{"id":"https://openalex.org/W2070766239","doi":"https://doi.org/10.1142/s0218127405014155","title":"CHAOTIC ATTRACTOR IN THE KURAMOTO MODEL","display_name":"CHAOTIC ATTRACTOR IN THE KURAMOTO MODEL","publication_year":2005,"publication_date":"2005-11-01","ids":{"openalex":"https://openalex.org/W2070766239","doi":"https://doi.org/10.1142/s0218127405014155","mag":"2070766239"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127405014155","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405014155","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053401102","display_name":"Yuri Maistrenko","orcid":"https://orcid.org/0000-0003-4683-7407"},"institutions":[{"id":"https://openalex.org/I190444043","display_name":"Institute of Mathematics","ror":"https://ror.org/04q3mp532","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I190444043"]}],"countries":["UA"],"is_corresponding":true,"raw_author_name":"YURI L. MAISTRENKO","raw_affiliation_strings":["Institute of Mathematics, Academy of Sciences of Ukraine, 01601 Kyiv, Ukraine","Institute of Medicine and Virtual Institute of Neuromodulation, Research Centre J\u00fclich, 52425 J\u00fclich, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Academy of Sciences of Ukraine, 01601 Kyiv, Ukraine","institution_ids":["https://openalex.org/I190444043"]},{"raw_affiliation_string":"Institute of Medicine and Virtual Institute of Neuromodulation, Research Centre J\u00fclich, 52425 J\u00fclich, Germany","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009674935","display_name":"Oleksandr V. Popovych","orcid":"https://orcid.org/0000-0001-9994-1764"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"OLEKSANDR V. POPOVYCH","raw_affiliation_strings":["Institute of Medicine and Virtual Institute of Neuromodulation, Research Centre J\u00fclich, 52425 J\u00fclich, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Medicine and Virtual Institute of Neuromodulation, Research Centre J\u00fclich, 52425 J\u00fclich, Germany","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078406508","display_name":"Peter A. Tass","orcid":"https://orcid.org/0000-0002-5736-7415"},"institutions":[{"id":"https://openalex.org/I4210153755","display_name":"University Hospital Cologne","ror":"https://ror.org/05mxhda18","country_code":"DE","type":"healthcare","lineage":["https://openalex.org/I4210153755"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"PETER A. TASS","raw_affiliation_strings":["Department of Stereotaxic and Functional Neurosurgery, University Hospital, 50924 Cologne, Germany","Institute of Medicine and Virtual Institute of Neuromodulation, Research Centre J\u00fclich, 52425 J\u00fclich, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Stereotaxic and Functional Neurosurgery, University Hospital, 50924 Cologne, Germany","institution_ids":["https://openalex.org/I4210153755"]},{"raw_affiliation_string":"Institute of Medicine and Virtual Institute of Neuromodulation, Research Centre J\u00fclich, 52425 J\u00fclich, Germany","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5053401102"],"corresponding_institution_ids":["https://openalex.org/I190444043"],"apc_list":null,"apc_paid":null,"fwci":0.8207,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.7862155,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"15","issue":"11","first_page":"3457","last_page":"3466"},"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/T13362","display_name":"Slime Mold and Myxomycetes Research","score":0.9322999715805054,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/kuramoto-model","display_name":"Kuramoto model","score":0.836100161075592},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.8118816614151001},{"id":"https://openalex.org/keywords/quasiperiodic-function","display_name":"Quasiperiodic function","score":0.6989641189575195},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6714053153991699},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.6263511776924133},{"id":"https://openalex.org/keywords/synchronization-of-chaos","display_name":"Synchronization of chaos","score":0.6170023083686829},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.58746337890625},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5812949538230896},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.56248539686203},{"id":"https://openalex.org/keywords/control-of-chaos","display_name":"Control of chaos","score":0.5344772934913635},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.5326805710792542},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.5324545502662659},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4914284944534302},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4900447130203247},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4396653473377228},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3122885227203369},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.2486189603805542},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24390408396720886},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.21509850025177002},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.177361398935318},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08001747727394104}],"concepts":[{"id":"https://openalex.org/C2780042749","wikidata":"https://www.wikidata.org/wiki/Q604374","display_name":"Kuramoto