{"id":"https://openalex.org/W2785517116","doi":"https://doi.org/10.1137/16m1080707","title":"Unpeeling a Homoclinic Banana in the FitzHugh--Nagumo System","display_name":"Unpeeling a Homoclinic Banana in the FitzHugh--Nagumo System","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2785517116","doi":"https://doi.org/10.1137/16m1080707","mag":"2785517116"},"language":"en","primary_location":{"id":"doi:10.1137/16m1080707","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1080707","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":["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/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Paul Carter","raw_affiliation_strings":["Department of Mathematics, University of Arizona, Tucson, AZ 85721"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Arizona, Tucson, AZ 85721","institution_ids":["https://openalex.org/I138006243"]}]},{"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/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bj\u00f6rn Sandstede","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, Providence, RI 02912"],"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, RI 02912","institution_ids":["https://openalex.org/I27804330"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101922295"],"corresponding_institution_ids":["https://openalex.org/I138006243"],"apc_list":null,"apc_paid":null,"fwci":2.1452,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.8827155,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"17","issue":"1","first_page":"236","last_page":"349"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9993000030517578,"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":0.9993000030517578,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9944000244140625,"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/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.8724955320358276},{"id":"https://openalex.org/keywords/excursion","display_name":"Excursion","score":0.6898128986358643},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6341112852096558},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.5972938537597656},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5807856321334839},{"id":"https://openalex.org/keywords/pulse","display_name":"Pulse (music)","score":0.5586089491844177},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.528531014919281},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5003106594085693},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4883684515953064},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.46533575654029846},{"id":"https://openalex.org/keywords/numerical-continuation","display_name":"Numerical continuation","score":0.4585447609424591},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4370286464691162},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28590381145477295},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17573469877243042},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.13397464156150818},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10454881191253662},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06954649090766907}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.8724955320358276},{"id":"https://openalex.org/C2780550144","wikidata":"https://www.wikidata.org/wiki/Q1156976","display_name":"Excursion","level":2,"score":0.6898128986358643},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6341112852096558},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.5972938537597656},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5807856321334839},{"id":"https://openalex.org/C2780167933","wikidata":"https://www.wikidata.org/wiki/Q1550652","display_name":"Pulse (music)","level":3,"score":0.5586089491844177},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.528531014919281},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5003106594085693},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4883684515953064},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.46533575654029846},{"id":"https://openalex.org/C2775978667","wikidata":"https://www.wikidata.org/wiki/Q7069654","display_name":"Numerical continuation","level":4,"score":0.4585447609424591},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4370286464691162},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28590381145477295},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17573469877243042},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.13397464156150818},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10454881191253662},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06954649090766907},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"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/C94915269","wikidata":"https://www.wikidata.org/wiki/Q1834857","display_name":"Detector","level":2,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1080707","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1080707","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:repository.arizona.edu:10150/631146","is_oa":false,"landing_page_url":"https://repository.arizona.edu/bitstream/10150/631146/1/16m1080707.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400271","display_name":"UA Campus Repository (The University of Arizona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138006243","host_organization_name":"University of Arizona","host_organization_lineage":["https://openalex.org/I138006243"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"349","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2283734597","display_name":"Nonlinear stability of patterns","funder_award_id":"1408742","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G324838419","display_name":null,"funder_award_id":"DMS-1408742","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G386890622","display_name":null,"funder_award_id":"1148284","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G468458577","display_name":null,"funder_award_id":"1408742","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G8739944772","display_name":null,"funder_award_id":"DMS-1148284","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1524260103","https://openalex.org/W1880775923","https://openalex.org/W1971039616","https://openalex.org/W1974746776","https://openalex.org/W1985940938","https://openalex.org/W1986739294","https://openalex.org/W1993901511","https://openalex.org/W1998602905","https://openalex.org/W1999170261","https://openalex.org/W2009058070","https://openalex.org/W2014863630","https://openalex.org/W2016767879","https://openalex.org/W2023070543","https://openalex.org/W2025623727","https://openalex.org/W2040718349","https://openalex.org/W2041574049","https://openalex.org/W2066605027","https://openalex.org/W2070823330","https://openalex.org/W2074505548","https://openalex.org/W2089995439","https://openalex.org/W2145391238","https://openalex.org/W2150180186","https://openalex.org/W2160578495","https://openalex.org/W2169487971","https://openalex.org/W2404712178","https://openalex.org/W3098464174","https://openalex.org/W3099448176","https://openalex.org/W3123803226"],"related_works":["https://openalex.org/W2018102019","https://openalex.org/W1673711094","https://openalex.org/W1973148663","https://openalex.org/W3044635415","https://openalex.org/W1004667392","https://openalex.org/W2046288907","https://openalex.org/W1984705454","https://openalex.org/W288677787","https://openalex.org/W4297878192","https://openalex.org/W2785517116"],"abstract_inverted_index":{"The":[0],"FitzHugh--Nagumo":[1],"equations":[2],"are":[3],"known":[4,17],"to":[5],"admit":[6],"fast":[7],"traveling":[8,22],"pulse":[9],"solutions":[10],"with":[11,24],"monotone":[12],"tails.":[13,28],"It":[14],"is":[15],"also":[16],"that":[18,39],"this":[19,62,73],"system":[20],"admits":[21],"pulses":[23,47],"exponentially":[25],"decaying":[26],"oscillatory":[27],"Upon":[29],"numerical":[30],"continuation":[31],"in":[32,42,66],"parameter":[33],"space,":[34],"it":[35],"has":[36],"been":[37],"observed":[38],"the":[40,43,46,58,68,79],"oscillations":[41],"tails":[44],"of":[45,57],"grow":[48],"into":[49],"a":[50,54],"secondary":[51],"excursion":[52],"resembling":[53],"second":[55],"copy":[56],"primary":[59],"pulse.":[60],"In":[61],"paper,":[63],"we":[64,77],"outline":[65],"detail":[67],"geometric":[69,83],"mechanism":[70],"responsible":[71],"for":[72],"single-to-double-pulse":[74],"transition,":[75],"and":[76,87],"construct":[78],"transition":[80],"analytically":[81],"using":[82],"singular":[84],"perturbation":[85],"theory":[86],"blow-up":[88],"techniques.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}