Premium
Stability and stabilization of Boolean networks
Author(s) -
Cheng Daizhan,
Qi Hongsheng,
Li Zhiqiang,
Liu Jiang B.
Publication year - 2011
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1581
Subject(s) - boolean network , algebraic number , mathematics , bilinear transform , matrix (chemical analysis) , product term , stability (learning theory) , boolean algebra , transformation (genetics) , discrete mathematics , boolean function , two element boolean algebra , algebra over a field , computer science , pure mathematics , algebra representation , mathematical analysis , digital filter , biochemistry , materials science , chemistry , filter (signal processing) , machine learning , gene , composite material , computer vision
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.