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Structural stability analysis of gene regulatory networks modeled by Boolean networks. (English) Zbl 1414.37016

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.

MSC:

37C75 Stability theory for smooth dynamical systems
34D30 Structural stability and analogous concepts of solutions to ordinary differential equations
92C42 Systems biology, networks
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