A Linear Representation of Dynamics of Boolean Networks

doi:10.1109/TAC.2010.2043294

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	A Linear Representation of Dynamics of Boolean Networks
	Cheng, Daizhan; Qi, Hongsheng
	2010-10-01
发表期刊	IEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN	0018-9286
卷号	55 期号:10 页码:2251-2258
摘要	A new matrix product, called semi-tensor product of matrices, is reviewed. Using it, a matrix expression of logic is proposed, where a logical variable is expressed as a vector, a logical function is expressed as a multiple linear mapping. Under this framework, a Boolean network equation is converted into an equivalent algebraic form as a conventional discrete-time linear system. Analyzing the transition matrix of the linear system, formulas are obtained to show a) the number of fixed points; b) the numbers of cycles of different lengths; c) transient period, for all points to enter the set of attractors; and d) basin of each attractor. The corresponding algorithms are developed and used to some examples.
关键词	Boolean network cycle fixed point semi-tensor product transient period
DOI	10.1109/TAC.2010.2043294
语种	英语
资助项目	National Natural Science Foundation (NNSF) of China[60736022] ; National Natural Science Foundation (NNSF) of China[60821091] ; National Natural Science Foundation (NNSF) of China[SIC 07010201]
WOS研究方向	Automation & Control Systems ; Engineering
WOS类目	Automation & Control Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000283362600003
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10632
专题	系统科学研究所
通讯作者	Cheng, Daizhan
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Inst Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Cheng, Daizhan,Qi, Hongsheng. A Linear Representation of Dynamics of Boolean Networks[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,2010,55(10):2251-2258.
APA	Cheng, Daizhan,&Qi, Hongsheng.(2010).A Linear Representation of Dynamics of Boolean Networks.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,55(10),2251-2258.
MLA	Cheng, Daizhan,et al."A Linear Representation of Dynamics of Boolean Networks".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 55.10(2010):2251-2258.