Stability analysis of large-scale Boolean networks via compositional method

This paper formulates a compositional method to alleviate the high computational cost of studying large-scale Boolean networks (BNs). The algebraic expression of conjunctive composition is firstly presented through the semi-tensor product method. Accordingly, the relationship of state transitions between component BNs and conjunctive compositional BN is revealed. To describe the merging process during the conjunctive composition of state transitions, the single-node compositional equation is constructed, based on which a new criterion is built to analyze the stability of conjunctive compositional BNs. The idea of compositional equation is used to further explore the multi-node composition. Finally, the application to the BN model of Yeast Apoptosis demonstrates the effectiveness of the compositional method.