A unified transform method for general robust property of probabilistic Boolean control networks

Abstract

This article proposes a unified transform method for general robust property of probabilistic Boolean control networks (PBCNs). Here, the general robust property of PBCNs means any given robust property of any given PBCN with probability one. Specifically, the method is that the investigation on any given robust property of any given PBCN with probability one can be equivalently transformed into the investigation on the given robust property of the corresponding Boolean control network (BCN). Note that the PBCN has time-varying probability distribution and the property can be set according to the needs of specific problems. As an application of the method, we study the robust set stabilization with probability one of PBCNs with positive time-varying probability distribution. We derive the results through a discussion of the robust set stabilization of the corresponding BCNs. Also, we characterize all of the time-optimal robust set stabilizers of the PBCNs. A reduced disturbed PBCN model of the lac operon in the Escherichia coli is provided to show the effectiveness of the achieved results.