{"id":"https://openalex.org/W1978610085","doi":"https://doi.org/10.1142/s0218127403008764","title":"THE ASYMPTOTIC STRUCTURE OF THE HODGKIN\u2013HUXLEY EQUATIONS","display_name":"THE ASYMPTOTIC STRUCTURE OF THE HODGKIN\u2013HUXLEY EQUATIONS","publication_year":2003,"publication_date":"2003-12-01","ids":{"openalex":"https://openalex.org/W1978610085","doi":"https://doi.org/10.1142/s0218127403008764","mag":"1978610085"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127403008764","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127403008764","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5068762664","display_name":"Rebecca Suckley","orcid":null},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"REBECCA SUCKLEY","raw_affiliation_strings":["Department of Mathematical Sciences,  University of Liverpool, Liverpool, L69 7ZL, UK","Department of Mathematical Sciences, University of Liverpool , Liverpool L69 7ZL , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences,  University of Liverpool, Liverpool, L69 7ZL, UK","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"Department of Mathematical Sciences, University of Liverpool , Liverpool L69 7ZL , UK","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042213995","display_name":"V. N. Biktashev","orcid":"https://orcid.org/0000-0001-6617-4677"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"VADIM N. BIKTASHEV","raw_affiliation_strings":["Department of Mathematical Sciences,  University of Liverpool, Liverpool, L69 7ZL, UK","Department of Mathematical Sciences, University of Liverpool , Liverpool L69 7ZL , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences,  University of Liverpool, Liverpool, L69 7ZL, UK","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"Department of Mathematical Sciences, University of Liverpool , Liverpool L69 7ZL , UK","institution_ids":["https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I146655781"],"apc_list":null,"apc_paid":null,"fwci":0.994,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.81179549,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"13","issue":"12","first_page":"3805","last_page":"3825"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9983000159263611,"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":0.9807999730110168,"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":0.7597166895866394},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.6365252733230591},{"id":"https://openalex.org/keywords/cusp","display_name":"Cusp (singularity)","score":0.6106765866279602},{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.5575001835823059},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5363012552261353},{"id":"https://openalex.org/keywords/slow-manifold","display_name":"Slow manifold","score":0.5154851078987122},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.503208577632904},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4236491918563843},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.23811548948287964},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1413060426712036},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.11764350533485413}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7597166895866394},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6365252733230591},{"id":"https://openalex.org/C2778400075","wikidata":"https://www.wikidata.org/wiki/Q655275","display_name":"Cusp (singularity)","level":2,"score":0.6106765866279602},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.5575001835823059},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5363012552261353},{"id":"https://openalex.org/C2778671503","wikidata":"https://www.wikidata.org/wiki/Q7542110","display_name":"Slow manifold","level":3,"score":0.5154851078987122},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.503208577632904},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4236491918563843},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.23811548948287964},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1413060426712036},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.11764350533485413},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127403008764","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127403008764","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1584245551","https://openalex.org/W1975904858","https://openalex.org/W1985940938","https://openalex.org/W1986023817","https://openalex.org/W2009375605","https://openalex.org/W2055072865","https://openalex.org/W2059551226","https://openalex.org/W2060797439","https://openalex.org/W2060809971","https://openalex.org/W2065842898","https://openalex.org/W2579392681","https://openalex.org/W2911423765"],"related_works":["https://openalex.org/W1980855435","https://openalex.org/W2067276499","https://openalex.org/W1580344297","https://openalex.org/W2348169464","https://openalex.org/W2952016911","https://openalex.org/W2020506589","https://openalex.org/W2381793807","https://openalex.org/W2950257836","https://openalex.org/W2032227660","https://openalex.org/W2074259495"],"abstract_inverted_index":{"We":[0,36,73],"analyze":[1],"the":[2,6,14,41,47,64,70,77,85,94],"asymptotic":[3,102],"structure":[4,45],"of":[5,9,13,16,28,30,33,46,53,63,100],"Hodgkin\u2013Huxley":[7],"system":[8],"equations,":[10,84],"in":[11,50,82,88],"terms":[12],"concepts":[15],"slow":[17,65],"manifold":[18,66],"and":[19,97],"fast":[20,71],"foliation,":[21],"based":[22],"on":[23,26],"Tikhonov's":[24],"theorem":[25],"asymptotics":[27],"solutions":[29],"slow\u2013fast":[31],"systems":[32],"differential":[34],"equations.":[35],"test":[37],"Zeeman's":[38],"conjecture":[39],"that":[40,75],"jump":[42],"onset\u2013slow":[43],"return":[44],"action":[48],"potential":[49],"realistic":[51],"equations":[52],"biological":[54],"excitability":[55],"may":[56],"be":[57,91],"due":[58],"to":[59,69],"a":[60],"cusp":[61,78],"singularity":[62,79],"with":[67],"respect":[68],"foliation.":[72],"find":[74],"although":[76],"can":[80],"appear":[81],"such":[83],"characteristic":[86],"features":[87],"question":[89],"cannot":[90],"reproduced":[92],"within":[93],"Tikhonov":[95],"scheme":[96],"require":[98],"development":[99],"different":[101],"approaches.":[103]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}