{"id":"https://openalex.org/W2087603570","doi":"https://doi.org/10.1137/110860136","title":"Mixed-Mode Oscillations in a Multiple Time Scale Phantom Bursting System","display_name":"Mixed-Mode Oscillations in a Multiple Time Scale Phantom Bursting System","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2087603570","doi":"https://doi.org/10.1137/110860136","mag":"2087603570"},"language":"en","primary_location":{"id":"doi:10.1137/110860136","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110860136","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1202.2705","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016275776","display_name":"Martin Krupa","orcid":"https://orcid.org/0000-0001-9330-4705"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Martin Krupa","raw_affiliation_strings":["SIgnals and SYstems in PHysiology & Engineering"],"affiliations":[{"raw_affiliation_string":"SIgnals and SYstems in PHysiology & Engineering","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062965566","display_name":"Alexandre Vidal","orcid":"https://orcid.org/0009-0008-1432-8820"},"institutions":[{"id":"https://openalex.org/I4210147464","display_name":"Laboratoire de Probabilit\u00e9s et Mod\u00e8les Al\u00e9atoires","ror":"https://ror.org/04hjc7403","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210147464"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alexandre Vidal","raw_affiliation_strings":["Laboratoire Analyse et Probabilit\u00e9s"],"affiliations":[{"raw_affiliation_string":"Laboratoire Analyse et Probabilit\u00e9s","institution_ids":["https://openalex.org/I4210147464"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077245992","display_name":"Mathieu Desroches","orcid":"https://orcid.org/0000-0002-9325-4207"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mathieu Desroches","raw_affiliation_strings":["SIgnals and SYstems in PHysiology & Engineering"],"affiliations":[{"raw_affiliation_string":"SIgnals and SYstems in PHysiology & Engineering","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090954804","display_name":"Fr\u00e9d\u00e9rique Cl\u00e9ment","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9rique Cl\u00e9ment","raw_affiliation_strings":["SIgnals and SYstems in PHysiology & Engineering"],"affiliations":[{"raw_affiliation_string":"SIgnals and SYstems in PHysiology & Engineering","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5016275776"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3443,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.92767364,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"11","issue":"4","first_page":"1458","last_page":"1498"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9980000257492065,"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":0.9980000257492065,"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":0.9975000023841858,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9843000173568726,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.6807641983032227},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.6344955563545227},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5883593559265137},{"id":"https://openalex.org/keywords/bursting","display_name":"Bursting","score":0.5835299491882324},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5472474098205566},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.5262897610664368},{"id":"https://openalex.org/keywords/imaging-phantom","display_name":"Imaging phantom","score":0.49686887860298157},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4884561598300934},{"id":"https://openalex.org/keywords/transient","display_name":"Transient (computer programming)","score":0.42894506454467773},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.41516950726509094},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.40567106008529663},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3304904103279114},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2957339882850647},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2572898864746094},{"id":"https://openalex.org/keywords/neuroscience","display_name":"Neuroscience","score":0.08070370554924011}],"concepts":[{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.6807641983032227},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6344955563545227},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5883593559265137},{"id":"https://openalex.org/C195221683","wikidata":"https://www.wikidata.org/wiki/Q5000649","display_name":"Bursting","level":2,"score":0.5835299491882324},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5472474098205566},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.5262897610664368},{"id":"https://openalex.org/C104293457","wikidata":"https://www.wikidata.org/wiki/Q28324852","display_name":"Imaging