{"id":"https://openalex.org/W2162745417","doi":"https://doi.org/10.1142/s0218127413500557","title":"APPLICATION OF A TWO-DIMENSIONAL HINDMARSH\u2013ROSE TYPE MODEL FOR BIFURCATION ANALYSIS","display_name":"APPLICATION OF A TWO-DIMENSIONAL HINDMARSH\u2013ROSE TYPE MODEL FOR BIFURCATION ANALYSIS","publication_year":2013,"publication_date":"2013-03-01","ids":{"openalex":"https://openalex.org/W2162745417","doi":"https://doi.org/10.1142/s0218127413500557","mag":"2162745417"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127413500557","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413500557","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/A5112156632","display_name":"Shyan-Shiou Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I134161618","display_name":"National Taiwan Normal University","ror":"https://ror.org/059dkdx38","country_code":"TW","type":"education","lineage":["https://openalex.org/I134161618"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"SHYAN-SHIOU CHEN","raw_affiliation_strings":["Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan","institution_ids":["https://openalex.org/I134161618"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062659630","display_name":"Chang\u2010Yuan Cheng","orcid":"https://orcid.org/0000-0001-9557-547X"},"institutions":[{"id":"https://openalex.org/I1309796872","display_name":"National Pingtung University","ror":"https://ror.org/03z698x91","country_code":"TW","type":"education","lineage":["https://openalex.org/I1309796872"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"CHANG-YUAN CHENG","raw_affiliation_strings":["Department of Applied Mathematics, National Pingtung University of Education, Pingtung, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National Pingtung University of Education, Pingtung, Taiwan","institution_ids":["https://openalex.org/I1309796872"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103577737","display_name":"Yi-Ru Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I134161618","display_name":"National Taiwan Normal University","ror":"https://ror.org/059dkdx38","country_code":"TW","type":"education","lineage":["https://openalex.org/I134161618"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"YI-RU LIN","raw_affiliation_strings":["Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan","institution_ids":["https://openalex.org/I134161618"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5112156632"],"corresponding_institution_ids":["https://openalex.org/I134161618"],"apc_list":null,"apc_paid":null,"fwci":0.7489,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.73788895,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"23","issue":"03","first_page":"1350055","last_page":"1350055"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9987999796867371,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"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/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.7764392495155334},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.7374035120010376},{"id":"https://openalex.org/keywords/bogdanov\u2013takens-bifurcation","display_name":"Bogdanov\u2013Takens bifurcation","score":0.6775357127189636},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.6647534966468811},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.6479879021644592},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6399590969085693},{"id":"https://openalex.org/keywords/bistability","display_name":"Bistability","score":0.6289107799530029},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.6039537191390991},{"id":"https://openalex.org/keywords/heteroclinic-bifurcation","display_name":"Heteroclinic bifurcation","score":0.5595638751983643},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.5128982067108154},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5013229846954346},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.4647570848464966},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.45349442958831787},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.44998738169670105},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37854164838790894},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35780656337738037},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.29955363273620605},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20500090718269348},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1724204421043396},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14720848202705383},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1139746904373169}],"concepts":[{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.7764392495155334},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7374035120010376},{"id":"https://openalex.org/C22257346","wikidata":"https://www.wikidata.org/wiki/Q4937510","display_name":"Bogdanov\u2013Takens bifurcation","level":5,"score":0.6775357127189636},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.6647534966468811},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.6479879021644592},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6399590969085693},{"id":"https://openalex.org/C97292510","wikidata":"https://www.wikidata.org/wiki/Q2304620","display_name":"Bistability","level":2,"score":0.6289107799530029},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.6039537191390991},{"id":"https://openalex.org/C73888704","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Heteroclinic