期刊
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
卷 20, 期 3, 页码 561-582出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127410025892
关键词
Logical network; semi-tensor product; attractor; transient period; controllability
资金
- National Natural Science Foundation (NNSF) of China [60674022, 60736022, 60821091]
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.
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