Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set

Wen Liu, Shihua Fu and Jianli Zhao
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Wen Liu: Research Center of Semi-Tensor Product of Matrices, School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China
Shihua Fu: Research Center of Semi-Tensor Product of Matrices, School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China
Jianli Zhao: Research Center of Semi-Tensor Product of Matrices, School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China

Mathematics, 2021, vol. 9, issue 22, 1-20

Abstract: The traditional set stability of Boolean networks (BNs) refers to whether all the states can converge to a given state subset. Different from the existing results, the set stability investigated in this paper is whether all states in a given initial set can converge to a given destination set. This paper studies the set stability and set stabilization avoiding undesirable sets of BNs and Boolean control networks (BCNs), respectively. First, by virtue of the semi-tensor product (STP) of matrices, the dynamics of BNs avoiding a given undesirable set are established. Then, the set reachability and set stability of BNs from the initial set to destination set avoiding an undesirable set are investigated, respectively. Furthermore, the set stabilization of BCNs from the initial set to destination set avoiding a given undesirable set are investigated. Finally, a design method for finding the time optimal set stabilizer is proposed, and an example is provided to illustrate the effectiveness of the results.

Keywords: Boolean networks; largest invariant set; semi-tensor product of matrices; set stability; set stabilization; state constraint (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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