{"id":"https://openalex.org/W2479615769","doi":"https://doi.org/10.1142/s0218127416500796","title":"Hopf and Generalized Hopf Bifurcations in a Recurrent Autoimmune Disease Model","display_name":"Hopf and Generalized Hopf Bifurcations in a Recurrent Autoimmune Disease Model","publication_year":2016,"publication_date":"2016-05-01","ids":{"openalex":"https://openalex.org/W2479615769","doi":"https://doi.org/10.1142/s0218127416500796","mag":"2479615769"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416500796","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500796","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/A5100407219","display_name":"Wenjing Zhang","orcid":"https://orcid.org/0000-0003-3451-7035"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Wenjing Zhang","raw_affiliation_strings":["Department of Applied Mathematics, Western University London, Ontario, N6A 5B7, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Western University London, Ontario, N6A 5B7, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100652002","display_name":"Pei Yu","orcid":"https://orcid.org/0000-0002-8848-0584"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Pei Yu","raw_affiliation_strings":["Department of Applied Mathematics, Western University London, Ontario, N6A 5B7, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Western University London, Ontario, N6A 5B7, Canada","institution_ids":["https://openalex.org/I125749732"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100407219"],"corresponding_institution_ids":["https://openalex.org/I125749732"],"apc_list":null,"apc_paid":null,"fwci":0.9254,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.81623757,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"26","issue":"05","first_page":"1650079","last_page":"1650079"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9965000152587891,"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"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9965000152587891,"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"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9864000082015991,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.9837999939918518,"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/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.8123574256896973},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.8045518398284912},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.6912747621536255},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6571702361106873},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.6423007845878601},{"id":"https://openalex.org/keywords/bogdanov\u2013takens-bifurcation","display_name":"Bogdanov\u2013Takens bifurcation","score":0.5959886312484741},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.5902098417282104},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.576996386051178},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5635241270065308},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.49708011746406555},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4941852390766144},{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.4713137745857239},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.45441943407058716},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.4512443244457245},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43078213930130005},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3724956512451172},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2099335491657257},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.18282341957092285},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07401922345161438},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.056695252656936646}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.8123574256896973},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.8045518398284912},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.6912747621536255},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6571702361106873},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.6423007845878601},{"id":"https://openalex.org/C22257346","wikidata":"https://www.wikidata.org/wiki/Q4937510","display_name":"Bogdanov\u2013Takens bifurcation","level":5,"score":0.5959886312484741},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.5902098417282104},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.576996386051178},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5635241270065308},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.49708011746406555},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4941852390766144},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.4713137745857239},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.45441943407058716},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.4512443244457245},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43078213930130005},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3724956512451172},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2099335491657257},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.18282341957092285},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07401922345161438},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.056695252656936646},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127416500796","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500796","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":[{"id":"https://openalex.org/G8338819528","display_name":null,"funder_award_id":"R2686A02","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W573847062","https://openalex.org/W1497825085","https://openalex.org/W1963899067","https://openalex.org/W1967497177","https://openalex.org/W1967896457","https://openalex.org/W1968517897","https://openalex.org/W2009497399","https://openalex.org/W2016452430","https://openalex.org/W2036117709","https://openalex.org/W2036978605","https://openalex.org/W2072797656","https://openalex.org/W2072853625","https://openalex.org/W2081879691","https://openalex.org/W2089876099","https://openalex.org/W2140959905","https://openalex.org/W2156647731","https://openalex.org/W2310072985","https://openalex.org/W3040940214","https://openalex.org/W4248348571","https://openalex.org/W4293244147"],"related_works":["https://openalex.org/W2325048728","https://openalex.org/W56905705","https://openalex.org/W1880931252","https://openalex.org/W2030734556","https://openalex.org/W1530420675","https://openalex.org/W2388294899","https://openalex.org/W2111150538","https://openalex.org/W1597625502","https://openalex.org/W2078078632","https://openalex.org/W2021742636"],"abstract_inverted_index":{"This":[0,26,139],"paper":[1],"is":[2,114],"concerned":[3],"with":[4,93,155],"bifurcation":[5,64,119],"and":[6,34,45,83,87,106,136],"stability":[7,48,108],"in":[8,147],"an":[9,17],"autoimmune":[10],"model,":[11],"which":[12,65,97,129],"was":[13],"established":[14],"to":[15,117,159],"study":[16,75],"important":[18],"phenomenon":[19,133],"\u2014":[20],"blips":[21],"arising":[22,124],"from":[23,67,96,125],"such":[24],"models.":[25],"model":[27,44],"has":[28],"two":[29],"equilibrium":[30,33,52,135],"solutions,":[31],"disease-free":[32,51],"disease":[35,69],"equilibrium.":[36,70],"The":[37],"positivity":[38],"of":[39,42,49,79,101,120],"the":[40,43,46,50,68,77,89,98,102,118,156],"solutions":[41],"global":[47],"have":[53],"been":[54],"proved.":[55],"In":[56],"this":[57],"paper,":[58],"we":[59],"particularly":[60],"focus":[61],"on":[62,76],"Hopf":[63,94,127],"occurs":[66],"We":[71],"present":[72],"a":[73,161],"detailed":[74],"use":[78],"center":[80],"manifold":[81],"theory":[82],"normal":[84,90],"form":[85,91],"theory,":[86],"derive":[88],"associated":[92],"bifurcation,":[95,128],"approximate":[99],"amplitude":[100],"bifurcating":[103],"limit":[104,122],"cycles":[105,123],"their":[107],"conditions":[109],"are":[110,153],"obtained.":[111],"Particular":[112],"attention":[113],"also":[115],"paid":[116],"multiple":[121],"generalized":[126],"may":[130,141],"yield":[131],"bistable":[132],"involving":[134],"oscillating":[137],"motion.":[138],"result":[140],"explain":[142],"some":[143],"complex":[144],"dynamical":[145],"behavior":[146],"real":[148],"biological":[149],"systems.":[150],"Numerical":[151],"simulations":[152],"compared":[154],"analytical":[157],"predictions":[158],"show":[160],"very":[162],"good":[163],"agreement.":[164]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
