State-space analysis of Boolean networks

Authors:
Daizhan Cheng;Hongsheng Qi
Affiliations:
Key Laboratory of Systems and Control, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China;Key Laboratory of Systems and Control, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China
Venue:
IEEE Transactions on Neural Networks
Year:
2010

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Abstract

This paper provides a comprehensive framework for the state-space approach to Boolean networks. First, it surveys the authors' recentwork on the topic: Using semitensor product of matrices and the matrix expression of logic, the logical dynamic equations of Boolean (control) networks can be converted into standard discrete-time dynamics. To use the state-space approach, the state space and its subspaces of a Boolean network have been carefully defined. The basis of a subspace has been constructed. Particularly, the regular subspace, Y-friendly subspace, and invariant subspace are precisely defined, and the verifying algorithms are presented. As an application, the indistinct rolling gear structure of a Boolean network is revealed.