State-space analysis of Boolean networks.
This paper provides a comprehensive framework for the state-space approach to Boolean networks. First, it surveys the authors' recent work 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.
Cheng
Daizhan
D
Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China. dcheng@iss.ac.cn
Qi
Hongsheng
H
D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D006801:Humans; D016015:Logistic Models; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D013997:Time Factors