{"id":"https://openalex.org/W1974132224","doi":"https://doi.org/10.1142/s021812740902502x","title":"MEASURING AND CONTROLLING THE CHAOTIC MOTION OF PROFITS","display_name":"MEASURING AND CONTROLLING THE CHAOTIC MOTION OF PROFITS","publication_year":2009,"publication_date":"2009-11-01","ids":{"openalex":"https://openalex.org/W1974132224","doi":"https://doi.org/10.1142/s021812740902502x","mag":"1974132224"},"language":"en","primary_location":{"id":"doi:10.1142/s021812740902502x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812740902502x","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10174/6774","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047367651","display_name":"Cristina Janu\u00e1rio","orcid":"https://orcid.org/0000-0002-6978-876X"},"institutions":[{"id":"https://openalex.org/I203847022","display_name":"Instituto Polit\u00e9cnico de Lisboa","ror":"https://ror.org/04ea70f07","country_code":"PT","type":"education","lineage":["https://openalex.org/I203847022"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"CRISTINA JANU\u00c1RIO","raw_affiliation_strings":["ISEL-Instituto Superior de Engenharia de Lisboa, Department of Chemistry, Mathematics Unit, Rua Conselheiro Em\u00eddio Navarro, 1949-014 Lisboa, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ISEL-Instituto Superior de Engenharia de Lisboa, Department of Chemistry, Mathematics Unit, Rua Conselheiro Em\u00eddio Navarro, 1949-014 Lisboa, Portugal","institution_ids":["https://openalex.org/I203847022"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029251488","display_name":"Clara Gr\u00e1cio","orcid":"https://orcid.org/0000-0002-0397-5669"},"institutions":[{"id":"https://openalex.org/I21803372","display_name":"University of \u00c9vora","ror":"https://ror.org/02gyps716","country_code":"PT","type":"education","lineage":["https://openalex.org/I21803372"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"CLARA GR\u00c1CIO","raw_affiliation_strings":["CIMA-UE, Universidade de \u00c9vora, Portugal","Department of Mathematics, Universidade de \u00c9vora, Rua Rom\u00e3o Ramalho, 59, 7000-585 \u00c9vora, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CIMA-UE, Universidade de \u00c9vora, Portugal","institution_ids":["https://openalex.org/I21803372"]},{"raw_affiliation_string":"Department of Mathematics, Universidade de \u00c9vora, Rua Rom\u00e3o Ramalho, 59, 7000-585 \u00c9vora, Portugal","institution_ids":["https://openalex.org/I21803372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023817716","display_name":"Diana Mendes","orcid":"https://orcid.org/0000-0002-8391-9113"},"institutions":[{"id":"https://openalex.org/I110026055","display_name":"Iscte \u2013 Instituto Universit\u00e1rio de Lisboa","ror":"https://ror.org/014837179","country_code":"PT","type":"education","lineage":["https://openalex.org/I110026055"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"DIANA A. MENDES","raw_affiliation_strings":["Department of Quantitative Methods, Instituto Superior de Ci\u00eancias do Trabalho e da Empresa, Avenida das For\u00e7as Armadas, 1649-026 Lisboa, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Quantitative Methods, Instituto Superior de Ci\u00eancias do Trabalho e da Empresa, Avenida das For\u00e7as Armadas, 1649-026 Lisboa, Portugal","institution_ids":["https://openalex.org/I110026055"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087672348","display_name":"Jorge Duarte","orcid":"https://orcid.org/0000-0003-2641-3199"},"institutions":[{"id":"https://openalex.org/I203847022","display_name":"Instituto Polit\u00e9cnico de Lisboa","ror":"https://ror.org/04ea70f07","country_code":"PT","type":"education","lineage":["https://openalex.org/I203847022"]},{"id":"https://openalex.org/I21803372","display_name":"University of \u00c9vora","ror":"https://ror.org/02gyps716","country_code":"PT","type":"education","lineage":["https://openalex.org/I21803372"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"JORGE DUARTE","raw_affiliation_strings":["CIMA-UE, Universidade de \u00c9vora, Portugal","ISEL-Instituto Superior de Engenharia de Lisboa, Department of Chemistry, Mathematics Unit, Rua Conselheiro Em\u00eddio Navarro, 1949-014 Lisboa, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CIMA-UE, Universidade de \u00c9vora, Portugal","institution_ids":["https://openalex.org/I21803372"]},{"raw_affiliation_string":"ISEL-Instituto Superior de Engenharia de Lisboa, Department of Chemistry, Mathematics Unit, Rua Conselheiro Em\u00eddio Navarro, 1949-014 Lisboa, Portugal","institution_ids":["https://openalex.org/I203847022"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.12826547,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"19","issue":"11","first_page":"3593","last_page":"3604"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9966999888420105,"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"}},"topics":[{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9966999888420105,"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/T10244","display_name":"Chaos control and synchronization","score":0.9925000071525574,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9775999784469604,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/chaotic","display_name":"Chaotic","score":0.7655847668647766},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6720475554466248},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5658625364303589},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5494810342788696},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5000176429748535},{"id":"https://openalex.org/keywords/topological-entropy","display_name":"Topological