Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control

Nan JIANG; Chi HUANG; Yao CHEN; Jürgen KURTHS

doi:10.1631/FITEE.1900447

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Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control

Special Issue on Complex Systems and Networks with Their Applications | Updated：2022-05-19

- Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control
- 带状态反馈控制的概率布尔网络上基于互模拟的稳定性研究
- Frontiers of Information Technology & Electronic Engineering Vol. 21, Issue 2, Pages: 268-303(2020)
- Affiliations：
  
  School of Economic Information Engineering, Southwestern University of Finance and Economics, Chengdu 611130, China
  School of Mathematics, Southeast University, Nanjing 210096, China
  Potsdam Institute for Climate Impact Research, Potsdam 14412, Germany
  Department of Physics, Humboldt-Universität zu Berlin, Berlin 12489, Germany
  Saratov State University, Saratov 410012, Russia
- Author bio：
  
  [ "JIANG Nan,E-mail:jangnan.chloe.1023@gmail.com" ]
  [ "HUANG Chi,E-mail:huangchi@swufe.edu.cn" ]
  [ "CHEN Yao,E-mail:chenyao@swufe.edu.cn" ]
  [ "KURTHS Jürgen,E-mail:Juergen.Kurths@pik-potsdam.de" ]
- Funds：
- DOI：10.1631/FITEE.1900447
  CLC： TP13
- Received：29 August 2019，
  
  Revised：2019-12-11，
  
  Published：2020-02
- Accepted：
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Nan JIANG, Chi HUANG, Yao CHEN, et al. Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(2): 268-303.
DOI：

Nan JIANG, Chi HUANG, Yao CHEN, et al. Bisimulation-based stabilization of probabilistic Boolean control networks with state feedback control[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(2): 268-303. DOI： 10.1631/FITEE.1900447.

摘要

研究具有状态反馈控制的概率布尔控制网络。为降低计算复杂度，定义一种新的互模拟概率布尔控制网络。为更好理解概率布尔控制网络之间的互模拟关系，使用一种半张量积的强大矩阵运算。由于网络稳定至关重要，考虑互模拟概率布尔控制网络之间的1-概率稳定传播，并证明可行性。如果两个概率布尔控制网络之间匹配互模拟关系，则它们的过渡阶段（实现稳定的最大步骤数）被证明相同。之后，将结果推广到概率布尔网络。

Abstract

This study is concerned with probabilistic Boolean control networks (PBCNs) with state feedback control. A novel definition of bisimilar PBCNs is proposed to lower computational complexity. To understand more on bisimulation relations between PBCNs

we resort to a powerful matrix manipulation called semi-tensor product (STP). Because stabilization of networks is of critical importance

the propagation of stabilization with probability one between bisimilar PBCNs is then considered and proved to be attainable. Additionally

the transient periods (the maximum number of steps to implement stabilization) of two PBCNs are certified to be identical if these two networks are paired with a bisimulation relation. The results are then extended to the probabilistic Boolean networks.

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Keywords

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