{"id":"https://openalex.org/W2804979473","doi":"https://doi.org/10.3934/nhm.2018013","title":"Uniform stability and mean-field limit for the augmented Kuramoto model","display_name":"Uniform stability and mean-field limit for the augmented Kuramoto model","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2804979473","doi":"https://doi.org/10.3934/nhm.2018013","mag":"2804979473"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2018013","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2018013","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=a5e592b5-45d8-466c-b8c3-6dbdf32cd86b","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/article/exportPdf?id=a5e592b5-45d8-466c-b8c3-6dbdf32cd86b","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009809362","display_name":"Seung\u2010Yeal Ha","orcid":"https://orcid.org/0000-0002-6403-5590"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Seung-Yeal Ha","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100396225","display_name":"Jeongho Kim","orcid":"https://orcid.org/0000-0002-5220-3139"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jeongho Kim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000879537","display_name":"Jinyeong Park","orcid":"https://orcid.org/0000-0002-1390-2623"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jinyeong Park","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5049439623","display_name":"Xiongtao Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiongtao Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5009809362"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1728,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.88597379,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"13","issue":"2","first_page":"297","last_page":"322"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9812999963760376,"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"}},{"id":"https://openalex.org/T13377","display_name":"Ecosystem dynamics and resilience","score":0.9186999797821045,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/kuramoto-model","display_name":"Kuramoto model","score":0.9053527116775513},{"id":"https://openalex.org/keywords/mean-field-theory","display_name":"Mean field theory","score":0.6588847041130066},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6462550759315491},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.607003390789032},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.5817915797233582},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5632834434509277},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.48200955986976624},{"id":"https://openalex.org/keywords/vlasov-equation","display_name":"Vlasov equation","score":0.47926804423332214},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43940433859825134},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.42901840806007385},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.4056876301765442},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3643442988395691},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.29394418001174927},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08557447791099548},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08543702960014343},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.0776287317276001},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07191577553749084},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06843060255050659}],"concepts":[{"id":"https://openalex.org/C2780042749","wikidata":"https://www.wikidata.org/wiki/Q604374","display_name":"Kuramoto model","level":4,"score":0.9053527116775513},{"id":"https://openalex.org/C202213908","wikidata":"https://www.wikidata.org/wiki/Q626011","display_name":"Mean field theory","level":2,"score":0.6588847041130066},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6462550759315491},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.607003390789032},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.5817915797233582},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5632834434509277},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.48200955986976624},{"id":"https://openalex.org/C186175660","wikidata":"https://www.wikidata.org/wiki/Q2323892","display_name":"Vlasov equation","level":3,"score":0.47926804423332214},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43940433859825134},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.42901840806007385},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.4056876301765442},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3643442988395691},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29394418001174927},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08557447791099548},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08543702960014343},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.0776287317276001},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07191577553749084},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06843060255050659},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/nhm.2018013","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2018013","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=a5e592b5-45d8-466c-b8c3-6dbdf32cd86b","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:206fe80d5abb4220897600e662830958","is_oa":false,"landing_page_url":"https://doaj.org/article/206fe80d5abb4220897600e662830958","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 13, Iss 2, Pp 297-322 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2018013","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2018013","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=a5e592b5-45d8-466c-b8c3-6dbdf32cd86b","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2804979473.pdf","grobid_xml":"https://content.openalex.org/works/W2804979473.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W111157985","https://openalex.org/W385466589","https://openalex.org/W1620414136","https://openalex.org/W1965336712","https://openalex.org/W1980586995","https://openalex.org/W1998945032","https://openalex.org/W2012565339","https://openalex.org/W2017819785","https://openalex.org/W2027756965","https://openalex.org/W2049860319","https://openalex.org/W2066821783","https://openalex.org/W2092812423","https://openalex.org/W2121976540","https://openalex.org/W2130518506","https://openalex.org/W2135397361","https://openalex.org/W2168448159","https://openalex.org/W2312565456","https://openalex.org/W2329269422","https://openalex.org/W2554035210","https://openalex.org/W2963784516","https://openalex.org/W3101384797","https://openalex.org/W3142756138"],"related_works":["https://openalex.org/W3118528670","https://openalex.org/W3114806004","https://openalex.org/W2969606317","https://openalex.org/W2143532446","https://openalex.org/W2779693104","https://openalex.org/W3128285507","https://openalex.org/W4226278607","https://openalex.org/W2908865648","https://openalex.org/W3104698108","https://openalex.org/W4308326803"],"abstract_inverted_index":{"We":[0,115],"present":[1,116],"two":[2],"uniform":[3,39,122],"estimates":[4],"on":[5],"stability":[6,40,123],"and":[7,41,124],"mean-field":[8,42,55,125],"limit":[9,43,126],"for":[10,27,50,57,71,84,93,112,127],"the":[11,18,22,51,58,62,79,85,90,94,102,108,113,121,128],"'augmented":[12],"Kuramoto":[13,24,69],"model":[14,25],"(AKM)'":[15],"arising":[16],"from":[17],"second-order":[19],"lifting":[20],"of":[21],"first-order":[23],"(KM)":[26],"synchronization.":[28,87],"In":[29,88],"particular,":[30],"we":[31],"address":[32],"three":[33],"issues":[34],"such":[35],"as":[36],"synchronization":[37],"estimate,":[38],"which":[44,106],"are":[45],"valid":[46],"uniformly":[47],"in":[48],"time":[49],"AKM.":[52,129],"The":[53,67],"derived":[54],"equation":[56,70,92,105],"AKM":[59,95],"corresponds":[60],"to":[61,120],"dissipative":[63],"Vlasov-McKean":[64],"type":[65],"equation.":[66],"kinetic":[68,91,103],"distributed":[72],"natural":[73],"frequencies":[74],"is":[75],"not":[76],"compatible":[77],"with":[78,101],"frequency":[80],"variance":[81],"functional":[82,110],"approach":[83,111],"complete":[86],"contrast,":[89],"has":[96],"a":[97],"similar":[98],"structural":[99],"similarity":[100],"Cucker-Smale":[104],"admits":[107],"Lyapunov":[109],"variance.":[114],"sufficient":[117],"frameworks":[118],"leading":[119]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}