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Function perturbation impact on stability in distribution of probabilistic Boolean networks

Author

Listed:
  • Li, Xiaodong
  • Li, Haitao
  • Li, Yalu
  • Yang, Xinrong

Abstract

In practical gene regulatory networks, function perturbation often occurs due to gene mutation. This paper studies the function perturbation impact on the stability and set stability in distribution of probabilistic Boolean networks (PBNs) by using the semi-tensor product of matrices. Firstly, the stability and set stability in distribution of PBNs is recalled and the function perturbation problem is formulated. Secondly, when a given PBN is stable at an equilibrium (or a set) in distribution, based on the transition probability matrix and reachable set with positive probability, some necessary and sufficient conditions are presented to guarantee that the PBN is still stable at an equilibrium (or a set) in distribution after function perturbation. Finally, illustrative examples are worked out to support the obtained new results.

Suggested Citation

  • Li, Xiaodong & Li, Haitao & Li, Yalu & Yang, Xinrong, 2020. "Function perturbation impact on stability in distribution of probabilistic Boolean networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 1-12.
    • Handle: RePEc:eee:matcom:v:177:y:2020:i:c:p:1-12
    DOI: 10.1016/j.matcom.2020.04.008
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    References listed on IDEAS

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    1. Ironi, Liliana & Tran, Diana X., 2016. "Nonlinear and temporal multiscale dynamics of gene regulatory networks: A qualitative simulator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 125(C), pages 15-37.
    2. Socha, Leslaw & Zhu, Quanxin, 2019. "Exponential stability with respect to part of the variables for a class of nonlinear stochastic systems with Markovian switchings," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 2-14.
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    Cited by:

    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).
    2. Qilong Sun & Haitao Li, 2022. "Robust Stabilization of Impulsive Boolean Control Networks with Function Perturbation," Mathematics, MDPI, vol. 10(21), pages 1-12, October.
    3. Xiangshan Kong & Qilong Sun & Haitao Li, 2022. "Survey on Mathematical Models and Methods of Complex Logical Dynamical Systems," Mathematics, MDPI, vol. 10(20), pages 1-17, October.

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