phantom","level":2,"score":0.49686887860298157},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4884561598300934},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.42894506454467773},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.41516950726509094},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.40567106008529663},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3304904103279114},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2957339882850647},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2572898864746094},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.08070370554924011},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/110860136","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110860136","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1202.2705","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1202.2705","pdf_url":"https://arxiv.org/pdf/1202.2705","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:10.1.1.397.3358","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.397.3358","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/66/94/86/PDF/MMO_in_a_Phantom_Bursting_System.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00669486v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00669486","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"SIAM Journal on Applied Dynamical Systems, 2012, 11 (4), pp. 1458-1498. ⟨10.1137/110860136⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1202.2705","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1202.2705","pdf_url":"https://arxiv.org/pdf/1202.2705","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":[{"id":"https://openalex.org/G1007405876","display_name":null,"funder_award_id":"EP/E032249/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W620067635","https://openalex.org/W653690259","https://openalex.org/W1484182740","https://openalex.org/W1553838213","https://openalex.org/W1965780186","https://openalex.org/W1967771793","https://openalex.org/W1974614991","https://openalex.org/W1979533263","https://openalex.org/W1983920324","https://openalex.org/W1986739294","https://openalex.org/W1987576052","https://openalex.org/W2002570644","https://openalex.org/W2022543096","https://openalex.org/W2024858188","https://openalex.org/W2038631673","https://openalex.org/W2040498452","https://openalex.org/W2041579436","https://openalex.org/W2065087707","https://openalex.org/W2074634343","https://openalex.org/W2077420456","https://openalex.org/W2089995439","https://openalex.org/W2098619385","https://openalex.org/W2113751538","https://openalex.org/W2153904027","https://openalex.org/W2157086299","https://openalex.org/W2169938087","https://openalex.org/W2740402523","https://openalex.org/W2741455208","https://openalex.org/W2909373143","https://openalex.org/W3102636207","https://openalex.org/W3106534923"],"related_works":["https://openalex.org/W2080788537","https://openalex.org/W3181055709","https://openalex.org/W2002830460","https://openalex.org/W2064213689","https://openalex.org/W2036451364","https://openalex.org/W3195397619","https://openalex.org/W4296292881","https://openalex.org/W2072413244","https://openalex.org/W3197610365","https://openalex.org/W2792679579"],"abstract_inverted_index":{"In":[0],"this":[1],"work":[2],"we":[3],"study":[4],"mixed-mode":[5],"oscillations":[6,70],"in":[7,114,156,189],"a":[8,20,80,89,146,160,168,172,201],"model":[9,18],"of":[10,12,24,50,59,75,83,91,95,99,122,137,149,154,159,182],"secretion":[11],"GnRH":[13],"(gonadotropin":[14],"releasing":[15],"hormone).":[16],"The":[17,34,176],"is":[19,145],"phantom":[21],"burster":[22],"consisting":[23],"two":[25,104],"feedforward":[26],"coupled":[27],"FitzHugh--Nagumo":[28],"systems,":[29],"with":[30,163],"three":[31,57],"time":[32,166],"scales.":[33],"forcing":[35],"system":[36,53],"(regulator)":[37],"evolves":[38],"on":[39,107,128,134],"the":[40,47,51,73,76,84,96,100,108,112,115,120,126,129,135,157,180],"slowest":[41],"scale":[42],"and":[43,68,125,152,195],"acts":[44],"by":[45],"moving":[46],"slow":[48,77],"nullcline":[49,78],"forced":[52],"(secretor).":[54],"There":[55],"are":[56],"modes":[58],"dynamics:":[60],"pulsatility":[61],"(transient":[62],"relaxation":[63],"oscillation),":[64],"surge":[65],"(quasi-steady":[66],"state),":[67],"small":[69,123,150],"related":[71],"to":[72,119],"passage":[74],"through":[79,200],"fold":[81,113],"point":[82],"fast":[85],"nullcline.":[86],"We":[87,102],"derive":[88],"variety":[90],"reductions,":[92],"taking":[93],"advantage":[94],"mentioned":[97],"features":[98],"system.":[101],"obtain":[103],"results:":[105],"one":[106],"local":[109,143],"dynamics":[110],"near":[111],"parameter":[116,191],"regime":[117],"corresponding":[118],"presence":[121],"oscillations,":[124],"other":[127],"global":[130,177],"dynamics,":[131],"more":[132],"specifically":[133],"existence":[136,181],"an":[138,164,183],"attracting":[139,184,194],"limit":[140,186],"cycle.":[141],"Our":[142],"result":[144,178],"rigorous":[147],"characterization":[148],"canards":[151],"sectors":[153],"rotation":[155],"case":[158],"folded":[161],"node":[162],"additional":[165],"scale,":[167],"feature":[169],"allowing":[170],"for":[171],"clear":[173],"geometric":[174],"argument.":[175],"gives":[179],"unique":[185,196],"cycle,":[187],"which,":[188],"some":[190],"regimes,":[192],"remains":[193],"even":[197],"during":[198],"passages":[199],"canard":[202],"explosion.":[203]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}