{"id":"https://openalex.org/W2782668958","doi":"https://doi.org/10.1155/2018/1263602","title":"Dynamic Analysis for a Kaldor\u2013Kalecki Model of Business Cycle with Time Delay and Diffusion Effect","display_name":"Dynamic Analysis for a Kaldor\u2013Kalecki Model of Business Cycle with Time Delay and Diffusion Effect","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2782668958","doi":"https://doi.org/10.1155/2018/1263602","mag":"2782668958"},"language":"en","primary_location":{"id":"doi:10.1155/2018/1263602","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/1263602","pdf_url":"http://downloads.hindawi.com/journals/complexity/2018/1263602.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":"http://downloads.hindawi.com/journals/complexity/2018/1263602.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101808800","display_name":"Wenjie Hu","orcid":"https://orcid.org/0000-0002-3691-7166"},"institutions":[{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]},{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenjie Hu","raw_affiliation_strings":["College of Economics and Business Administration, Chongqing University, Chongqing 400030, China","College of Economics and Management, Chongqing University of Posts and Telecommunications, Chongqing 400065, China","College of Economics and Business Administration, Chongqing University, Chongqing 400030","College of Economics and Management, Chongqing University of Posts and Telecommunications, Chongqing 400065"],"affiliations":[{"raw_affiliation_string":"College of Economics and Business Administration, Chongqing University, Chongqing 400030, China","institution_ids":["https://openalex.org/I158842170"]},{"raw_affiliation_string":"College of Economics and Management, Chongqing University of Posts and Telecommunications, Chongqing 400065, China","institution_ids":["https://openalex.org/I10535382"]},{"raw_affiliation_string":"College of Economics and Business Administration, Chongqing University, Chongqing 400030","institution_ids":["https://openalex.org/I158842170"]},{"raw_affiliation_string":"College of Economics and Management, Chongqing University of Posts and Telecommunications, Chongqing 400065","institution_ids":["https://openalex.org/I10535382"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109980731","display_name":"Hua Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I145581781","display_name":"Chongqing Technology and Business University","ror":"https://ror.org/05hqf1284","country_code":"CN","type":"education","lineage":["https://openalex.org/I145581781"]},{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hua Zhao","raw_affiliation_strings":["College of Economics and Business Administration, Chongqing University, Chongqing 400030, China","School of Management, Chongqing Technology and Business University, Chongqing 4000067, China","School of Management, Chongqing Technology and Business University, Chongqing 4000067","College of Economics and Business Administration, Chongqing University, Chongqing 400030"],"affiliations":[{"raw_affiliation_string":"College of Economics and Business Administration, Chongqing University, Chongqing 400030, China","institution_ids":["https://openalex.org/I158842170"]},{"raw_affiliation_string":"School of Management, Chongqing Technology and Business University, Chongqing 4000067, China","institution_ids":["https://openalex.org/I145581781"]},{"raw_affiliation_string":"School of Management, Chongqing Technology and Business University, Chongqing 4000067","institution_ids":["https://openalex.org/I145581781"]},{"raw_affiliation_string":"College of Economics and Business Administration, Chongqing University, Chongqing 400030","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035908164","display_name":"Tao Dong","orcid":"https://orcid.org/0000-0003-0555-2720"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Dong","raw_affiliation_strings":["College of Electronics and Information Engineering, Southwest University, Chongqing 400715, China","College of Electronics and Information Engineering, Southwest University, Chongqing 400715"],"affiliations":[{"raw_affiliation_string":"College of Electronics and Information Engineering, Southwest University, Chongqing 400715, China","institution_ids":["https://openalex.org/I142108993"]},{"raw_affiliation_string":"College of Electronics and Information Engineering, Southwest University, Chongqing 400715","institution_ids":["https://openalex.org/I142108993"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5109980731"],"corresponding_institution_ids":["https://openalex.org/I145581781","https://openalex.org/I158842170"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":1.297,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.79939848,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2018","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T10591","display_name":"Theoretical and Computational Physics","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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":0.989300012588501,"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/T12137","display_name":"Economic theories and models","score":0.9872000217437744,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.7968400120735168},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.7288994789123535},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6085972189903259},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5826828479766846},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5529174208641052},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5310688018798828},{"id":"https://openalex.org/keywords/business-cycle","display_name":"Business