Approximate Synchronization in Distribution of Coupled Probabilistic Boolean Networks

This study explores the approximate synchronization in the distribution of coupled probabilistic Boolean networks (CPBNs). A parallel algebraic expression for CPBN is established based on the semi-tensor product (STP) of matrices. Furthermore, an eigenvalue-based sufficient criterion is developed to characterize approximate limiting behavior, and an algorithm is proposed to support the computation of the approximate matrices of limit matrices. On this basis, a criterion for approximate synchronization in the distribution of CPBNs is derived. Additionally, the feasibility of the proposed method and results is verified through examples.