Uniqueness of Solution and Fixed Points Analysis for Singular Conjunctive Boolean Networks

Singular conjunctive Boolean networks are finite valued dynamic systems with special logical functions, which have several special mathematical properties. Based on “and” operator, this paper studies the existence and uniqueness of solution and fixed points for singular conjunctive Boolean networks. Firstly, using the special properties of “and” operator, the singular conjunctive Boolean networks are transformed into vector expressions. Based on these vector representations, the existence and uniqueness of solution for singular conjunctive Boolean networks are discussed. In addition, fixed points of singular conjunctive Boolean networks are explored. Finally, an example is used to verify the obtained results.