Function perturbation impact on asymptotical stability of probabilistic Boolean networks: Changing to finite-time stability

摘要

Asymptotical stability is a special property of probabilistic Boolean networks (PBNs) comparing with deterministic Boolean networks which are always finite-time stable. This paper analyzes the influence of deterministic function perturbation on the asymptotical stability of PBNs. Firstly, the stability of PBNs is recalled and the concepts of positive-probability fixed point and positive-probability cycle are given. Secondly, the topological structure of asymptotically stable PBNs is analyzed, based on which, some criteria are proposed to guarantee that an asymptotically stable PBN changes to finite-time stability with probability one (FTSPO) subject to function perturbation. Finally, the results are applied to the lac operon in the Escherichia coli. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.