Asymptotical stability and stabilisation of probabilistic Boolean networks subject to function perturbation

This paper focuses on the effects of function perturbation for probabilistic Boolean networks (PBNs), including asymptotical stability and stabilisation. Firstly, by constructing a proper set, a necessary and sufficient condition is presented for the asymptotically stable PBN being stable in distrib...

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Bibliographic Details
Published in:International journal of control Vol. 95; no. 11; pp. 3118 - 3126
Main Authors: Yang, Xinrong, Li, Haitao
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.11.2022
Taylor & Francis Ltd
Subjects:
algebraic state space representation
Asymptotic properties
asymptotical stabilisation
asymptotical stability
Boolean functions
function perturbation
Mathematical analysis
Networks
Perturbation
Probabilistic Boolean network
Probability theory
Stability criteria
Statistical analysis
ISSN:0020-7179, 1366-5820
Online Access:Get full text
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Summary:This paper focuses on the effects of function perturbation for probabilistic Boolean networks (PBNs), including asymptotical stability and stabilisation. Firstly, by constructing a proper set, a necessary and sufficient condition is presented for the asymptotically stable PBN being stable in distribution after function perturbation. Secondly, by removing the case of changing to finite-time stability with probability one from the case of changing to stability in distribution, some criteria are given for the asymptotically stable PBN keeping asymptotically stable after function perturbation. These criteria need to calculate the number of positive-probability cycles. In order to simplify the calculation, two sufficient conditions are further established. Finally, as an application, the robustness of asymptotical feedback stabilisers is further studied for probabilistic Boolean control networks subject to function perturbation.
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ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2021.1955977