ALGEBRAIC APPROACH TO DYNAMICS OF MULTIVALUED NETWORKS

doi:10.1142/S0218127410025892

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	ALGEBRAIC APPROACH TO DYNAMICS OF MULTIVALUED NETWORKS
	Li, Zhiqiang; Cheng, Daizhan
	2010-03-01
发表期刊	INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
ISSN	0218-1274
卷号	20 期号:3 页码:561-582
摘要	Using semi-tensor product of matrices, a matrix expression for multivalued logic is proposed, where a logical variable is expressed as a vector, and a logical function is expressed as a multilinear mapping. Under this framework, the dynamics of a multivalued logical network is converted into a standard discrete-time linear system. Analyzing the network transition matrix, easily computable formulas are obtained to show ( a) the number of equilibriums; (b) the numbers of cycles of different lengths; ( c) transient period, the minimum time for all points to enter the set of attractors, respectively. A method to reconstruct the logical network from its network transition matrix is also presented. This approach can also be used to convert the dynamics of a multivalued control network into a discrete-time bilinear system. Then, the structure and the controllability of multivalued logical control networks are revealed.
关键词	Logical network semi-tensor product attractor transient period controllability
DOI	10.1142/S0218127410025892
语种	英语
资助项目	National Natural Science Foundation (NNSF) of China[60674022] ; National Natural Science Foundation (NNSF) of China[60736022] ; National Natural Science Foundation (NNSF) of China[60821091]
WOS研究方向	Mathematics ; Science & Technology - Other Topics
WOS类目	Mathematics, Interdisciplinary Applications ; Multidisciplinary Sciences
WOS记录号	WOS:000279238400001
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11101
专题	系统科学研究所
通讯作者	Li, Zhiqiang
作者单位	Chinese Acad Sci, AMSS, Key Lab Syst & Control, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Zhiqiang,Cheng, Daizhan. ALGEBRAIC APPROACH TO DYNAMICS OF MULTIVALUED NETWORKS[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,2010,20(3):561-582.
APA	Li, Zhiqiang,&Cheng, Daizhan.(2010).ALGEBRAIC APPROACH TO DYNAMICS OF MULTIVALUED NETWORKS.INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,20(3),561-582.
MLA	Li, Zhiqiang,et al."ALGEBRAIC APPROACH TO DYNAMICS OF MULTIVALUED NETWORKS".INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 20.3(2010):561-582.