{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,20]],"date-time":"2024-07-20T16:56:43Z","timestamp":1721494603615},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2013,8]]},"abstract":"<jats:p> This paper is devoted to the synchronization of a dynamical system defined by two different coupling versions of two identical piecewise linear bimodal maps. We consider both local and global studies, using different tools as natural transversal Lyapunov exponent, Lyapunov functions, eigenvalues and eigenvectors and numerical simulations. We obtain theoretical results for the existence of synchronization on coupling parameter range. We characterize the synchronization manifold as an attractor and measure the synchronization speed. In one coupling version, we give a necessary and sufficient condition for the synchronization. We study the basins of synchronization and show that, depending upon the type of coupling, they can have very different shapes and are not necessarily constituted by the whole phase space; in some cases, they can be riddled. <\/jats:p>","DOI":"10.1142\/s0218127413501344","type":"journal-article","created":{"date-parts":[[2013,9,18]],"date-time":"2013-09-18T07:08:56Z","timestamp":1379488136000},"page":"1350134","source":"Crossref","is-referenced-by-count":1,"title":["SYNCHRONIZATION AND BASINS OF SYNCHRONIZED STATES IN TWO-DIMENSIONAL PIECEWISE MAPS VIA COUPLING THREE PIECES OF ONE-DIMENSIONAL MAPS"],"prefix":"10.1142","volume":"23","author":[{"given":"DANIELE","family":"FOURNIER-PRUNARET","sequence":"first","affiliation":[{"name":"LAAS-CNRS, INSA, University of Toulouse, 7 avenue du Colonel Roche, 31077 Toulouse, France"}]},{"given":"J. LEONEL","family":"ROCHA","sequence":"additional","affiliation":[{"name":"Instituto Superior de Engenharia de Lisboa, ADM and CEAUL, Rua Conselheiro Emdio Navarro 1, 1959-007 Lisboa, Portugal"}]},{"given":"ACILINA","family":"CANECO","sequence":"additional","affiliation":[{"name":"Instituto Superior de Engenharia de Lisboa, ADM and CIMA-UE, Rua Conselheiro Emdio Navarro 1, 1959-007 Lisboa, Portugal"}]},{"given":"SARA","family":"FERNANDES","sequence":"additional","affiliation":[{"name":"DMat, CIMA-UE, Universidade de \u00c9vora, Largo dos Colegiais 2, 7000 Evora, Portugal"}]},{"given":"CLARA","family":"GRACIO","sequence":"additional","affiliation":[{"name":"DMat, CIMA-UE, Universidade de \u00c9vora, Largo dos Colegiais 2, 7000 Evora, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2013,9,18]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2006.08.038"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127492000446"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/9\/3\/006"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1016\/S0370-1573(02)00137-0"},{"key":"p_5","first-page":"167","author":"Canale E.","year":"2008","journal-title":"Systems Structure and Control"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409025183"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1063\/1.2178448"},{"key":"p_9","first-page":"856","volume":"44","author":"Hasler M.","year":"1987","journal-title":"Fund. 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