Stabilization and set stabilization of switched Boolean control networks via flipping mechanism. (August 2021)

• Record Type: Journal Article
• Authors: Zhang, Qiliang; Feng, Jun-e; Zhao, Ying; Zhao, Jianli
• Is Part Of: Nonlinear analysis. Volume 41(2021)
• Publication Date: 2021-08
• Subjects: Flipping nodes -- Semi-tensor product -- Set stabilization -- Stabilization -- Switched Boolean networks; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2021.101055
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: Stabilization and set stabilization of switched Boolean control networks are investigated by using flipping mechanism in this paper. Firstly, with the help of Warshall algorithm, an explicit criterion for the stabilization of switched Boolean control networks is derived. Secondly, the necessary and sufficient condition for the solvability of stabilization of switched Boolean control networks, by flipping some elements of perturbation set once, is presented. Thirdly, a search algorithm is proposed to calculate the minimum number of stabilization flipped nodes and what exactly they are. Furthermore, a necessary and sufficient condition is established for the solvability of set stabilization of switched Boolean control networks by flipping some elements of perturbation set once. Analogously, an algorithm is given to find the minimum number of set stabilization flipped nodes. Finally, examples are shown to demonstrate the feasibility of the above results. Highlights: An explicit criterion for the stabilization of switched Boolean control networks is derived. Necessary and sufficient condition for the stabilization of switched Boolean control networks, by flipping some elements of perturbation set once, is presented. A search algorithm is proposed to calculate the minimum number of stabilization flipped nodes and what exactly they are. A necessary and sufficient condition is established for the set stabilization of switched Boolean control networks by flipping some elements of perturbation set once. An algorithm is given to find the minimum number of set stabilization flipped nodes.