Stability analysis of activation-inhibition Boolean networks with stochastic function structures

This paper analyzes the stability of activation-inhibition Boolean networks with stochastic function structures. First, the activation-inhibition Boolean networks with stochastic function structures are converted to the form of logical networks by the method of semitensor product of matrices. Second, based on the obtained algebraic forms, we use matrices to denote the index set of possible logical operators and transition probabilities for activation-inhibition Boolean networks. Third, equivalence criterions are presented for the stabilities analysis of activation-inhibition Boolean networks with stochastic function structures. Finally, an example is given to verify the validity of the results.