boolean networks (BNs) with stochastic function perturbations. First, the definition of one-column function perturbation for BNs is defined, and two kinds of stochastic function perturbations are formulated. Second, by constructing a state transition matrix, a new criterion is proposed for the set stability of BNs with probabilistic function perturbation. Third, the set stability of BNs with Markov jump function perturbation is studied by calculating the state probability distribution. Finally, the obtained results are applied to D. melanogaster segmentation polarity gene network.