{"id":"https://openalex.org/W2025861510","doi":"https://doi.org/10.1142/s0218127413501344","title":"SYNCHRONIZATION AND BASINS OF SYNCHRONIZED STATES IN TWO-DIMENSIONAL PIECEWISE MAPS VIA COUPLING THREE PIECES OF ONE-DIMENSIONAL MAPS","display_name":"SYNCHRONIZATION AND BASINS OF SYNCHRONIZED STATES IN TWO-DIMENSIONAL PIECEWISE MAPS VIA COUPLING THREE PIECES OF ONE-DIMENSIONAL MAPS","publication_year":2013,"publication_date":"2013-08-01","ids":{"openalex":"https://openalex.org/W2025861510","doi":"https://doi.org/10.1142/s0218127413501344","mag":"2025861510"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127413501344","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413501344","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10174/9943","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031427355","display_name":"Dani\u00e8le Fournier-Prunaret","orcid":"https://orcid.org/0000-0003-0036-8932"},"institutions":[{"id":"https://openalex.org/I190497903","display_name":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes","ror":"https://ror.org/03vcm6439","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I190497903","https://openalex.org/I196454796","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210095849","https://openalex.org/I4210159245","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"DANIELE FOURNIER-PRUNARET","raw_affiliation_strings":["LAAS-CNRS, INSA, University of Toulouse, 7 avenue du Colonel Roche, 31077 Toulouse, France"],"affiliations":[{"raw_affiliation_string":"LAAS-CNRS, INSA, University of Toulouse, 7 avenue du Colonel Roche, 31077 Toulouse, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I190497903"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057211137","display_name":"J. Leonel Rocha","orcid":"https://orcid.org/0000-0001-8053-6822"},"institutions":[{"id":"https://openalex.org/I203847022","display_name":"Instituto Polit\u00e9cnico de Lisboa","ror":"https://ror.org/04ea70f07","country_code":"PT","type":"education","lineage":["https://openalex.org/I203847022"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"J. LEONEL ROCHA","raw_affiliation_strings":["Instituto Superior de Engenharia de Lisboa, ADM and CEAUL, Rua Conselheiro Emdio Navarro 1, 1959-007 Lisboa, Portugal"],"affiliations":[{"raw_affiliation_string":"Instituto Superior de Engenharia de Lisboa, ADM and CEAUL, Rua Conselheiro Emdio Navarro 1, 1959-007 Lisboa, Portugal","institution_ids":["https://openalex.org/I203847022"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012921222","display_name":"Acilina Caneco","orcid":"https://orcid.org/0000-0003-1374-5282"},"institutions":[{"id":"https://openalex.org/I203847022","display_name":"Instituto Polit\u00e9cnico de Lisboa","ror":"https://ror.org/04ea70f07","country_code":"PT","type":"education","lineage":["https://openalex.org/I203847022"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"ACILINA CANECO","raw_affiliation_strings":["Instituto Superior de Engenharia de Lisboa, ADM and CIMA-UE, Rua Conselheiro Emdio Navarro 1, 1959-007 Lisboa, Portugal"],"affiliations":[{"raw_affiliation_string":"Instituto Superior de Engenharia de Lisboa, ADM and CIMA-UE, Rua Conselheiro Emdio Navarro 1, 1959-007 Lisboa, Portugal","institution_ids":["https://openalex.org/I203847022"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083489402","display_name":"Sara Fernandes","orcid":"https://orcid.org/0000-0003-1551-0532"},"institutions":[{"id":"https://openalex.org/I21803372","display_name":"University of \u00c9vora","ror":"https://ror.org/02gyps716","country_code":"PT","type":"education","lineage":["https://openalex.org/I21803372"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"SARA FERNANDES","raw_affiliation_strings":["DMat, CIMA-UE, Universidade de \u00c9vora, Largo dos Colegiais 2, 7000 Evora, Portugal"],"affiliations":[{"raw_affiliation_string":"DMat, CIMA-UE, Universidade de \u00c9vora, Largo dos Colegiais 2, 7000 Evora, Portugal","institution_ids":["https://openalex.org/I21803372"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029251488","display_name":"Clara Gr\u00e1cio","orcid":"https://orcid.org/0000-0002-0397-5669"},"institutions":[{"id":"https://openalex.org/I21803372","display_name":"University of \u00c9vora","ror":"https://ror.org/02gyps716","country_code":"PT","type":"education","lineage":["https://openalex.org/I21803372"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"CLARA GRACIO","raw_affiliation_strings":["DMat, CIMA-UE, Universidade de \u00c9vora, Largo dos Colegiais 2, 7000 Evora, Portugal"],"affiliations":[{"raw_affiliation_string":"DMat, CIMA-UE, Universidade de \u00c9vora, Largo dos Colegiais 2, 7000 Evora, Portugal","institution_ids":["https://openalex.org/I21803372"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5031427355"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I190497903"],"apc_list":null,"apc_paid":null,"fwci":0.3625,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.64681811,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"23","issue":"08","first_page":"1350134","last_page":"1350134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.7381656169891357},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.7278290390968323},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6883422136306763},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.6251042485237122},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5498514175415039},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.54902583360672},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5244708061218262},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5154557824134827},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5070760250091553},{"id":"https://openalex.org/keywords/phase-synchronization","display_name":"Phase