On pinning reachability of probabilistic Boolean control networks

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  1. 1

    Kauffman S A. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theory Biol, 1969, 22: 437–467

    MathSciNet  Article  Google Scholar 

  2. 2

    Davidson E H. A genomic regulatory network for development. Science, 2002, 295: 1669–1678

    Article  Google Scholar 

  3. 3

    Shmulevich I, Dougherty E R, Kim S, et al. Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics, 2002, 18: 261–274

    Article  Google Scholar 

  4. 4

    Lu J Q, Li M L, Liu Y, et al. Nonsingularity of Grainlike cascade FSRs via semi-tensor product. Sci China Inf Sci, 2018, 61: 010204

    MathSciNet  Article  Google Scholar 

  5. 5

    Wang L Q, Liu Y, Wu Z G, et al. Strategy optimization for static games based on STP method. Appl Math Comput, 2018, 316: 390–399

    MathSciNet  MATH  Google Scholar 

  6. 6

    Li R, Yang M, Chu T G. State feedback stabilization for probabilistic Boolean networks. Automatica, 2014, 50: 1272–1278

    MathSciNet  Article  MATH  Google Scholar 

  7. 7

    Zhu Q X, Liu Y, Lu J Q, et al. Observability of Boolean control networks. Sci China Inf Sci, 2018, 61: 092201

    MathSciNet  Article  Google Scholar 

  8. 8

    Wu Y H, Shen T L. An algebraic expression of finite horizon optimal control algorithm for stochastic logical dynamical systems. Syst Control Lett, 2015, 82: 108–114

    MathSciNet  Article  MATH  Google Scholar 

  9. 9

    Qi H S, Cheng D Z. Analysis and control of Boolean networks: a semi-tensor product approach. In: Proceedings of the 7th Asian Control Conference, 2009

Download references


This work was supported by Zhejiang Provincial Natural Science Foundation (Grant No. LD19A010001), National Natural Science Foundation of China (Grant Nos. 11671361, 61573096, 61833005), China Postdoctoral Science Foundation (Grant Nos. 2016T90406, 2015M580378), and in part supported by Jiangsu Provincial Key Laboratory of Networked Collective Intelligence (Grant No. BM2017002).

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Correspondence to Jinde Cao.

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Liu, Y., Cao, J., Wang, L. et al. On pinning reachability of probabilistic Boolean control networks. Sci. China Inf. Sci. 63, 169201 (2020). https://doi.org/10.1007/s11432-018-9575-4

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