{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T01:23:38Z","timestamp":1773797018696,"version":"3.50.1"},"reference-count":24,"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":[[2009,11]]},"abstract":"<jats:p> In this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the unidirectional and bidirectional coupled identical chaotic Duffing equations is given. We discuss the complete synchronization of two identical double-well Duffing oscillators, from the point of view of symbolic dynamics. Working with Poincar\u00e9 cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized. <\/jats:p>","DOI":"10.1142\/s0218127409025183","type":"journal-article","created":{"date-parts":[[2010,2,24]],"date-time":"2010-02-24T01:07:55Z","timestamp":1266973675000},"page":"3855-3868","source":"Crossref","is-referenced-by-count":13,"title":["TOPOLOGICAL ENTROPY IN THE SYNCHRONIZATION OF PIECEWISE LINEAR AND MONOTONE MAPS: COUPLED DUFFING OSCILLATORS"],"prefix":"10.1142","volume":"19","author":[{"given":"ACILINA","family":"CANECO","sequence":"first","affiliation":[{"name":"Instituto Superior de Engenharia de Lisboa, Mathematics Unit, DEETC and CIMA-UE, Rua Conselheiro Emidio Navarro, 1, 1959-007 Lisboa, Portugal"}]},{"given":"J. LEONEL","family":"ROCHA","sequence":"additional","affiliation":[{"name":"Instituto Superior de Engenharia de Lisboa, Mathematics Unit, DEQ and CEAUL, Rua Conselheiro Emidio Navarro, 1, 1959-007 Lisboa, Portugal"}]},{"given":"CLARA","family":"GR\u00c1CIO","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Universidade de \u00c9vora and CIMA-UE, Rua Rom\u00e3o Ramalho, 59, 7000-671 \u00c9vora, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2005.01.002"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127407019111"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1070\/RM1982v037n02ABEH003915"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0370-1573(02)00137-0"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.2991\/jnmp.2008.15.s3.11"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2009.03.040"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1063\/1.2178448"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/18\/1\/023"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/9781860945229"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(01)00250-8"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406015660"},{"key":"rf13","first-page":"1","volume":"54","author":"Lampreia J. 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