Revisiting singular Boolean networks

The general singular Boolean networks (SBNs) are proposed in this paper according to the algebraic form of dynamic-algebraic Boolean networks. First, the solvability theorems of this kind SBNs are presented. Then, the transition matrix of an SBN is defined, based on which the results on fixed points and cycles of SBNs are obtained. Furthermore, general singular Boolean control networks (SBCNs) are discussed, as well as the solvability of SBCNs. Several examples illustrate the feasibility of the theoretical results.