{"id":"https://openalex.org/W1176193736","doi":"https://doi.org/10.1137/15m1010191","title":"Forward-Time and Backward-Time Isochrons and Their Interactions","display_name":"Forward-Time and Backward-Time Isochrons and Their Interactions","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1176193736","doi":"https://doi.org/10.1137/15m1010191","mag":"1176193736"},"language":"en","primary_location":{"id":"doi:10.1137/15m1010191","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1010191","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/A5034471475","display_name":"Peter Langfield","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peter Langfield","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072817844","display_name":"Bernd Krauskopf","orcid":"https://orcid.org/0000-0002-8940-230X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bernd Krauskopf","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078314587","display_name":"Hinke M. Osinga","orcid":"https://orcid.org/0000-0003-2169-0883"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hinke M. Osinga","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1925,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.77760947,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"14","issue":"3","first_page":"1418","last_page":"1453"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9988999962806702,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9970999956130981,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/isochron-dating","display_name":"Isochron dating","score":0.8519818186759949},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5872775316238403},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.5147619247436523},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4714028835296631},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.46099546551704407},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.4111683964729309},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3733551502227783},{"id":"https://openalex.org/keywords/isochron","display_name":"Isochron","score":0.29690903425216675},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24660545587539673},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.13616278767585754},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12860432267189026}],"concepts":[{"id":"https://openalex.org/C46381822","wikidata":"https://www.wikidata.org/wiki/Q223488","display_name":"Isochron dating","level":3,"score":0.8519818186759949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5872775316238403},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.5147619247436523},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4714028835296631},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.46099546551704407},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.4111683964729309},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3733551502227783},{"id":"https://openalex.org/C487381","wikidata":"https://www.wikidata.org/wiki/Q17098413","display_name":"Isochron","level":2,"score":0.29690903425216675},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24660545587539673},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.13616278767585754},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12860432267189026},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1010191","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1010191","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W578100665","https://openalex.org/W1582828056","https://openalex.org/W1584873371","https://openalex.org/W1600110616","https://openalex.org/W1964810201","https://openalex.org/W1967771793","https://openalex.org/W1968274458","https://openalex.org/W1974005577","https://openalex.org/W1985155290","https://openalex.org/W1990636640","https://openalex.org/W2003884541","https://openalex.org/W2008187346","https://openalex.org/W2009375605","https://openalex.org/W2012430741","https://openalex.org/W2013469794","https://openalex.org/W2016315007","https://openalex.org/W2022911541","https://openalex.org/W2054589454","https://openalex.org/W2076219511","https://openalex.org/W2114876173","https://openalex.org/W2134358519","https://openalex.org/W2171453145","https://openalex.org/W2963554196"],"related_works":["https://openalex.org/W1956257808","https://openalex.org/W1660035104","https://openalex.org/W2318314814","https://openalex.org/W3141604987","https://openalex.org/W2322776206","https://openalex.org/W1971325475","https://openalex.org/W2039449607","https://openalex.org/W2084930737","https://openalex.org/W2162237651","https://openalex.org/W2472056014"],"abstract_inverted_index":{"We":[0,40,69,100],"consider":[1],"isochrons":[2,35,49,98],"of":[3,16,36,44,50,64,73,97,127],"a":[4,37,57,62,75,85,109,111,115,124,131],"periodic":[5,22],"orbit":[6,23],"in":[7,24,123],"the":[8,14,21,42,51,92,119,135],"planar":[9],"FitzHugh--Nagumo":[10],"system,":[11,53],"that":[12,18,56,117],"is,":[13],"curves":[15],"points":[17],"converge":[19],"to":[20,34],"phase":[25,128],"with":[26],"each":[27],"other,":[28],"and":[29,54,66,102,130],"we":[30],"extend":[31],"this":[32,71],"notion":[33,43],"focus":[38],"equilibrium.":[39],"introduce":[41],"backward-time":[45,67],"isochrons,":[46],"which":[47],"are":[48],"reversed-time":[52],"show":[55],"cubic":[58,76],"tangency":[59,74,79],"occurs":[60],"between":[61],"set":[63],"forward-time":[65],"isochrons.":[68],"call":[70],"moment":[72],"isochron":[77],"foliation":[78],"(CIFT).":[80],"This":[81],"phenomenon":[82],"is":[83],"not":[84],"local":[86,125],"feature":[87],"but":[88],"happens":[89],"globally":[90],"throughout":[91],"annulus":[93],"where":[94],"both":[95],"sets":[96],"coexist.":[99],"construct":[101],"discuss":[103],"examples":[104],"for":[105,108],"three":[106],"mechanisms":[107],"CIFT:":[110],"global":[112],"time-scale":[113],"separation;":[114],"perturbation":[116],"increases":[118],"velocity":[120],"along":[121],"trajectories":[122],"region":[126],"space;":[129],"canard":[132],"explosion":[133],"(in":[134],"Van":[136],"der":[137],"Pol":[138],"system).":[139]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}