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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| Veröffentlicht in: | International journal of control Jg. 95; H. 11; S. 3118 - 3126 |
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| Sprache: | Englisch |
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Abingdon
Taylor & Francis
02.11.2022
Taylor & Francis Ltd |
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| Abstract | 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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| AbstractList | 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. 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. |
| Author | Li, Haitao Yang, Xinrong |
| Author_xml | – sequence: 1 givenname: Xinrong surname: Yang fullname: Yang, Xinrong organization: School of Mathematics and Statistics, Shandong Normal University – sequence: 2 givenname: Haitao surname: Li fullname: Li, Haitao email: haitaoli09@gmail.com organization: School of Mathematics and Statistics, Shandong Normal University |
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| SubjectTerms | 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 |
| Title | Asymptotical stability and stabilisation of probabilistic Boolean networks subject to function perturbation |
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