{"id":"https://openalex.org/W2008190810","doi":"https://doi.org/10.1103/physreve.67.031904","title":"Condition for alternans and stability of the 1:1 response pattern in a \u201cmemory\u201d model of paced cardiac dynamics","display_name":"Condition for alternans and stability of the 1:1 response pattern in a \u201cmemory\u201d model of paced cardiac dynamics","publication_year":2003,"publication_date":"2003-03-12","ids":{"openalex":"https://openalex.org/W2008190810","doi":"https://doi.org/10.1103/physreve.67.031904","mag":"2008190810","pmid":"https://pubmed.ncbi.nlm.nih.gov/12689098"},"language":"en","primary_location":{"id":"doi:10.1103/physreve.67.031904","doi":"https://doi.org/10.1103/physreve.67.031904","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.67.031904","pdf_url":null,"source":{"id":"https://openalex.org/S4210224030","display_name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","issn_l":"1063-651X","issn":["1063-651X","1095-3787","1538-4519"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","pubmed"],"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/A5065149954","display_name":"Elena G. Tolkacheva","orcid":"https://orcid.org/0000-0003-1624-5793","observed_orcids":["https://orcid.org/0000-0003-1624-5793"]},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E. G. Tolkacheva","raw_affiliation_strings":["Department of Physics, Duke University, Box 90305, Durham, North Carolina 27708, USA","Department of Physics, Duke University, Box 90305, Durham, North Carolina 27708"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Duke University, Box 90305, Durham, North Carolina 27708, USA","institution_ids":["https://openalex.org/I170897317"]},{"raw_affiliation_string":"Department of Physics, Duke University, Box 90305, Durham, North Carolina 27708","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105935537","display_name":"David G. Schaeffer","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. G. Schaeffer","raw_affiliation_strings":["Department of Mathematics, Duke University, Box 90305, Durham, North Carolina 27708"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Duke University, Box 90305, Durham, North Carolina 27708","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084210354","display_name":"Daniel J. Gauthier","orcid":"https://orcid.org/0000-0002-4473-217X","observed_orcids":["https://orcid.org/0000-0002-4473-217X"]},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel J. Gauthier","raw_affiliation_strings":["Department of Biomedical Engineering, and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708","Department of Physics, Duke University, Box 90305, Durham, North Carolina 27708"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biomedical Engineering, and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708","institution_ids":["https://openalex.org/I170897317"]},{"raw_affiliation_string":"Department of Physics, Duke University, Box 90305, Durham, North Carolina 27708","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070588034","display_name":"Wanda Krassowska","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"W. Krassowska","raw_affiliation_strings":["Department of Biomedical Engineering, and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biomedical Engineering, and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I170897317"],"apc_list":null,"apc_paid":null,"fwci":6.2839,"has_fulltext":false,"cited_by_count":113,"citation_normalized_percentile":{"value":0.96832479,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":"67","issue":"3","first_page":"031904","last_page":"031904"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10217","display_name":"Cardiac electrophysiology and arrhythmias","score":0.9657999873161316,"subfield":{"id":"https://openalex.org/subfields/2705","display_name":"Cardiology and Cardiovascular Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10217","display_name":"Cardiac electrophysiology and arrhythmias","score":0.9657999873161316,"subfield":{"id":"https://openalex.org/subfields/2705","display_name":"Cardiology and Cardiovascular Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.018699999898672104,"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/T10745","display_name":"Heart Rate Variability and Autonomic Control","score":0.004800000227987766,"subfield":{"id":"https://openalex.org/subfields/2705","display_name":"Cardiology and Cardiovascular Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cardiac-alternans","display_name":"cardiac alternans","score":0.8140000104904175},{"id":"https://openalex.org/keywords/stability-criteria","display_name":"stability criteria","score":0.6600000262260437},{"id":"https://openalex.org/keywords/action-potential-restitution","display_name":"action potential duration restitution","score":0.800000011920929},{"id":"https://openalex.org/keywords/bifurcation","display_name":"bifurcation","score":0.7799999713897705},{"id":"https://openalex.org/keywords/diastolic-interval","display_name":"diastolic interval","score":0.6340000033378601}],"concepts":[{"id":"https://openalex.org/C2778392301","wikidata":"https://www.wikidata.org/wiki/Q1156800","display_name":"Restitution","level":2,"score":0.9097179174423218},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6620445251464844},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.5640609264373779},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5045214891433716},{"id":"https://openalex.org/C2778925954","wikidata":"https://www.wikidata.org/wiki/Q16883749","display_name":"Stability criterion","level":3,"score":0.49106788635253906},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4800644814968109},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.44458338618278503},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.4267951548099518},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4226749837398529},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3876328468322754},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3426080644130707},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24422499537467957},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18790185451507568},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11266699433326721},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.10282507538795471},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08240523934364319},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","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},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000200","descriptor_name":"Action