{"id":"https://openalex.org/W2540417212","doi":"https://doi.org/10.1142/s0218127416501819","title":"Complexity and Hopf Bifurcation Analysis on a Kind of Fractional-Order IS-LM Macroeconomic System","display_name":"Complexity and Hopf Bifurcation Analysis on a Kind of Fractional-Order IS-LM Macroeconomic System","publication_year":2016,"publication_date":"2016-10-01","ids":{"openalex":"https://openalex.org/W2540417212","doi":"https://doi.org/10.1142/s0218127416501819","mag":"2540417212"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416501819","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218127416501819","pdf_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218127416501819","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","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":true,"oa_status":"hybrid","oa_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218127416501819","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037162105","display_name":"Junhai Ma","orcid":"https://orcid.org/0000-0002-0827-5143"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junhai Ma","raw_affiliation_strings":["Nonlinear Dynamics and Chaos Group, College of Management and Economics, Tianjin University, Tianjin 300072, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nonlinear Dynamics and Chaos Group, College of Management and Economics, Tianjin University, Tianjin 300072, P. R. China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048495304","display_name":"Wenbo Ren","orcid":null},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenbo Ren","raw_affiliation_strings":["Nonlinear Dynamics and Chaos Group, College of Management and Economics, Tianjin University, Tianjin 300072, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nonlinear Dynamics and Chaos Group, College of Management and Economics, Tianjin University, Tianjin 300072, P. R. China","institution_ids":["https://openalex.org/I162868743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I162868743"],"apc_list":null,"apc_paid":null,"fwci":2.5783,"has_fulltext":true,"cited_by_count":40,"citation_normalized_percentile":{"value":0.90356908,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"26","issue":"11","first_page":"1650181","last_page":"1650181"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9825000166893005,"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/T10244","display_name":"Chaos control and synchronization","score":0.9825000166893005,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9821000099182129,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9168000221252441,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.7625131607055664},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6663945913314819},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6613485217094421},{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.6274263858795166},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5709033608436584},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.512897253036499},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.4745548367500305},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.4473171830177307},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4400930106639862},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3602721095085144},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.33589544892311096},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.33184653520584106},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.24514147639274597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2001224160194397},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.15593311190605164},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.15193045139312744},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10325279831886292},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.0987933874130249}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.7625131607055664},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6663945913314819},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6613485217094421},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.6274263858795166},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5709033608436584},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.512897253036499},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.4745548367500305},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.4473171830177307},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4400930106639862},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3602721095085144},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.33589544892311096},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.33184653520584106},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.24514147639274597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2001224160194397},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.15593311190605164},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.15193045139312744},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10325279831886292},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0987933874130249},{"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/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/s0218127416501819","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218127416501819","pdf_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218127416501819","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1142/s0218127416501819","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218127416501819","pdf_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218127416501819","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.4300000071525574,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G2746463770","display_name":null,"funder_award_id":"61273231","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3560401187","display_name":null,"funder_award_id":"20130032110073","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G362885854","display_name":null,"funder_award_id":"20130032110073","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321106","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2540417212.pdf","grobid_xml":"https://content.openalex.org/works/W2540417212.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1966767366","https://openalex.org/W1972345373","https://openalex.org/W1976451792","https://openalex.org/W1977132609","https://openalex.org/W1977303376","https://openalex.org/W1981943635","https://openalex.org/W1984257705","https://openalex.org/W1985439127","https://openalex.org/W1989484457","https://openalex.org/W1990033217","https://openalex.org/W2008052025","https://openalex.org/W2009699965","https://openalex.org/W2020427565","https://openalex.org/W2032820503","https://openalex.org/W2034058244","https://openalex.org/W2036442409","https://openalex.org/W2045777621","https://openalex.org/W2053840485","https://openalex.org/W2054151158","https://openalex.org/W2056134058","https://openalex.org/W2057168606","https://openalex.org/W2089837532","https://openalex.org/W2137696066","https://openalex.org/W2145975275","https://openalex.org/W2165372720","https://openalex.org/W2259227674","https://openalex.org/W2478495703","https://openalex.org/W3143244837","https://openalex.org/W3198644217","https://openalex.org/W4232347461","https://openalex.org/W4245425871"],"related_works":["https://openalex.org/W2083968322","https://openalex.org/W2070724789","https://openalex.org/W2313198288","https://openalex.org/W4382985020","https://openalex.org/W1973339055","https://openalex.org/W2106609868","https://openalex.org/W2115351049","https://openalex.org/W2353430195","https://openalex.org/W4214588273","https://openalex.org/W3039757618"],"abstract_inverted_index":{"On":[0],"the":[1,27,37,40,43,48,52,58,75,85,91,110,122,130,134,143,146,151,157,160,165],"basis":[2],"of":[3,13,30,39,51,64,90,133,148,159],"our":[4],"previous":[5],"research,":[6],"we":[7,33],"deepen":[8],"and":[9,46,74,102,109,162,180],"complete":[10],"a":[11,23,139],"kind":[12],"macroeconomics":[14],"IS-LM":[15],"model":[16],"with":[17,115,156],"fractional-order":[18,68,152],"calculus":[19],"theory,":[20],"which":[21],"is":[22,82,113],"good":[24],"reflection":[25],"on":[26,36,42,129],"memory":[28],"characteristics":[29,89,106],"economic":[31,54],"variables,":[32],"also":[34],"focus":[35],"influence":[38,128],"variables":[41],"real":[44],"system,":[45],"improve":[47],"analysis":[49],"capabilities":[50],"traditional":[53],"models":[55,70],"to":[56,117,175],"suit":[57],"actual":[59],"macroeconomic":[60,178],"environment.":[61],"The":[62,136],"conditions":[63,147],"Hopf":[65,79,149],"bifurcation":[66,80],"in":[67],"system":[69,123,137,153,168],"are":[71,107],"briefly":[72],"demonstrated,":[73],"fractional":[76],"order":[77,111,124,144,161],"when":[78,142],"occurs":[81],"calculated,":[83],"showing":[84],"inherent":[86],"complex":[87,104],"dynamic":[88,105],"system.":[92,135],"With":[93],"numerical":[94],"simulation,":[95],"bifurcation,":[96],"strange":[97],"attractor,":[98],"limit":[99],"cycle,":[100],"waveform":[101],"other":[103],"given;":[108],"condition":[112],"obtained":[114],"respect":[116],"time.":[118],"We":[119],"find":[120],"that":[121],"has":[125,138,172],"an":[126],"important":[127],"running":[131],"state":[132],"periodic":[140],"motion":[141],"meets":[145],"bifurcation;":[150],"gradually":[154],"stabilizes":[155],"change":[158],"parameters":[163],"while":[164],"corresponding":[166],"integer-order":[167],"diverges.":[169],"This":[170],"study":[171],"certain":[173],"significance":[174],"policy-making":[176],"about":[177],"regulation":[179],"control.":[181]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}