{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:23:56Z","timestamp":1772292236789,"version":"3.50.1"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2010,11]]},"abstract":"<jats:p> In this paper, strictly A-coupled-expanding maps in bounded and closed subsets of complete metric spaces are investigated, where A = (a<jats:sub>ij<\/jats:sub>) is an m \u00d7 m irreducible transition matrix with one row-sum no less than 2. A map f is said to be strictly A-coupled-expanding in m sets V<jats:sub>i<\/jats:sub> if f(V<jats:sub>i<\/jats:sub>) \u2283 V<jats:sub>j<\/jats:sub> whenever a<jats:sub>ij<\/jats:sub> = 1 and the distance between any two different sets of these V<jats:sub>i<\/jats:sub> is positive. A new result on the subshift for matrix A is obtained. Based on this result, two criteria of chaos are established, which generalize and relax the conditions of some existing results. These maps are proved to be chaotic either in the sense of both Li\u2013Yorke and Wiggins or in the sense of both Li\u2013Yorke and Devaney. One example is provided to illustrate the theoretical results with a computer simulation for demonstration. <\/jats:p>","DOI":"10.1142\/s0218127410028094","type":"journal-article","created":{"date-parts":[[2010,12,9]],"date-time":"2010-12-09T03:41:40Z","timestamp":1291866100000},"page":"3769-3783","source":"Crossref","is-referenced-by-count":17,"title":["COUPLED-EXPANDING MAPS FOR IRREDUCIBLE TRANSITION MATRICES"],"prefix":"10.1142","volume":"20","author":[{"given":"XU","family":"ZHANG","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China"}]},{"given":"YUMING","family":"SHI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.2307\/2324899"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0086977"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0084762"},{"key":"rf4","volume-title":"An Introduction to Chaotic Dynamical Systems","author":"Devaney R. L.","year":"1989"},{"key":"rf5","volume-title":"The Theory of Matrices","author":"Gantmacher F. R.","year":"1959"},{"key":"rf6","first-page":"27","volume":"4","author":"Hadamard J.","journal-title":"J. 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