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A state-flipped approach to complete synchronization of Boolean networks

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  • Du, Leihao
  • Zhang, Zhipeng
  • Xia, Chengyi

Abstract

State flipping is an effective control method that has just recently been proposed. In this paper, the state-flipped mechanism is introduced to implement the complete synchronization problem of BNs by use of the semi-tensor product (STP) of matrices. Firstly, an algebraic expression of BNs with state-flipped mechanism is constructed, and under such representation, the validation conditions for the existence of the complete synchronization of drive-response BNs are derived. Subsequently, the synchronization results with state-flipped control of the above system is further extended to more general BNs by analyzing the synchronous flip sequence. Meanwhile, some algorithms are developed to find and determine the corresponding sequence of synchronous flips and the set of minimum synchronous flips. Finally, several typical numerical examples are offered in detail to demonstrate the validity of obtained results. To sum up, the current research may further enrich and develop the study of network synchronization problem.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:443:y:2023:i:c:s0096300322008566
    DOI: 10.1016/j.amc.2022.127788
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    References listed on IDEAS

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    1. Fangfei Li, 2016. "Feedback control design for the complete synchronisation of two coupled Boolean networks," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(12), pages 2996-3003, September.
    2. 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.
    3. 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.
    4. Zhang, Zhipeng & Xia, Chengyi & Chen, Zengqiang, 2020. "On the stabilization of nondeterministic finite automata via static output feedback," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    5. Li, Fangfei & Li, Jianning & Shen, Lijuan, 2018. "State feedback controller design for the synchronization of Boolean networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1267-1276.
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    Cited by:

    1. 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).
    2. He, Zhipeng & Zhang, Shuguang & Hu, Jun & Dai, Fei, 2024. "An adaptive time series segmentation algorithm based on visibility graph and particle swarm optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 636(C).

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