Function Perturbation Impact on Conjunctive Boolean Networks Under Asynchronous Update

In this paper, the function perturbation impact on the conjunctive Boolean network (CBN) under asynchronous update is considered. By resorting to the matrix semi-tensor product, the logical form of the addressed CBN is first transformed into its algebraic form, and some properties are then obtained. In order to globally asymptotic stabilize the considered CBN, a new concept is introduced with maximum probability transition, and the one-bit or multi-bit function perturbations are performed, which are summarized in an algorithm. Finally, a necessary and sufficient condition is presented for the global asymptotic stability of the CBN system. Several illustrative examples are simultaneously given to show validity of the derived results.