synchronization","score":0.49453040957450867},{"id":"https://openalex.org/keywords/synchronization-of-chaos","display_name":"Synchronization of chaos","score":0.4700447618961334},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.41824042797088623},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.385018527507782},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.2759033739566803},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22504833340644836},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20865106582641602},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.20642295479774475},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08895912766456604}],"concepts":[{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.7381656169891357},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.7278290390968323},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6883422136306763},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.6251042485237122},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5498514175415039},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.54902583360672},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5244708061218262},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5154557824134827},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5070760250091553},{"id":"https://openalex.org/C194027367","wikidata":"https://www.wikidata.org/wiki/Q4420475","display_name":"Phase synchronization","level":3,"score":0.49453040957450867},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.4700447618961334},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.41824042797088623},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.385018527507782},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2759033739566803},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22504833340644836},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20865106582641602},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.20642295479774475},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08895912766456604},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127413501344","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413501344","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:dspace.uevora.pt:10174/9943","is_oa":true,"landing_page_url":"http://hdl.handle.net/10174/9943","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"}],"best_oa_location":{"id":"pmh:oai:dspace.uevora.pt:10174/9943","is_oa":true,"landing_page_url":"http://hdl.handle.net/10174/9943","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310654","display_name":"Indian National Science Academy","ror":"https://ror.org/051475v86"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W29182310","https://openalex.org/W950991549","https://openalex.org/W1528240262","https://openalex.org/W1620414136","https://openalex.org/W1967588640","https://openalex.org/W1967958957","https://openalex.org/W1970442252","https://openalex.org/W1991545838","https://openalex.org/W1995869753","https://openalex.org/W2030308994","https://openalex.org/W2030381387","https://openalex.org/W2043122625","https://openalex.org/W2058465502","https://openalex.org/W2062063272","https://openalex.org/W2063250679","https://openalex.org/W2072210701","https://openalex.org/W2080646411","https://openalex.org/W2093627340","https://openalex.org/W2094780448","https://openalex.org/W2098331784","https://openalex.org/W2139031875","https://openalex.org/W2157500986","https://openalex.org/W2160932744","https://openalex.org/W2165468259","https://openalex.org/W2478338665","https://openalex.org/W2504229404","https://openalex.org/W3098481220","https://openalex.org/W4256560209","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2064165820","https://openalex.org/W2110498084","https://openalex.org/W2136889839","https://openalex.org/W2411553537","https://openalex.org/W2378640948","https://openalex.org/W2116440947","https://openalex.org/W2166753700","https://openalex.org/W2031541481","https://openalex.org/W2095704199","https://openalex.org/W2075475425"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2],"devoted":[3],"to":[4],"the":[5,52,62,70,85,89,98,114],"synchronization":[6,55,63,71,92],"of":[7,17,54,91,100],"a":[8,79],"dynamical":[9],"system":[10],"defined":[11],"by":[12,113],"two":[13,18],"different":[14,32,106],"coupling":[15,57,75],"versions":[16],"identical":[19],"piecewise":[20],"linear":[21],"bimodal":[22],"maps.":[23],"We":[24,47,60,87],"consider":[25],"both":[26],"local":[27],"and":[28,42,44,68,81,93,108],"global":[29],"studies,":[30],"using":[31],"tools":[33],"as":[34,65],"natural":[35],"transversal":[36],"Lyapunov":[37,39],"exponent,":[38],"functions,":[40],"eigenvalues":[41],"eigenvectors":[43],"numerical":[45],"simulations.":[46],"obtain":[48],"theoretical":[49],"results":[50],"for":[51,84],"existence":[53],"on":[56],"parameter":[58],"range.":[59],"characterize":[61],"manifold":[64],"an":[66],"attractor":[67],"measure":[69],"speed.":[72],"In":[73],"one":[74],"version,":[76],"we":[77],"give":[78],"necessary":[80],"sufficient":[82],"condition":[83],"synchronization.":[86],"study":[88],"basins":[90],"show":[94],"that,":[95],"depending":[96],"upon":[97],"type":[99],"coupling,":[101],"they":[102,121],"can":[103,122],"have":[104],"very":[105],"shapes":[107],"are":[109],"not":[110],"necessarily":[111],"constituted":[112],"whole":[115],"phase":[116],"space;":[117],"in":[118],"some":[119],"cases,":[120],"be":[123],"riddled.":[124]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
