Stability Analysis of Probabilistic Boolean Networks With Switching Discrete Probability Distribution

Abstract

This article analyzes the stability of probabilistic Boolean networks (PBNs) with switching discrete probability distribution (DPD). First, the dynamics of PBNs with switching DPD is converted to an algebraic form by using the semitensor product of matrices. Second, based on the algebraic form, two essential concepts, that is, expectation of number of trajectories (ENT) and state expectation matrix, are proposed. Third, some criteria are presented for the finite-time stability and asymptotical stability of PBNs with switching DPD by resorting to the properties of ENT. Finally, two illustrative examples are worked out to show the effectiveness of the obtained new results. Computational complexity is still challenging for this article, which limits the application of ENT-based framework to large-size PBNs with switching DPD.