{"id":"https://openalex.org/W1968199724","doi":"https://doi.org/10.1142/s0218127405014222","title":"HYPERBOLIC PLYKIN ATTRACTOR CAN EXIST IN NEURON MODELS","display_name":"HYPERBOLIC PLYKIN ATTRACTOR CAN EXIST IN NEURON MODELS","publication_year":2005,"publication_date":"2005-11-01","ids":{"openalex":"https://openalex.org/W1968199724","doi":"https://doi.org/10.1142/s0218127405014222","mag":"1968199724"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127405014222","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405014222","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/A5005812355","display_name":"\u0412. \u041d. \u0411\u0435\u043b\u044b\u0445","orcid":"https://orcid.org/0000-0002-8736-8849"},"institutions":[{"id":"https://openalex.org/I4210160515","display_name":"Nizhny Novgorod State Agricultural Academy","ror":"https://ror.org/05mfk1s45","country_code":"RU","type":"other","lineage":["https://openalex.org/I4210160515"]},{"id":"https://openalex.org/I2800235127","display_name":"Moscow Architectural Institute","ror":"https://ror.org/03k883a47","country_code":"RU","type":"education","lineage":["https://openalex.org/I2800235127"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"VLADIMIR BELYKH","raw_affiliation_strings":["Mathematics Department, Volga State Academy, 5, Nesterov st., Nizhny Novgorod 603 600, Russia"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Volga State Academy, 5, Nesterov st., Nizhny Novgorod 603 600, Russia","institution_ids":["https://openalex.org/I4210160515","https://openalex.org/I2800235127"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101678275","display_name":"Igor Belykh","orcid":"https://orcid.org/0000-0002-2168-9324"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"IGOR BELYKH","raw_affiliation_strings":["Laboratory of Nonlinear Systems, Swiss Federal Institute of Technology Lausanne (EPFL), EPFL-IC-ISC-LANOS, Station 14, 1015 Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Laboratory of Nonlinear Systems, Swiss Federal Institute of Technology Lausanne (EPFL), EPFL-IC-ISC-LANOS, Station 14, 1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076322824","display_name":"Erik Mosekilde","orcid":"https://orcid.org/0000-0001-7575-8543"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"ERIK MOSEKILDE","raw_affiliation_strings":["Department of Physics, The Technical University of Denmark, 2800 Kongens Lyngby, Denmark"],"affiliations":[{"raw_affiliation_string":"Department of Physics, The Technical University of Denmark, 2800 Kongens Lyngby, Denmark","institution_ids":["https://openalex.org/I96673099"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005812355"],"corresponding_institution_ids":["https://openalex.org/I2800235127","https://openalex.org/I4210160515"],"apc_list":null,"apc_paid":null,"fwci":1.9904,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.85042333,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"15","issue":"11","first_page":"3567","last_page":"3578"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","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"}},"topics":[{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","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/T10581","display_name":"Neural dynamics and brain function","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9973000288009644,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.9015827178955078},{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.7679367065429688},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.638374388217926},{"id":"https://openalex.org/keywords/bursting","display_name":"Bursting","score":0.5513279438018799},{"id":"https://openalex.org/keywords/biological-neuron-model","display_name":"Biological neuron model","score":0.531048595905304},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5143531560897827},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.45357242226600647},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.450716108083725},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40359532833099365},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3971503973007202},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.31031709909439087},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.28694891929626465},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16855069994926453},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.1317809522151947}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.9015827178955078},{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.7679367065429688},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.638374388217926},{"id":"https://openalex.org/C195221683","wikidata":"https://www.wikidata.org/wiki/Q5000649","display_name":"Bursting","level":2,"score":0.5513279438018799},{"id":"https://openalex.org/C186565885","wikidata":"https://www.wikidata.org/wiki/Q1651163","display_name":"Biological