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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Autores principales:	Wen Liu, Shihua Fu, Jianli Zhao
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Boolean networks largest invariant set semi-tensor product of matrices set stability set stabilization state constraint Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/f6c756126ef04f1d9619111831e08614
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spelling	oai:doaj.org-article:f6c756126ef04f1d9619111831e086142021-11-25T18:16:41ZSet Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set10.3390/math92228642227-7390https://doaj.org/article/f6c756126ef04f1d9619111831e086142021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2864https://doaj.org/toc/2227-7390The 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.Wen LiuShihua FuJianli ZhaoMDPI AGarticleBoolean networkslargest invariant setsemi-tensor product of matricesset stabilityset stabilizationstate constraintMathematicsQA1-939ENMathematics, Vol 9, Iss 2864, p 2864 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Boolean networks largest invariant set semi-tensor product of matrices set stability set stabilization state constraint Mathematics QA1-939
spellingShingle	Boolean networks largest invariant set semi-tensor product of matrices set stability set stabilization state constraint Mathematics QA1-939 Wen Liu Shihua Fu Jianli Zhao Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set
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.
format	article
author	Wen Liu Shihua Fu Jianli Zhao
author_facet	Wen Liu Shihua Fu Jianli Zhao
author_sort	Wen Liu
title	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_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_sort	set stability and set stabilization of boolean control networks avoiding undesirable set
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/f6c756126ef04f1d9619111831e08614
work_keys_str_mv	AT wenliu setstabilityandsetstabilizationofbooleancontrolnetworksavoidingundesirableset AT shihuafu setstabilityandsetstabilizationofbooleancontrolnetworksavoidingundesirableset AT jianlizhao setstabilityandsetstabilizationofbooleancontrolnetworksavoidingundesirableset
_version_	1718411415610458112

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

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