{"id":"https://openalex.org/W2132965964","doi":"https://doi.org/10.1109/tac.2012.2229811","title":"Global Analysis of a Continuum Model for Monotone Pulse-Coupled Oscillators","display_name":"Global Analysis of a Continuum Model for Monotone Pulse-Coupled Oscillators","publication_year":2012,"publication_date":"2012-11-22","ids":{"openalex":"https://openalex.org/W2132965964","doi":"https://doi.org/10.1109/tac.2012.2229811","mag":"2132965964"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2012.2229811","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2229811","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1102.4511","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019128476","display_name":"Alexandre Mauroy","orcid":"https://orcid.org/0000-0002-1594-4317"},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]},{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["BE","US"],"is_corresponding":true,"raw_author_name":"Alexandre Mauroy","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Li\u00e8ge, Li\u00e8ge, Belgium","Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, United States of America"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Li\u00e8ge, Li\u00e8ge, Belgium","institution_ids":["https://openalex.org/I157674565"]},{"raw_affiliation_string":"Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, United States of America","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067642477","display_name":"Rodolphe Sepulchre","orcid":"https://orcid.org/0000-0002-7047-3124"},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Rodolphe J. Sepulchre","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Li\u00e8ge, Li\u00e8ge, Belgium","Department of Electrical Engineering and Computer Science University of Li\u00e8ge Li\u00e8ge Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Li\u00e8ge, Li\u00e8ge, Belgium","institution_ids":["https://openalex.org/I157674565"]},{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science University of Li\u00e8ge Li\u00e8ge Belgium","institution_ids":["https://openalex.org/I157674565"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019128476"],"corresponding_institution_ids":["https://openalex.org/I154570441","https://openalex.org/I157674565"],"apc_list":null,"apc_paid":null,"fwci":1.4901,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.84476102,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"58","issue":"5","first_page":"1154","last_page":"1166"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":1.0,"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":1.0,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9958999752998352,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9836000204086304,"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/monotone-polygon","display_name":"Monotone polygon","score":0.6682553887367249},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6284998059272766},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5628378391265869},{"id":"https://openalex.org/keywords/asynchronous-communication","display_name":"Asynchronous communication","score":0.47358614206314087},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4609992504119873},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.4409669041633606},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4386581480503082},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40668755769729614},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38146573305130005},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23896166682243347},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17552068829536438},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10717079043388367},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.07590314745903015}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6682553887367249},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6284998059272766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5628378391265869},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.47358614206314087},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4609992504119873},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.4409669041633606},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4386581480503082},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40668755769729614},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38146573305130005},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23896166682243347},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17552068829536438},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10717079043388367},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.07590314745903015},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":6,"locations":[{"id":"doi:10.1109/tac.2012.2229811","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2229811","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1102.4511","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1102.4511","pdf_url":"https://arxiv.org/pdf/1102.4511","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.745.1797","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.745.1797","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1102.4511.