model","level":4,"score":0.836100161075592},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.8118816614151001},{"id":"https://openalex.org/C55637507","wikidata":"https://www.wikidata.org/wiki/Q5870963","display_name":"Quasiperiodic function","level":2,"score":0.6989641189575195},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6714053153991699},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.6263511776924133},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.6170023083686829},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.58746337890625},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5812949538230896},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.56248539686203},{"id":"https://openalex.org/C95518870","wikidata":"https://www.wikidata.org/wiki/Q49315702","display_name":"Control of chaos","level":5,"score":0.5344772934913635},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.5326805710792542},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.5324545502662659},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4914284944534302},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4900447130203247},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4396653473377228},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3122885227203369},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2486189603805542},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24390408396720886},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.21509850025177002},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.177361398935318},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08001747727394104},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127405014155","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405014155","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:juser.fz-juelich.de:14750","is_oa":false,"landing_page_url":"http://juser.fz-juelich.de/search?p=id:%22PreJuSER-14750%22","pdf_url":null,"source":{"id":"https://openalex.org/S4306401090","display_name":"JuSER (Forschungszentrum J\u00fclich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I171892758","host_organization_name":"Forschungszentrum J\u00fclich","host_organization_lineage":["https://openalex.org/I171892758"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International journal of bifurcation and chaos (IJBC) 15, 3457 - 3466 (2005). doi:10.1142/S0218127405014155","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.6800000071525574,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W91152030","https://openalex.org/W111157985","https://openalex.org/W161994494","https://openalex.org/W1577873058","https://openalex.org/W1988922563","https://openalex.org/W1992406658","https://openalex.org/W2011287669","https://openalex.org/W2012668406","https://openalex.org/W2017102422","https://openalex.org/W2023379985","https://openalex.org/W2031464967","https://openalex.org/W2043635613","https://openalex.org/W2050316820","https://openalex.org/W2053596424","https://openalex.org/W2069032592","https://openalex.org/W2086195341","https://openalex.org/W2088678566","https://openalex.org/W2093120175","https://openalex.org/W2130518506","https://openalex.org/W2141575246","https://openalex.org/W2164727176","https://openalex.org/W2186321983","https://openalex.org/W2973869319","https://openalex.org/W4256319244"],"related_works":["https://openalex.org/W2148938960","https://openalex.org/W2029156903","https://openalex.org/W2075700314","https://openalex.org/W2291981741","https://openalex.org/W1975119414","https://openalex.org/W2070766239","https://openalex.org/W655927367","https://openalex.org/W4308145566","https://openalex.org/W2386717867","https://openalex.org/W3104865783"],"abstract_inverted_index":{"The":[0,53],"Kuramoto":[1,25,47,83],"model":[2,26,48,84],"of":[3,30,35,59],"globally":[4],"coupled":[5],"phase":[6,104],"oscillators":[7],"is":[8,57,89],"an":[9],"essentially":[10],"nonlinear":[11],"dynamical":[12,37],"system":[13],"with":[14,92],"a":[15,41],"rich":[16],"dynamics":[17],"including":[18],"synchronization":[19],"and":[20,32,49,112],"chaos.":[21],"We":[22,39,77,97],"study":[23,50],"the":[24,28,45,60,82,85,93,99],"from":[27],"standpoint":[29],"bifurcation":[31,101],"chaos":[33,65,88],"theory":[34],"low-dimensional":[36],"systems.":[38],"find":[40],"chaotic":[42],"attractor":[43],"in":[44,81,90],"four-dimensional":[46],"its":[51,75],"origin.":[52],"torus":[54,94],"destruction":[55,95],"scenario":[56],"one":[58],"major":[61],"mechanisms":[62],"by":[63],"which":[64],"arises.":[66],"L.":[67],"P.":[68],"Shilnikov":[69],"has":[70],"made":[71],"decisive":[72],"contributions":[73],"to":[74,87],"discovery.":[76],"show":[78],"also":[79],"that":[80],"transition":[86],"accordance":[91],"scenario.":[96],"present":[98],"general":[100],"diagram":[102],"containing":[103],"chaos,":[105],"Cherry":[106],"flow":[107],"as":[108,110],"well":[109],"periodic":[111],"quasiperiodic":[113],"dynamics.":[114]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}