Function perturbation impact on stability in distribution of probabilistic Boolean networks

Abstract

In practical gene regulatory networks, function perturbation often occurs due to gene mutation. This paper studies the function perturbation impact on the stability and set stability in distribution of probabilistic Boolean networks (PBNs) by using the semi-tensor product of matrices. Firstly, the stability and set stability in distribution of PBNs is recalled and the function perturbation problem is formulated. Secondly, when a given PBN is stable at an equilibrium (or a set) in distribution, based on the transition probability matrix and reachable set with positive probability, some necessary and sufficient conditions are presented to guarantee that the PBN is still stable at an equilibrium (or a set) in distribution after function perturbation. Finally, illustrative examples are worked out to support the obtained new results.