{"id":"https://openalex.org/W2060007300","doi":"https://doi.org/10.1137/s0036139902411132","title":"System of Phase Oscillators with Diagonalizable Interaction","display_name":"System of Phase Oscillators with Diagonalizable Interaction","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2060007300","doi":"https://doi.org/10.1137/s0036139902411132","mag":"2060007300"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139902411132","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139902411132","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","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/A5110253970","display_name":"Frank C. Hoppensteadt","orcid":null},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Frank C. Hoppensteadt","raw_affiliation_strings":["Arizona State University"],"affiliations":[{"raw_affiliation_string":"Arizona State University","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066219206","display_name":"Takashi Nishikawa","orcid":"https://orcid.org/0000-0002-2147-0242"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Takashi Nishikawa","raw_affiliation_strings":["Arizona State University"],"affiliations":[{"raw_affiliation_string":"Arizona State University","institution_ids":["https://openalex.org/I55732556"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110253970"],"corresponding_institution_ids":["https://openalex.org/I55732556"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1655353,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"63","issue":"5","first_page":"1615","last_page":"1626"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9890000224113464,"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":0.9890000224113464,"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/T12162","display_name":"Cellular Automata and Applications","score":0.930899977684021,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/diagonalizable-matrix","display_name":"Diagonalizable matrix","score":0.8422203063964844},{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.6538600325584412},{"id":"https://openalex.org/keywords/coupling-strength","display_name":"Coupling strength","score":0.567345142364502},{"id":"https://openalex.org/keywords/phase-locking","display_name":"Phase locking","score":0.5379709601402283},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.5124271512031555},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.46235191822052},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.45894303917884827},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.448454350233078},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43563351035118103},{"id":"https://openalex.org/keywords/kuramoto-model","display_name":"Kuramoto model","score":0.4135456085205078},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.4056600332260132},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.3610336184501648},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.3390599489212036},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27574580907821655},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.19255876541137695},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.1891169548034668},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.16099420189857483},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.12779894471168518},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12102389335632324}],"concepts":[{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.8422203063964844},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.6538600325584412},{"id":"https://openalex.org/C2986219828","wikidata":"https://www.wikidata.org/wiki/Q1193095","display_name":"Coupling strength","level":2,"score":0.567345142364502},{"id":"https://openalex.org/C2989183493","wikidata":"https://www.wikidata.org/wiki/Q2040587","display_name":"Phase locking","level":3,"score":0.5379709601402283},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.5124271512031555},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.46235191822052},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.45894303917884827},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.448454350233078},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43563351035118103},{"id":"https://openalex.org/C2780042749","wikidata":"https://www.wikidata.org/wiki/Q604374","display_name":"Kuramoto model","level":4,"score":0.4135456085205078},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4056600332260132},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3610336184501648},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3390599489212036},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27574580907821655},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.19255876541137695},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.1891169548034668},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.16099420189857483},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.12779894471168518},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12102389335632324},{"id":"https://openalex.org/C191897082","wikidata":"https://www.wikidata.org/wiki/Q11467","display_name":"Metallurgy","level":1,"score":0.0},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139902411132","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139902411132","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W111157985","https://openalex.org/W1508775032","https://openalex.org/W1551791849","https://openalex.org/W1574092249","https://openalex.org/W1577873058","https://openalex.org/W1992406658","https://openalex.org/W2018314770","https://openalex.org/W2020534123","https://openalex.org/W2027564420","https://openalex.org/W2027866240","https://openalex.org/W2035538683","https://openalex.org/W2036655194","https://openalex.org/W2039977592","https://openalex.org/W2048419276","https://openalex.org/W2058522416","https://openalex.org/W2112332687","https://openalex.org/W2130518506","https://openalex.org/W2149525340","https://openalex.org/W2169071224","https://openalex.org/W2489872516","https://openalex.org/W2739614167","https://openalex.org/W3003193617","https://openalex.org/W4213230606","https://openalex.org/W4254303229"],"related_works":["https://openalex.org/W3165160669","https://openalex.org/W2769053611","https://openalex.org/W2074983995","https://openalex.org/W4287177413","https://openalex.org/W1983011554","https://openalex.org/W2069914481","https://openalex.org/W2470945791","https://openalex.org/W1619769310","https://openalex.org/W3105267206","https://openalex.org/W4386203106"],"abstract_inverted_index":{"We":[0,19],"consider":[1],"a":[2,33],"system":[3,34],"of":[4,25,31,43],"N":[5],"phase":[6],"oscillators":[7],"having":[8],"randomly":[9],"distributed":[10],"natural":[11],"frequencies":[12],"and":[13],"diagonalizable":[14],"interactions":[15],"among":[16],"the":[17,23,58],"oscillators.":[18],"show":[20],"that,":[21],"in":[22,63],"limit":[24],"$N":[26],"\\to":[27],"\\infty$,":[28],"all":[29],"solutions":[30],"such":[32],"are":[35],"incoherent":[36],"with":[37],"probability":[38],"one":[39],"for":[40],"any":[41],"strength":[42,60],"coupling,":[44],"which":[45],"implies":[46],"that":[47],"there":[48],"is":[49,61],"no":[50],"sharp":[51],"transition":[52],"from":[53],"incoherence":[54],"to":[55,66],"coherence":[56],"as":[57],"coupling":[59],"increased,":[62],"striking":[64],"contrast":[65],"Kuramoto's":[67],"(special)":[68],"oscillator":[69],"system.":[70]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}