Set stabilization of probabilistic cascading Boolean networks and its applications

With the rapid development of systems biology and medical science, gene regulatory networks have become a heated research field. As an important model for studying biological systems and gene regulatory networks, in the past few decades, Boolean networks have attracted extensive attention from many scholars including biologists and system scientists. This paper studies the set stabilization problem of probabilistic cascading Boolean networks (PCBNs). Firstly, the concept of set stabilization of PCBNs has been proposed, and the considered PCBN is converted to an equivalent algebraic form by using the semi-tensor product of matrices. Secondly, based on the equivalent algebraic form, a series of probabilistic reachable sets is defined and a necessary and sufficient condition is presented for the set stabilization of PCBNs. Finally, as applications of set stabilization of PCBNs, the synchronization of PCBNs and strategy consensus of n-person random cascading evolutionary Boolean games are investigated, respectively, and several necessary and sufficient conditions are presented. © 2019, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.