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.920.736","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.920.736","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://orbi.ulg.ac.be/bitstream/2268/165108/1/IEEETAC_MS.pdf","raw_type":"text"},{"id":"pmh:oai:generic.eprints.org:579626","is_oa":false,"landing_page_url":"http://publications.eng.cam.ac.uk/579626/","pdf_url":null,"source":{"id":"https://openalex.org/S4406922847","display_name":"Cambridge University Engineering Department Publications Database","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":"","raw_type":"Article"},{"id":"pmh:oai:orbi.ulg.ac.be:2268/165108","is_oa":true,"landing_page_url":"https://orbi.uliege.be/handle/2268/165108","pdf_url":null,"source":{"id":"https://openalex.org/S4306400651","display_name":"Open Repository and Bibliography (University of Li\u00e8ge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I157674565","host_organization_name":"University of Li\u00e8ge","host_organization_lineage":["https://openalex.org/I157674565"],"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":"IEEE Transactions on Automatic Control, 58 (5), 1154-1166 (2013)","raw_type":"peer reviewed"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1102.4511","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1102.4511","pdf_url":"https://arxiv.org/pdf/1102.4511","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1542782021","https://openalex.org/W1576838367","https://openalex.org/W1577873058","https://openalex.org/W1966624173","https://openalex.org/W1971518591","https://openalex.org/W1989495963","https://openalex.org/W1996977089","https://openalex.org/W2002489263","https://openalex.org/W2009375605","https://openalex.org/W2015410655","https://openalex.org/W2020173888","https://openalex.org/W2020510671","https://openalex.org/W2029342452","https://openalex.org/W2036655194","https://openalex.org/W2041669594","https://openalex.org/W2042652332","https://openalex.org/W2045636563","https://openalex.org/W2046424015","https://openalex.org/W2061191702","https://openalex.org/W2077866122","https://openalex.org/W2088678566","https://openalex.org/W2089876099","https://openalex.org/W2102917484","https://openalex.org/W2110209467","https://openalex.org/W2121586658","https://openalex.org/W2126841507","https://openalex.org/W2128084896","https://openalex.org/W2131397159","https://openalex.org/W2147080633","https://openalex.org/W2150312211","https://openalex.org/W2153514246","https://openalex.org/W2154953441","https://openalex.org/W2164653071","https://openalex.org/W2164727176","https://openalex.org/W2335062971","https://openalex.org/W2562983303","https://openalex.org/W3217350819","https://openalex.org/W4206600001","https://openalex.org/W4214617048","https://openalex.org/W4238614602","https://openalex.org/W4248004290","https://openalex.org/W4298576603"],"related_works":["https://openalex.org/W2116677773","https://openalex.org/W2155261584","https://openalex.org/W2584231425","https://openalex.org/W2150611273","https://openalex.org/W2210722882","https://openalex.org/W2009168760","https://openalex.org/W1495650726","https://openalex.org/W2963043651","https://openalex.org/W2057820893","https://openalex.org/W170012745"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,51,59,90,126,141],"continuum":[3,31],"of":[4,43,70,79,108,132,148],"phase":[5,115],"oscillators":[6,84,116],"on":[7,21,103],"the":[8,25,30,36,41,44,71,76,80,83,104,109,119,130,145],"circle":[9],"interacting":[10],"through":[11],"an":[12,98],"impulsive":[13],"instantaneous":[14],"coupling.":[15],"In":[16,137],"contrast":[17],"with":[18],"previous":[19],"studies":[20],"related":[22],"pulse-coupled":[23,149],"models,":[24],"stability":[26],"results":[27,107],"obtained":[28],"in":[29,86],"limit":[32],"are":[33],"global.":[34],"For":[35],"nonlinear":[37],"transport":[38],"equation":[39],"governing":[40],"evolution":[42,69],"oscillators,":[45],"we":[46],"propose":[47],"(under":[48],"technical":[49],"assumptions)":[50],"global":[52],"Lyapunov":[53,72],"function":[54,73],"which":[55],"is":[56],"induced":[57],"by":[58],"total":[60],"variation":[61],"distance":[62],"between":[63,129],"quantile":[64],"densities.":[65],"The":[66,106],"monotone":[67],"time":[68,88],"completely":[74],"characterizes":[75],"dichotomic":[77],"behavior":[78],"oscillators:":[81],"either":[82],"converge":[85,96],"finite":[87,133],"to":[89,97,113],"synchronous":[91],"state":[92,100],"or":[93],"they":[94,139],"asymptotically":[95],"asynchronous":[99],"uniformly":[101],"spread":[102],"circle.":[105],"present":[110],"paper":[111],"apply":[112],"popular":[114],"models":[117],"(e.g.,":[118],"well-known":[120],"leaky":[121],"integrate-and-fire":[122],"model)":[123],"and":[124,134],"show":[125],"strong":[127],"parallel":[128],"analysis":[131,147],"infinite":[135],"populations.":[136],"addition,":[138],"provide":[140],"novel":[142],"approach":[143],"for":[144],"(global)":[146],"oscillators.":[150]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
