References
Kauffman S A. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theory Biol, 1969, 22: 437–467
Davidson E H. A genomic regulatory network for development. Science, 2002, 295: 1669–1678
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
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
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
Li R, Yang M, Chu T G. State feedback stabilization for probabilistic Boolean networks. Automatica, 2014, 50: 1272–1278
Zhu Q X, Liu Y, Lu J Q, et al. Observability of Boolean control networks. Sci China Inf Sci, 2018, 61: 092201
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
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
Acknowledgements
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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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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DOI: https://doi.org/10.1007/s11432-018-9575-4