{"id":"https://openalex.org/W2908977116","doi":"https://doi.org/10.1155/2019/6715036","title":"Hopf Bifurcation and Chaos of a Delayed Finance System","display_name":"Hopf Bifurcation and Chaos of a Delayed Finance System","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2908977116","doi":"https://doi.org/10.1155/2019/6715036","mag":"2908977116"},"language":"en","primary_location":{"id":"doi:10.1155/2019/6715036","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/6715036","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/6715036.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2019/6715036.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100745894","display_name":"Xuebing Zhang","orcid":"https://orcid.org/0000-0003-0561-5576"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xuebing Zhang","raw_affiliation_strings":["College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China","College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I200845125"]},{"raw_affiliation_string":"College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028939639","display_name":"Honglan Zhu","orcid":"https://orcid.org/0000-0002-3205-1051"},"institutions":[{"id":"https://openalex.org/I4210153869","display_name":"Huaiyin Institute of Technology","ror":"https://ror.org/0555ezg60","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210153869"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Honglan Zhu","raw_affiliation_strings":["Business School, Huaiyin Institute of Technology, Huaian, China","Business School, Huaiyin Institute of Technology, Huaian"],"affiliations":[{"raw_affiliation_string":"Business School, Huaiyin Institute of Technology, Huaian, China","institution_ids":["https://openalex.org/I4210153869"]},{"raw_affiliation_string":"Business School, Huaiyin Institute of Technology, Huaian","institution_ids":["https://openalex.org/I4210153869"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100745894"],"corresponding_institution_ids":["https://openalex.org/I200845125"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":3.7742,"has_fulltext":true,"cited_by_count":27,"citation_normalized_percentile":{"value":0.92652476,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"2019","issue":"1","first_page":null,"last_page":null},"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":0.9976999759674072,"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":0.9976999759674072,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9930999875068665,"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/T10244","display_name":"Chaos control and synchronization","score":0.9886999726295471,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.7709028124809265},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.7393559217453003},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6169153451919556},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6149498820304871},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5715933442115784},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5498440861701965},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4705135226249695},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.45391160249710083},{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.42831653356552124},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37396538257598877},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3225785195827484},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2256748080253601},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17304924130439758},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12918850779533386}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.7709028124809265},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.7393559217453003},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6169153451919556},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6149498820304871},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5715933442115784},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5498440861701965},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4705135226249695},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.45391160249710083},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.42831653356552124},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37396538257598877},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3225785195827484},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2256748080253601},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17304924130439758},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12918850779533386},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2019/6715036","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/6715036","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/6715036.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:6715036","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2019/6715036.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:955bb55b823248699f97a52d018249db","is_oa":true,"landing_page_url":"https://doaj.org/article/955bb55b823248699f97a52d018249db","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2019 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2019/6715036","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/6715036","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/6715036.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2030376154","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G6402716614","display_name":null,"funder_award_id":"BK20150420","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"}],"funders":[{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324849","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19"},{"id":"https://openalex.org/F4320335990","display_name":"Startup Foundation for Introducing Talent of Nanjing University of Information Science and Technology","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2908977116.pdf","grobid_xml":"https://content.openalex.org/works/W2908977116.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1605753492","https://openalex.org/W1967510217","https://openalex.org/W1972345373","https://openalex.org/W1976451792","https://openalex.org/W1977303376","https://openalex.org/W1977471311","https://openalex.org/W1979208642","https://openalex.org/W1981938655","https://openalex.org/W1999647937","https://openalex.org/W2012613827","https://openalex.org/W2027659735","https://openalex.org/W2036448156","https://openalex.org/W2045645156","https://openalex.org/W2048552085","https://openalex.org/W2054151158","https://openalex.org/W2080847646","https://openalex.org/W2082995214","https://openalex.org/W2087464656","https://openalex.org/W2090347294","https://openalex.org/W2094551465","https://openalex.org/W2103999702","https://openalex.org/W2158828508","https://openalex.org/W2398070649","https://openalex.org/W2463688182","https://openalex.org/W2793935480","https://openalex.org/W4232347461","https://openalex.org/W4245425871"],"related_works":["https://openalex.org/W2352502327","https://openalex.org/W4242722972","https://openalex.org/W2884051366","https://openalex.org/W2737309493","https://openalex.org/W2020348172","https://openalex.org/W2377965236","https://openalex.org/W627193461","https://openalex.org/W2017478823","https://openalex.org/W2513783521","https://openalex.org/W2331733846"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,82,86],"finance":[4],"system":[5,84],"with":[6],"delay":[7,79],"is":[8,21,31],"considered.":[9],"By":[10],"analyzing":[11],"the":[12,16,29,38,44,47,55,71],"corresponding":[13],"characteristic":[14],"equations,":[15],"local":[17],"stability":[18,45],"of":[19,25,40,46],"equilibrium":[20,30],"established.":[22],"The":[23],"existence":[24],"Hopf":[26,41],"bifurcations":[27],"at":[28],"also":[32],"discussed.":[33],"Furthermore,":[34],"formulas":[35],"for":[36],"determining":[37],"direction":[39],"bifurcation":[42],"and":[43,59],"bifurcating":[48],"periodic":[49],"solutions":[50],"are":[51,67],"derived":[52],"by":[53],"applying":[54],"normal":[56],"form":[57],"method":[58],"center":[60],"manifold":[61],"theorem.":[62],"Finally,":[63],"numerical":[64],"simulation":[65,75],"results":[66,76],"presented":[68],"to":[69],"validate":[70],"theoretical":[72],"analysis.":[73],"Numerical":[74],"show":[77],"that":[78],"can":[80],"lead":[81],"stable":[83],"into":[85],"chaotic":[87],"state.":[88]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}