cycle","score":0.5286192297935486},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47654443979263306},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.43655309081077576},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.4212125837802887},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33971595764160156},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19662261009216309},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.15960898995399475},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1503753662109375},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.09892797470092773},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09363439679145813}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.7968400120735168},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.7288994789123535},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6085972189903259},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5826828479766846},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5529174208641052},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5310688018798828},{"id":"https://openalex.org/C83873408","wikidata":"https://www.wikidata.org/wiki/Q192311","display_name":"Business cycle","level":2,"score":0.5286192297935486},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47654443979263306},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.43655309081077576},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.4212125837802887},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33971595764160156},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19662261009216309},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.15960898995399475},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1503753662109375},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.09892797470092773},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09363439679145813},{"id":"https://openalex.org/C165556158","wikidata":"https://www.wikidata.org/wiki/Q83937","display_name":"Keynesian economics","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},{"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:10.1155/2018/1263602","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/1263602","pdf_url":"http://downloads.hindawi.com/journals/complexity/2018/1263602.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:1263602","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2018/1263602.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:08bc8d8664a54ac0a05aad80ca63dba0","is_oa":true,"landing_page_url":"https://doaj.org/article/08bc8d8664a54ac0a05aad80ca63dba0","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 2018 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2018/1263602","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/1263602","pdf_url":"http://downloads.hindawi.com/journals/complexity/2018/1263602.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/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1592599751","display_name":null,"funder_award_id":"2017CDJSK","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G2082826544","display_name":null,"funder_award_id":"Postdoctoral","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2376276132","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G37568934","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4020255992","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6252504151","display_name":null,"funder_award_id":"61503310","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6364770894","display_name":null,"funder_award_id":"2015CDJSK","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G7033253288","display_name":null,"funder_award_id":"Grants","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8951484681","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2782668958.pdf","grobid_xml":"https://content.openalex.org/works/W2782668958.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W195084069","https://openalex.org/W1605753492","https://openalex.org/W2007548162","https://openalex.org/W2015095989","https://openalex.org/W2028180578","https://openalex.org/W2047559644","https://openalex.org/W2052431612","https://openalex.org/W2281772120","https://openalex.org/W2346851971","https://openalex.org/W2519946226","https://openalex.org/W2568578428","https://openalex.org/W2601233470","https://openalex.org/W2617535932","https://openalex.org/W2623278705","https://openalex.org/W2623299508","https://openalex.org/W2625711953","https://openalex.org/W2748072858","https://openalex.org/W3125457638"],"related_works":["https://openalex.org/W1987790493","https://openalex.org/W2153388945","https://openalex.org/W2038701038","https://openalex.org/W1975783007","https://openalex.org/W2382752082","https://openalex.org/W1988489950","https://openalex.org/W4312255936","https://openalex.org/W4313700716","https://openalex.org/W1986426368","https://openalex.org/W2363522146"],"abstract_inverted_index":{"The":[0],"dynamics":[1],"behaviors":[2],"of":[3,24,57,72,86],"Kaldor\u2013Kalecki":[4],"business":[5],"cycle":[6],"model":[7],"with":[8],"diffusion":[9,104,116],"effect":[10],"and":[11,26,68,83],"time":[12,36,47],"delay":[13,37,48],"under":[14],"the":[15,22,35,42,46,54,64,73,80,84,87,96,103,111,115],"Neumann":[16],"boundary":[17],"conditions":[18,23],"are":[19,29],"investigated.":[20,30],"First":[21],"time\u2010independent":[25],"time\u2010dependent":[27],"stability":[28,85],"Then,":[31],"we":[32],"find":[33],"that":[34,102],"can":[38,78],"give":[39],"rise":[40],"to":[41],"Hopf":[43,58],"bifurcation":[44,81],"when":[45],"passes":[49],"a":[50,107],"critical":[51],"value.":[52],"Moreover,":[53],"normal":[55,69],"form":[56,70],"bifurcations":[59],"is":[60],"obtained":[61,97],"by":[62],"using":[63],"center":[65],"manifold":[66],"theorem":[67],"theory":[71],"partial":[74],"differential":[75],"equation,":[76],"which":[77],"determine":[79],"direction":[82],"periodic":[88],"solutions.":[89],"Finally,":[90],"numerical":[91],"results":[92],"not":[93],"only":[94],"validate":[95],"theorems,":[98],"but":[99],"also":[100],"show":[101],"coefficients":[105,117],"play":[106],"key":[108],"role":[109],"in":[110],"spatial":[112],"pattern.":[113],"With":[114],"increasing,":[118],"different":[119],"patterns":[120],"appear.":[121]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}