Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set
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...
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| Format: | Article |
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MDPI AG
2021-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/22/2864 |
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| author | Wen Liu Shihua Fu Jianli Zhao |
| author_facet | Wen Liu Shihua Fu Jianli Zhao |
| author_sort | Wen Liu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T05:19:19Z |
| format | Article |
| id | doaj.art-f6c756126ef04f1d9619111831e08614 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:19:19Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f6c756126ef04f1d9619111831e086142023-11-23T00:14:10ZengMDPI AGMathematics2227-73902021-11-01922286410.3390/math9222864Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable SetWen Liu0Shihua Fu1Jianli Zhao2Research Center of Semi-Tensor Product of Matrices, School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, ChinaResearch Center of Semi-Tensor Product of Matrices, School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, ChinaResearch Center of Semi-Tensor Product of Matrices, School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, ChinaThe 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.https://www.mdpi.com/2227-7390/9/22/2864Boolean networkslargest invariant setsemi-tensor product of matricesset stabilityset stabilizationstate constraint |
| spellingShingle | Wen Liu Shihua Fu Jianli Zhao Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set Mathematics Boolean networks largest invariant set semi-tensor product of matrices set stability set stabilization state constraint |
| title | Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set |
| title_full | Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set |
| title_fullStr | Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set |
| title_full_unstemmed | Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set |
| title_short | Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set |
| title_sort | set stability and set stabilization of boolean control networks avoiding undesirable set |
| topic | Boolean networks largest invariant set semi-tensor product of matrices set stability set stabilization state constraint |
| url | https://www.mdpi.com/2227-7390/9/22/2864 |
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