{"id":"https://openalex.org/W1880775923","doi":"https://doi.org/10.1137/140999177","title":"Fast Pulses with Oscillatory Tails in the FitzHugh--Nagumo System","display_name":"Fast Pulses with Oscillatory Tails in the FitzHugh--Nagumo System","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1880775923","doi":"https://doi.org/10.1137/140999177","mag":"1880775923"},"language":"en","primary_location":{"id":"doi:10.1137/140999177","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140999177","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5101922295","display_name":"Paul Carter","orcid":"https://orcid.org/0000-0003-1884-9988"},"institutions":[{"id":"https://openalex.org/I175594653","display_name":"John Brown University","ror":"https://ror.org/02ct41q97","country_code":"US","type":"education","lineage":["https://openalex.org/I175594653"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Paul Carter","raw_affiliation_strings":["Brown University"],"affiliations":[{"raw_affiliation_string":"Brown University","institution_ids":["https://openalex.org/I175594653"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024502637","display_name":"Bj\u00f6rn Sandstede","orcid":"https://orcid.org/0000-0002-5432-1235"},"institutions":[{"id":"https://openalex.org/I175594653","display_name":"John Brown University","ror":"https://ror.org/02ct41q97","country_code":"US","type":"education","lineage":["https://openalex.org/I175594653"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bj\u00f6rn Sandstede","raw_affiliation_strings":["Brown University"],"affiliations":[{"raw_affiliation_string":"Brown University","institution_ids":["https://openalex.org/I175594653"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101922295"],"corresponding_institution_ids":["https://openalex.org/I175594653"],"apc_list":null,"apc_paid":null,"fwci":4.198,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.94402339,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"47","issue":"5","first_page":"3393","last_page":"3441"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998000264167786,"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":0.9998000264167786,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9997000098228455,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9995999932289124,"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/mathematics","display_name":"Mathematics","score":0.7505588531494141},{"id":"https://openalex.org/keywords/slow-manifold","display_name":"Slow manifold","score":0.7062974572181702},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.6101806163787842},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5706573128700256},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5201849937438965},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5153209567070007},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5133485198020935},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4973197281360626},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2672264277935028},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09514826536178589}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7505588531494141},{"id":"https://openalex.org/C2778671503","wikidata":"https://www.wikidata.org/wiki/Q7542110","display_name":"Slow manifold","level":3,"score":0.7062974572181702},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.6101806163787842},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5706573128700256},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5201849937438965},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5153209567070007},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5133485198020935},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4973197281360626},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2672264277935028},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09514826536178589},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140999177","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140999177","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W170447982","https://openalex.org/W1565264866","https://openalex.org/W1966995045","https://openalex.org/W1986739294","https://openalex.org/W1998602905","https://openalex.org/W2009058070","https://openalex.org/W2009375605","https://openalex.org/W2014241231","https://openalex.org/W2016767879","https://openalex.org/W2023070543","https://openalex.org/W2040718349","https://openalex.org/W2041574049","https://openalex.org/W2061191702","https://openalex.org/W2066605027","https://openalex.org/W2070823330","https://openalex.org/W2086294119","https://openalex.org/W2089995439","https://openalex.org/W2104916047","https://openalex.org/W2116643462","https://openalex.org/W2123299726","https://openalex.org/W2160578495","https://openalex.org/W2169487971","https://openalex.org/W3098464174","https://openalex.org/W3123803226"],"related_works":["https://openalex.org/W1965619029","https://openalex.org/W1980855435","https://openalex.org/W4327639758","https://openalex.org/W2339866760","https://openalex.org/W3214458670","https://openalex.org/W1580344297","https://openalex.org/W1526668334","https://openalex.org/W2348169464","https://openalex.org/W2952016911","https://openalex.org/W1998082046"],"abstract_inverted_index":{"Numerical":[0],"studies":[1],"indicate":[2],"that":[3,54,63],"the":[4,17,26,34,41,56,79,82,88,95],"FitzHugh--Nagumo":[5,35],"system":[6,36],"exhibits":[7,37],"stable":[8],"traveling":[9],"pulses":[10,21,45,62],"with":[11,78],"oscillatory":[12],"tails.":[13],"In":[14,39],"this":[15],"paper,":[16],"existence":[18,71],"of":[19,43],"such":[20],"is":[22,46,52,85],"proved":[23],"analytically":[24],"in":[25,66],"singular":[27],"perturbation":[28],"limit":[29],"near":[30,90],"parameter":[31],"values":[32],"where":[33,98],"folds.":[38],"addition,":[40],"stability":[42],"these":[44],"investigated":[47],"numerically,":[48],"and":[49],"a":[50],"mechanism":[51],"proposed":[53],"explains":[55],"transition":[57],"from":[58],"single":[59],"to":[60,86],"double":[61],"was":[64],"observed":[65],"earlier":[67],"numerical":[68],"studies.":[69],"The":[70],"proof":[72],"utilizes":[73],"geometric":[74],"blow-up":[75],"techniques":[76],"combined":[77],"exchange":[80],"lemma:":[81],"main":[83],"challenge":[84],"understand":[87],"passage":[89],"two":[91],"fold":[92],"points":[93],"on":[94],"slow":[96],"manifold":[97],"normal":[99],"hyperbolicity":[100],"fails.":[101]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
