Liang, Shuang; Zhao, Guodong; Li, Haitao; Ding, Xueying Structural stability analysis of gene regulatory networks modeled by Boolean networks. (English) Zbl 1414.37016 Math. Methods Appl. Sci. 42, No. 7, 2221-2230 (2019). Summary: This paper studies the structural monostability and structural cycle-stability of Boolean networks (BNs). Firstly, the structural-equivalent Boolean networks are converted to the algebraic forms by using the semitensor product of matrices. Secondly, the concepts of structural monostability and structural cycle-stability for Boolean networks are proposed. On the basis of the algebraic forms of structural-equivalent Boolean networks, some necessary and sufficient conditions are presented for the structural monostability and structural cycle-stability of Boolean networks. Finally, an illustrative example is worked out to show the effectiveness of the obtained results. Cited in 11 Documents MSC: 37C75 Stability theory for smooth dynamical systems 34D30 Structural stability and analogous concepts of solutions to ordinary differential equations 92C42 Systems biology, networks Keywords:Boolean networks; semitensor product of matrices; structural cycle-stability; structural monostability PDFBibTeX XMLCite \textit{S. Liang} et al., Math. Methods Appl. Sci. 42, No. 7, 2221--2230 (2019; Zbl 1414.37016) Full Text: DOI