{"id":"https://openalex.org/W2014131620","doi":"https://doi.org/10.1137/s0036139993259337","title":"A Delay Equation Representation of Pulse Circulation on a Ring in Excitable Media","display_name":"A Delay Equation Representation of Pulse Circulation on a Ring in Excitable Media","publication_year":1996,"publication_date":"1996-02-01","ids":{"openalex":"https://openalex.org/W2014131620","doi":"https://doi.org/10.1137/s0036139993259337","mag":"2014131620"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139993259337","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139993259337","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/A5052966958","display_name":"Marc Courtemanche","orcid":null},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]},{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]},{"id":"https://openalex.org/I70931966","display_name":"Universit\u00e9 de Montr\u00e9al","ror":"https://ror.org/0161xgx34","country_code":"CA","type":"education","lineage":["https://openalex.org/I70931966"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Marc Courtemanche","raw_affiliation_strings":["McGill University","University of Arizona","University of Montreal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"McGill University","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"University of Arizona","institution_ids":["https://openalex.org/I138006243"]},{"raw_affiliation_string":"University of Montreal","institution_ids":["https://openalex.org/I70931966"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071828704","display_name":"James P. Keener","orcid":"https://orcid.org/0000-0001-9216-4157"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"James P. Keener","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5048160756","display_name":"Leon Glass","orcid":"https://orcid.org/0000-0001-9536-1463"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Leon Glass","raw_affiliation_strings":["McGill University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"McGill University","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.4131,"has_fulltext":false,"cited_by_count":90,"citation_normalized_percentile":{"value":0.92138026,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"56","issue":"1","first_page":"119","last_page":"142"},"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9954000115394592,"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":0.982200026512146,"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/pulse","display_name":"Pulse (music)","score":0.7573422789573669},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.641438364982605},{"id":"https://openalex.org/keywords/circulation","display_name":"Circulation (fluid dynamics)","score":0.6249216198921204},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.5296661257743835},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5240336060523987},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5166714191436768},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.46482542157173157},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4583517909049988},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.44140610098838806},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4378115236759186},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.4211900234222412},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.42083829641342163},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.12139159440994263},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.12031680345535278},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07524272799491882},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.0701833963394165}],"concepts":[{"id":"https://openalex.org/C2780167933","wikidata":"https://www.wikidata.org/wiki/Q1550652","display_name":"Pulse (music)","level":3,"score":0.7573422789573669},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.641438364982605},{"id":"https://openalex.org/C11111821","wikidata":"https://www.wikidata.org/wiki/Q205880","display_name":"Circulation (fluid dynamics)","level":2,"score":0.6249216198921204},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.5296661257743835},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5240336060523987},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5166714191436768},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.46482542157173157},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4583517909049988},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.44140610098838806},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4378115236759186},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.4211900234222412},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.42083829641342163},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.12139159440994263},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.12031680345535278},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07524272799491882},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0701833963394165},{"id":"https://openalex.org/C94915269","wikidata":"https://www.wikidata.org/wiki/Q1834857","display_name":"Detector","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},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139993259337","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139993259337","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":17,"referenced_works":["https://openalex.org/W1501102208","https://openalex.org/W1978421966","https://openalex.org/W1984336411","https://openalex.org/W2004922280","https://openalex.org/W2013137073","https://openalex.org/W2013346937","https://openalex.org/W2031879728","https://openalex.org/W2036043228","https://openalex.org/W2059716861","https://openalex.org/W2077331262","https://openalex.org/W2078344772","https://openalex.org/W2079871064","https://openalex.org/W2087248065","https://openalex.org/W2122576752","https://openalex.org/W2139891426","https://openalex.org/W2171878126","https://openalex.org/W2545104828"],"related_works":["https://openalex.org/W2347493350","https://openalex.org/W2389117401","https://openalex.org/W2391496396","https://openalex.org/W2389322380","https://openalex.org/W2381337682","https://openalex.org/W2360385795","https://openalex.org/W2389067877","https://openalex.org/W2374714774","https://openalex.org/W2391605708","https://openalex.org/W2029287765"],"abstract_inverted_index":{"This":[0],"paper":[1],"develops":[2],"a":[3,9,12,18,29,50],"theory":[4],"for":[5,56,65],"pulse":[6,42,84],"circulation":[7,58],"on":[8,28],"ring":[10,31],"in":[11,43],"continuous":[13],"excitable":[14,45],"medium.":[15],"Simulations":[16],"of":[17,25,32,39,73,92,105],"partial":[19],"differential":[20],"equation":[21,95],"(PDE)":[22],"modeling":[23],"propagation":[24],"electrical":[26],"pulses":[27],"one-dimensional":[30],"cardiac":[33],"tissue":[34],"are":[35,47,59,63],"presented.":[36],"The":[37,86],"dynamics":[38],"the":[40,66,77,93,97,106],"circulating":[41],"this":[44],"medium":[46],"reduced":[48],"to":[49,82],"single":[51],"integral-delay":[52],"equation.":[53],"Stability":[54],"conditions":[55],"steady":[57,80],"obtained,":[60],"and":[61,70,96,100],"estimates":[62],"derived":[64],"wavelength,":[67],"growth":[68],"rate,":[69],"asymptotic":[71],"amplitude":[72],"oscillating":[74],"solutions":[75,104],"near":[76],"transition":[78],"from":[79],"rotation":[81],"oscillatory":[83],"dynamics.":[85],"analytical":[87],"results":[88],"agree":[89],"with":[90],"simulations":[91],"delay":[94],"PDE":[98,107],"model":[99],"uncover":[101],"previously":[102],"uncharted":[103],"equations.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
