Stability analysis of probabilistic Boolean networks with switching topology

• Published in: Nonlinear analysis. Hybrid systems Vol. 42; p. 101076
• Main Authors: Zhang, Qingle, Feng, Jun-e, Wang, Biao
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2021
• Subjects: Probabilistic Boolean networks; Set reachability; Set stability; Switching topology; The largest invariant set family; Probabilistic Boolean networks; Switching topology; Set stability; Set reachability; The largest invariant set family
• ISSN: 1751-570X
• DOI: 10.1016/j.nahs.2021.101076

This paper investigates the set stability of probabilistic Boolean networks (PBNs) with switching topology. To deal with this problem, two novel concepts, set reachability and the largest invariant set family, are defined. By constructing an auxiliary system, the necessary and sufficient conditions for verifying set reachability are given and the calculation method for the largest invariant set family is obtained. Based on these two results, an equivalent condition of set stability is derived, which can be used to determine whether a PBN with switching topology can be stabilized to a given set. In addition, the design method of switching signal is proposed by combining the characteristic of the largest invariant set family, and a numerical example is reported to demonstrate the efficiency of presented approach.