Abstract
This paper investigates the global stability of large-scale switched conjunctive Boolean networks (SCBNs) under arbitrary switching signal from the graph-theoretic perspective. With the help of node removal technique, the Thomas’ rule in Boolean case is proved, that is, a Boolean network is globally stable when its network graph is acyclic, and meanwhile the stable equilibrium is constructed. Secondly, the combination of node removal and Thomas’ rule is used to analyse the stability of each mode in SCBNs. Thirdly, when the joint graph is weakly connected and acyclic, a polynomial-time criterion is built for the global stability of large-scale SCBNs under arbitrary switching signal. Finally, the application on the SCBN model in the processing of Toll ligand Spz demonstrates the effectiveness of the criterion.
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