bifurcation","level":5,"score":0.5595638751983643},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.5128982067108154},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5013229846954346},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.4647570848464966},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.45349442958831787},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.44998738169670105},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37854164838790894},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35780656337738037},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.29955363273620605},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20500090718269348},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1724204421043396},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14720848202705383},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1139746904373169},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127413500557","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413500557","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/F4320311041","display_name":"National Center for Theoretical Sciences","ror":"https://ror.org/02mfp0b67"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1576838367","https://openalex.org/W1971444835","https://openalex.org/W1983069678","https://openalex.org/W1985940938","https://openalex.org/W1987869613","https://openalex.org/W1995992845","https://openalex.org/W1999170261","https://openalex.org/W2002317454","https://openalex.org/W2003743055","https://openalex.org/W2009375605","https://openalex.org/W2028567792","https://openalex.org/W2040728373","https://openalex.org/W2042316744","https://openalex.org/W2044172180","https://openalex.org/W2044564991","https://openalex.org/W2048567223","https://openalex.org/W2059881362","https://openalex.org/W2061191702","https://openalex.org/W2063536285","https://openalex.org/W2072210701","https://openalex.org/W2082380332","https://openalex.org/W2093685279","https://openalex.org/W2094346521","https://openalex.org/W2113868787","https://openalex.org/W2136894332","https://openalex.org/W2154660704","https://openalex.org/W2157239334","https://openalex.org/W2163057446","https://openalex.org/W4253775301"],"related_works":["https://openalex.org/W2025138898","https://openalex.org/W2559450076","https://openalex.org/W2923981205","https://openalex.org/W3008253414","https://openalex.org/W4388961837","https://openalex.org/W152938242","https://openalex.org/W2387129305","https://openalex.org/W4365441268","https://openalex.org/W2102865807","https://openalex.org/W2775656422"],"abstract_inverted_index":{"In":[0,123],"this":[1,29,185,190],"study,":[2],"we":[3,101],"examine":[4],"the":[5,40,43,47,52,63,67,70,81,85,104,108,133,141,145,148,154,162,168,201],"bifurcation":[6,91,95,142],"scenarios":[7],"of":[8,25,42,51,69,127,140,147,170,181,189,203],"a":[9,59,93,165,171,179],"two-dimensional":[10],"Hindmarsh\u2013Rose":[11],"type":[12],"model":[13,30],"[Tsuji":[14],"et":[15],"al.,":[16],"2007]":[17],"with":[18],"four":[19],"parameters":[20,150,198],"and":[21,49,73,92,99,111,135],"simulate":[22],"some":[23],"resemblances":[24,202],"neurophysiological":[26],"features":[27],"for":[28,88,107,117,164,184,199],"using":[31,58],"spike-and-reset":[32],"conditions.":[33],"We":[34],"present":[35,178],"possible":[36],"classifications":[37],"based":[38],"on":[39],"results":[41,177,188],"following":[44],"assessments:":[45],"(1)":[46],"number":[48],"stability":[50,68],"equilibria":[53,78],"are":[54,96,120,130,151],"analyzed":[55],"in":[56,65,144,195],"detail":[57],"table":[60],"to":[61,74,160],"demonstrate":[62],"matter":[64],"which":[66,76],"equilibrium":[71],"changes":[72],"determine":[75],"two":[77,125],"collapse":[79],"through":[80],"saddle-node":[82,94],"bifurcation;":[83],"(2)":[84],"sufficient":[86,105],"conditions":[87,106,119],"an":[89],"Andronov\u2013Hopf":[90],"mathematically":[97],"confirmed;":[98],"(3)":[100],"elaborately":[102],"evaluate":[103],"Bogdanov\u2013Takens":[109],"(BT)":[110],"Bautin":[112,136],"bifurcations.":[113,137],"Several":[114],"numerical":[115],"simulations":[116],"these":[118],"also":[121],"presented.":[122],"particular,":[124],"types":[126],"bistable":[128],"behaviors":[129,183],"numerically":[131],"demonstrated:":[132],"BT":[134],"Notably,":[138],"all":[139],"curves":[143],"domain":[146],"remaining":[149],"similar":[152],"when":[153],"time":[155],"scale":[156],"is":[157,174],"large.":[158],"Additionally,":[159],"show":[161],"potential":[163],"limit":[166],"cycle,":[167],"existence":[169],"trapping":[172],"region":[173],"demonstrated.":[175],"These":[176],"variety":[180],"diverse":[182],"model.":[186],"The":[187],"study":[191],"will":[192],"be":[193],"helpful":[194],"assessing":[196],"suitable":[197],"fitting":[200],"experimental":[204],"observations.":[205]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}