Potentials","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000200","descriptor_name":"Action Potentials","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000200","descriptor_name":"Action Potentials","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D004285","descriptor_name":"Dogs","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D004285","descriptor_name":"Dogs","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D004285","descriptor_name":"Dogs","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006321","descriptor_name":"Heart","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D006321","descriptor_name":"Heart","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D006321","descriptor_name":"Heart","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D006329","descriptor_name":"Heart Conduction System","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D006329","descriptor_name":"Heart Conduction System","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D006329","descriptor_name":"Heart Conduction System","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D007477","descriptor_name":"Ions","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007477","descriptor_name":"Ions","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007477","descriptor_name":"Ions","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008955","descriptor_name":"Models, Cardiovascular","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008955","descriptor_name":"Models, Cardiovascular","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008955","descriptor_name":"Models, Cardiovascular","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":2,"locations":[{"id":"doi:10.1103/physreve.67.031904","doi":"https://doi.org/10.1103/physreve.67.031904","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.67.031904","pdf_url":null,"source":{"id":"https://openalex.org/S4210224030","display_name":"Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics","issn_l":"1063-651X","issn":["1063-651X","1095-3787","1538-4519"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},{"id":"pmid:12689098","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/12689098","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical review. E, Statistical, nonlinear, and soft matter physics","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1970118879","https://openalex.org/W1986023817","https://openalex.org/W2017095658","https://openalex.org/W2020859911","https://openalex.org/W2034786923","https://openalex.org/W2056727407","https://openalex.org/W2062017475","https://openalex.org/W2078033190","https://openalex.org/W2104844745","https://openalex.org/W2120309072","https://openalex.org/W2135454160","https://openalex.org/W2139510409","https://openalex.org/W2442822067"],"related_works":["https://openalex.org/W2332743925","https://openalex.org/W2995498550","https://openalex.org/W3151666417","https://openalex.org/W2337106664","https://openalex.org/W4237717824","https://openalex.org/W3198455544","https://openalex.org/W4254319424","https://openalex.org/W2944158396","https://openalex.org/W3127244438","https://openalex.org/W2115350443"],"abstract_inverted_index":{"We":[0,61,114,147,180],"analyze":[1],"a":[2,11,54,63,159,165,177,186,192,213],"mathematical":[3],"model":[4,40,195,221],"of":[5,10,16,37,56,68,88,125,201,226,233],"paced":[6],"cardiac":[7],"muscle":[8],"consisting":[9],"map":[12,188],"relating":[13],"the":[14,21,28,46,59,66,69,81,86,90,98,105,116,119,123,126,138,141,150,199,202,219,224,227,231,234],"duration":[15],"an":[17],"action":[18,30],"potential":[19,31],"to":[20,136,145,222],"preceding":[22,29],"diastolic":[23],"interval":[24],"as":[25,27],"well":[26],"duration,":[32],"thereby":[33],"containing":[34],"some":[35],"degree":[36],"\"memory.\"":[38],"The":[39,130],"displays":[41],"rate-dependent":[42],"restitution":[43,50,94,128],"so":[44],"that":[45,80,97,149,198],"dynamic":[47,91],"and":[48,92,96,122,196,230],"S1-S2":[49,93],"curves":[51],"are":[52,108],"different,":[53],"manifestation":[55],"memory":[57],"in":[58,156],"model.":[60,76,179],"derive":[62],"criterion":[64,83,121,131,151],"for":[65,167],"stability":[67,82,120,200],"1:1":[70,142,203],"response":[71,143],"pattern":[72,99,144,204],"displayed":[73],"by":[74,175,184,208],"this":[75],"It":[77],"is":[78,172,205,216],"found":[79],"depends":[84],"on":[85],"slope":[87,124],"both":[89],"curves,":[95],"can":[100,132,152],"be":[101,134,153],"stable":[102],"even":[103],"when":[104],"individual":[106],"slopes":[107],"greater":[109],"or":[110],"less":[111],"than":[112],"one.":[113],"discuss":[115],"relation":[117],"between":[118],"constant-BCL":[127],"curve.":[129],"also":[133],"used":[135],"determine":[137],"bifurcation":[139],"from":[140,191],"alternans.":[146],"demonstrate":[148],"evaluated":[154],"readily":[155],"experiments":[157],"using":[158,218],"simple":[160],"pacing":[161,228],"protocol,":[162],"thus":[163],"establishing":[164],"method":[166],"determining":[168],"whether":[169],"actual":[170],"myocardium":[171],"accurately":[173,206],"described":[174,207],"such":[176],"mapping":[178],"illustrate":[181,223],"our":[182,209],"results":[183],"considering":[185],"specific":[187],"recently":[189],"derived":[190],"three-current":[193,220],"membrane":[194],"find":[197],"criterion.":[210,235],"In":[211],"addition,":[212],"numerical":[214],"experiment":[215],"performed":[217],"application":[225],"protocol":[229],"evaluation":[232]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":7}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}