{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T19:55:52Z","timestamp":1771703752959,"version":"3.50.1"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2010,3]]},"abstract":"<jats:p> 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. <\/jats:p>","DOI":"10.1142\/s0218127410025892","type":"journal-article","created":{"date-parts":[[2010,4,9]],"date-time":"2010-04-09T03:26:31Z","timestamp":1270783591000},"page":"561-582","source":"Crossref","is-referenced-by-count":98,"title":["ALGEBRAIC APPROACH TO DYNAMICS OF MULTIVALUED NETWORKS"],"prefix":"10.1142","volume":"20","author":[{"given":"ZHIQIANG","family":"LI","sequence":"first","affiliation":[{"name":"Key Laboratory of Systems and Control, AMSS, Chinese Academy of Sciences, Beijing 100190, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DAIZHAN","family":"CHENG","sequence":"additional","affiliation":[{"name":"Key Laboratory of Systems and Control, AMSS, Chinese Academy of Sciences, Beijing 100190, P. R. 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