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Stability analysis of Boolean networks: An eigenvalue approach

Author

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  • Ji, Hankang
  • Li, Yuanyuan
  • Ding, Xueying
  • Alghamdi, Sultan M.
  • Lu, Jianquan

Abstract

This article investigates the stability of probabilistic Boolean networks (PBNs) and switched Boolean networks (SBNs). To begin with, a unique Boolean network is presented with both stochastic signal and switching signal. It is then converted to algebraic form using semi-tensor product. An important concept named “existed path” is proposed, and further a novel method based on eigenvalue and trace-based method is used to derive some necessary and sufficient stability criteria for the first time. Moreover, these criteria are extended to include ordinary PBNs and SBNs. Finally, several examples are given to illustrate the main results.

Suggested Citation

  • Ji, Hankang & Li, Yuanyuan & Ding, Xueying & Alghamdi, Sultan M. & Lu, Jianquan, 2024. "Stability analysis of Boolean networks: An eigenvalue approach," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    • Handle: RePEc:eee:apmaco:v:463:y:2024:i:c:s0096300323005301
    DOI: 10.1016/j.amc.2023.128361
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    References listed on IDEAS

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    1. Gao, Bo & Deng, Zheng-hong & Zhao, Da-wei & Song, Qun, 2017. "State analysis of Boolean control networks with impulsive and uncertain disturbances," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 187-192.
    2. Dai, Shaoyu & Li, Bowen & Lu, Jianquan & Zhong, Jie & Liu, Yang, 2023. "A unified transform method for general robust property of probabilistic Boolean control networks," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    3. Du, Leihao & Zhang, Zhipeng & Xia, Chengyi, 2023. "A state-flipped approach to complete synchronization of Boolean networks," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    4. Li, Haitao & Xu, Xiaojing & Ding, Xueying, 2019. "Finite-time stability analysis of stochastic switched boolean networks with impulsive effect," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 557-565.
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