Stability and stabilization of Boolean networks

The stability of Boolean networks and the stabilization of Boolean control networks are investigated. Using semi‐tensor product of matrices and the matrix expression of logic, the dynamics of a Boolean (control) network can be converted to a discrete time linear (bilinear) dynamics, called the algeb...

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Bibliographic Details
Published inInternational journal of robust and nonlinear control Vol. 21; no. 2; pp. 134 - 156
Main Authors Cheng, Daizhan, Qi, Hongsheng, Li, Zhiqiang, Liu, Jiang B.
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 25.01.2011
Subjects
Algebra
Boolean (control) system
Boolean algebra
Discrete time systems
Logic
Networks
Nonlinear dynamics
semi-tensor product of matrices
Stability
Stabilization
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Summary:The stability of Boolean networks and the stabilization of Boolean control networks are investigated. Using semi‐tensor product of matrices and the matrix expression of logic, the dynamics of a Boolean (control) network can be converted to a discrete time linear (bilinear) dynamics, called the algebraic form of the Boolean (control) network. Then the stability can be revealed by analyzing the transition matrix of the corresponding discrete time system. Main results consist of two parts: (i) Using logic coordinate transformation, the known sufficient condition based on incidence matrix has been improved. It can also be used in stabilizer design. (ii) Based on algebraic form, necessary and sufficient conditions for stability and stabilization, respectively, are obtained. Copyright © 2010 John Wiley & Sons, Ltd.
Bibliography:NNSF - No. 60674022; No. 60736022; No. 60821091
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ArticleID:RNC1581
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content type line 23
ISSN:1049-8923
1099-1239
1099-1239
DOI:10.1002/rnc.1581