{"id":"https://openalex.org/W2052828399","doi":"https://doi.org/10.1142/s0218127405012880","title":"HOPF BIFURCATION OF A THREE-DIMENSIONAL SYSTEM","display_name":"HOPF BIFURCATION OF A THREE-DIMENSIONAL SYSTEM","publication_year":2005,"publication_date":"2005-05-01","ids":{"openalex":"https://openalex.org/W2052828399","doi":"https://doi.org/10.1142/s0218127405012880","mag":"2052828399"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127405012880","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405012880","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/A5077019923","display_name":"Xuanliang Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]},{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]},{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"XUANLIANG LIU","raw_affiliation_strings":["Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, China","Department of Mathematics, Shanghai Normal University, Shanghai 200234, China","School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China","institution_ids":["https://openalex.org/I21945476"]},{"raw_affiliation_string":"School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030649439","display_name":"Maoan Han","orcid":"https://orcid.org/0000-0001-8792-1256"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]},{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]},{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"MAOAN HAN","raw_affiliation_strings":["Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, China","Department of Mathematics, Shanghai Normal University, Shanghai 200234, China","School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China","institution_ids":["https://openalex.org/I21945476"]},{"raw_affiliation_string":"School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China","institution_ids":["https://openalex.org/I90610280"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6843,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.76552478,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"15","issue":"05","first_page":"1603","last_page":"1614"},"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":0.998199999332428,"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":0.998199999332428,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9977999925613403,"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"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9926999807357788,"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/bifurcation","display_name":"Bifurcation","score":0.740534782409668},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.6930776834487915},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.6846757531166077},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6724180579185486},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.6466565728187561},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6463483572006226},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.6192224025726318},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5391694903373718},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.49669891595840454},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.494674414396286},{"id":"https://openalex.org/keywords/bogdanov\u2013takens-bifurcation","display_name":"Bogdanov\u2013Takens bifurcation","score":0.49377378821372986},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.4865819215774536},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.48327261209487915},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.4698955714702606},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.42834970355033875},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1950300633907318},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14433249831199646},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.07302504777908325}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.740534782409668},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.6930776834487915},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.6846757531166077},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6724180579185486},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.6466565728187561},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6463483572006226},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.6192224025726318},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5391694903373718},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.49669891595840454},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.494674414396286},{"id":"https://openalex.org/C22257346","wikidata":"https://www.wikidata.org/wiki/Q4937510","display_name":"Bogdanov\u2013Takens bifurcation","level":5,"score":0.49377378821372986},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.4865819215774536},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.48327261209487915},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.4698955714702606},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.42834970355033875},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1950300633907318},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14433249831199646},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.07302504777908325},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/s0218127405012880","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405012880","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":[{"score":0.8100000023841858,"id":"https://metadata.un.org/sdg/3","display_name":"Good health and well-being"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1603340857","https://openalex.org/W1986512346","https://openalex.org/W1991665978","https://openalex.org/W1992942797","https://openalex.org/W2074879692","https://openalex.org/W2075489080","https://openalex.org/W2089876099","https://openalex.org/W2148704323","https://openalex.org/W2489426763","https://openalex.org/W4214513274"],"related_works":["https://openalex.org/W2546487931","https://openalex.org/W3020506472","https://openalex.org/W2775656422","https://openalex.org/W4245057904","https://openalex.org/W2025138898","https://openalex.org/W2325048728","https://openalex.org/W2978098199","https://openalex.org/W4281733204","https://openalex.org/W3081645617","https://openalex.org/W2054978396"],"abstract_inverted_index":{"Consider":[0],"a":[1,9,60],"three-dimensional":[2],"system":[3],"having":[4],"an":[5],"invariant":[6,17],"surface":[7],"and":[8,23,40],"weak":[10,38,52],"focus":[11,39],"of":[12,27,47,56],"order":[13],"k":[14],"on":[15],"the":[16,25,32,37,42,45,51],"surface.":[18],"By":[19],"using":[20],"bifurcation":[21,28,34],"techniques":[22],"analyzing":[24],"solutions":[26],"equations,":[29],"we":[30],"study":[31],"spatial":[33],"phenomena":[35],"near":[36,50],"obtain":[41],"conditions":[43],"for":[44],"existence":[46],"periodic":[48],"orbits":[49],"focus.":[53],"An":[54],"application":[55],"our":[57],"results":[58],"to":[59],"SIRS":[61],"epidemiological":[62],"model":[63],"is":[64],"given.":[65]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
