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Results on the realization of Boolean control networks by the vertex partition method

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Abstract

Realization problems, including the minimum realization of Boolean control networks (BCNs), are investigated by the vertex partition method. A general definition of the realization for BCNs that does not involve any subspaces is proposed. For the new and existing realization definitions, by a common concolorous perfect vertex partition (CCP-VP) of vertex-colored state transition graphs, an equivalence relation and a quotient mapping are defined, which induce a quotient system, i.e., the realization of original BCNs. In addition, if the CCP-VP is an equal partition, a realization induced by a γ-friendly controlled invariant regular subspace is constructed. Finally, an algorithm is designed to construct the minimum realization of BCNs for different realization definitions, and three examples are given to illustrate the obtained results.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11991020, 11991024, 61673012, 11971240), Research Project of Chongqing National Center for Applied Mathematics (Grant No. ncamc2022-msxm05), and Chongqing Normal University Foundation (Grant No. 21XLB045).

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Authors and Affiliations

  1. National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing, 401331, China

    Yifeng Li & Xuewen Liu

  2. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

    Jiandong Zhu

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  1. Yifeng Li
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  2. Jiandong Zhu
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  3. Xuewen Liu
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Correspondence to Jiandong Zhu.

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Li, Y., Zhu, J. & Liu, X. Results on the realization of Boolean control networks by the vertex partition method. Sci. China Inf. Sci. 66, 172205 (2023). https://doi.org/10.1007/s11432-022-3607-6

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  • DOI: https://doi.org/10.1007/s11432-022-3607-6

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