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Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set

Author

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  • Wen Liu

    (Research Center of Semi-Tensor Product of Matrices, School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China)

  • Shihua Fu

    (Research Center of Semi-Tensor Product of Matrices, School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China)

  • Jianli Zhao

    (Research Center of Semi-Tensor Product of Matrices, School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China)

Abstract

The traditional set stability of Boolean networks (BNs) refers to whether all the states can converge to a given state subset. Different from the existing results, the set stability investigated in this paper is whether all states in a given initial set can converge to a given destination set. This paper studies the set stability and set stabilization avoiding undesirable sets of BNs and Boolean control networks (BCNs), respectively. First, by virtue of the semi-tensor product (STP) of matrices, the dynamics of BNs avoiding a given undesirable set are established. Then, the set reachability and set stability of BNs from the initial set to destination set avoiding an undesirable set are investigated, respectively. Furthermore, the set stabilization of BCNs from the initial set to destination set avoiding a given undesirable set are investigated. Finally, a design method for finding the time optimal set stabilizer is proposed, and an example is provided to illustrate the effectiveness of the results.

Suggested Citation

  • Wen Liu & Shihua Fu & Jianli Zhao, 2021. "Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set," Mathematics, MDPI, vol. 9(22), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2864-:d:676773
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    References listed on IDEAS

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    1. Li, Yalu & Li, Haitao & Li, Yuanyuan, 2021. "Constrained set controllability of logical control networks with state constraints and its applications," Applied Mathematics and Computation, Elsevier, vol. 405(C).
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    Cited by:

    1. 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).
    2. Hongfeng Guo & Bing Xing & Ziwei Ming & Jun-E Feng, 2022. "Algebraic Representation of Topologies on a Finite Set," Mathematics, MDPI, vol. 10(7), pages 1-11, April.
    3. Wang, Jianjun & Liu, Wen & Fu, Shihua & Xia, Jianwei, 2022. "On robust set stability and set stabilization of probabilistic Boolean control networks," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    4. Qilong Sun & Haitao Li, 2022. "Robust Stabilization of Impulsive Boolean Control Networks with Function Perturbation," Mathematics, MDPI, vol. 10(21), pages 1-12, October.

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