neuron model","level":3,"score":0.531048595905304},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5143531560897827},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.45357242226600647},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.450716108083725},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40359532833099365},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3971503973007202},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31031709909439087},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.28694891929626465},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16855069994926453},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.1317809522151947},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127405014222","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405014222","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"},{"id":"pmh:oai:pure.atira.dk:publications/3f1e5824-f5f7-4fdf-85c7-6305da602e4e","is_oa":false,"landing_page_url":"https://orbit.dtu.dk/en/publications/3f1e5824-f5f7-4fdf-85c7-6305da602e4e","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Belykh , V , Belykh , I &amp; Mosekilde , E 2005 , ' Hyperbolic Plykin attractor can exist in neuron models ' , International Journal of Bifurcation and Chaos in Applied Sciences and Engineering , vol. 15 , no. 11 , pp. 3567-3578 .","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W17399409","https://openalex.org/W1542177822","https://openalex.org/W1582770960","https://openalex.org/W1999170261","https://openalex.org/W2012055439","https://openalex.org/W2016397389","https://openalex.org/W2035651162","https://openalex.org/W2036870533","https://openalex.org/W2043250458","https://openalex.org/W2048710389","https://openalex.org/W2063341797","https://openalex.org/W2064108635","https://openalex.org/W2066715774","https://openalex.org/W2069765806","https://openalex.org/W2089876099","https://openalex.org/W2093362963","https://openalex.org/W2093685279","https://openalex.org/W2093699033","https://openalex.org/W2105144092","https://openalex.org/W2119443761","https://openalex.org/W2130502308","https://openalex.org/W2148897094","https://openalex.org/W2163057446","https://openalex.org/W2307072262","https://openalex.org/W2476121101","https://openalex.org/W2497345333","https://openalex.org/W2795407492","https://openalex.org/W3199415720"],"related_works":["https://openalex.org/W2890492950","https://openalex.org/W2279706884","https://openalex.org/W2010606039","https://openalex.org/W3115184012","https://openalex.org/W2397038510","https://openalex.org/W1906329374","https://openalex.org/W9644552","https://openalex.org/W1964759045","https://openalex.org/W2313034084","https://openalex.org/W2009600486"],"abstract_inverted_index":{"Strange":[0],"hyperbolic":[1,36,112,125],"attractors":[2],"are":[3],"hard":[4],"to":[5,32,42,123],"find":[6],"in":[7,131],"real":[8],"physical":[9],"systems.":[10],"This":[11,149],"paper":[12],"provides":[13],"the":[14,43,46,60,68,97,106,118,132,154],"first":[15],"example":[16,108],"of":[17,26,45,59,86,99,109,117,140,146,151],"a":[18,21,34,39,51,64,84,87,100,110,138,141,147],"realistic":[19],"system,":[20],"canonical":[22],"three-dimensional":[23],"(3D)":[24],"model":[25,121],"bursting":[27],"neurons,":[28],"that":[29],"is":[30,96,128],"likely":[31],"have":[33,160],"strange":[35],"attractor.":[37,113],"Using":[38],"geometrical":[40],"approach":[41],"study":[44],"neuron":[47,69,120],"model,":[48],"we":[49],"derive":[50],"flow-defined":[52],"Poincar\u00e9":[53],"map":[54,82,85,98],"giving":[55],"an":[56],"accurate":[57],"account":[58],"system's":[61],"dynamics.":[62],"In":[63],"parameter":[65],"region":[66],"where":[67],"system":[70],"undergoes":[71],"bifurcations":[72],"causing":[73],"transitions":[74],"between":[75],"tonic":[76],"spiking":[77],"and":[78,135,153],"bursting,":[79],"this":[80],"two-dimensional":[81],"becomes":[83],"disk":[88,101],"with":[89,102],"several":[90],"periodic":[91],"holes.":[92],"A":[93],"particular":[94],"case":[95],"three":[103],"holes,":[104],"matching":[105],"Plykin":[107],"planar":[111],"The":[114],"corresponding":[115],"attractor":[116],"3D":[119],"appears":[122],"be":[124],"(this":[126],"property":[127],"not":[129,161],"verified":[130],"present":[133],"paper)":[134],"arises":[136],"as":[137],"result":[139],"two-loop":[142],"(secondary)":[143],"homoclinic":[144],"bifurcation":[145],"saddle.":[148],"type":[150],"bifurcation,":[152],"complex":[155],"behavior":[156],"it":[157],"can":[158],"produce,":[159],"been":[162],"previously":[163],"examined.":[164]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