entropy","score":0.4987056255340576},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.477373331785202},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.4755025804042816},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.45777177810668945},{"id":"https://openalex.org/keywords/complex-dynamics","display_name":"Complex dynamics","score":0.44524919986724854},{"id":"https://openalex.org/keywords/chaotic-hysteresis","display_name":"Chaotic hysteresis","score":0.4443589746952057},{"id":"https://openalex.org/keywords/symbolic-dynamics","display_name":"Symbolic dynamics","score":0.420606791973114},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38560622930526733},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.36771875619888306},{"id":"https://openalex.org/keywords/synchronization-of-chaos","display_name":"Synchronization of chaos","score":0.2600176930427551},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.248653382062912},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1835763156414032},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1719016432762146},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1379115879535675}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.7655847668647766},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6720475554466248},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5658625364303589},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5494810342788696},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5000176429748535},{"id":"https://openalex.org/C2780350623","wikidata":"https://www.wikidata.org/wiki/Q3055355","display_name":"Topological entropy","level":2,"score":0.4987056255340576},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.477373331785202},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.4755025804042816},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.45777177810668945},{"id":"https://openalex.org/C126701199","wikidata":"https://www.wikidata.org/wiki/Q264224","display_name":"Complex dynamics","level":2,"score":0.44524919986724854},{"id":"https://openalex.org/C207219937","wikidata":"https://www.wikidata.org/wiki/Q5072841","display_name":"Chaotic hysteresis","level":5,"score":0.4443589746952057},{"id":"https://openalex.org/C16101541","wikidata":"https://www.wikidata.org/wiki/Q1350838","display_name":"Symbolic dynamics","level":2,"score":0.420606791973114},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38560622930526733},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.36771875619888306},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.2600176930427551},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.248653382062912},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1835763156414032},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1719016432762146},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1379115879535675},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s021812740902502x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812740902502x","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"},{"id":"pmh:oai:dspace.uevora.pt:10174/6774","is_oa":true,"landing_page_url":"http://hdl.handle.net/10174/6774","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"},{"id":"pmh:oai:repositorio.ipl.pt:10400.21/1283","is_oa":true,"landing_page_url":"http://hdl.handle.net/10400.21/1283","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"}],"best_oa_location":{"id":"pmh:oai:dspace.uevora.pt:10174/6774","is_oa":true,"landing_page_url":"http://hdl.handle.net/10174/6774","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","score":0.47999998927116394,"display_name":"Decent work and economic growth"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W132845994","https://openalex.org/W1537935065","https://openalex.org/W1581792503","https://openalex.org/W1595764735","https://openalex.org/W1972077473","https://openalex.org/W2001162474","https://openalex.org/W2016243419","https://openalex.org/W2028227052","https://openalex.org/W2049293757","https://openalex.org/W2058864627","https://openalex.org/W2081817659","https://openalex.org/W2327768229","https://openalex.org/W2499055842","https://openalex.org/W3123410966","https://openalex.org/W4251015067","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2349517432","https://openalex.org/W2611393871","https://openalex.org/W4249780665","https://openalex.org/W2964770422","https://openalex.org/W2136722017","https://openalex.org/W2788206731","https://openalex.org/W2030895931","https://openalex.org/W2080579408","https://openalex.org/W2076884346","https://openalex.org/W1963995324"],"abstract_inverted_index":{"The":[0,41,141,208],"study":[1,76],"of":[2,13,33,47,53,58,88,96,102,107,113,126,137,143,146,216,233,237,249],"economic":[3,79,238],"systems":[4,49,252],"has":[5],"generated":[6],"deep":[7],"interest":[8,34],"in":[9,16,22,35,50,67,104,150],"exploring":[10],"the":[11,25,45,51,56,72,82,94,105,118,122,138,144,174,187,193,214,244],"complexity":[12],"chaotic":[14,39,164,175],"motions":[15],"economy.":[17],"Due":[18],"to":[19,43,158,161],"important":[20],"developments":[21],"nonlinear":[23,36,250],"dynamics,":[24,115],"last":[26],"two":[27],"decades":[28],"have":[29],"witnessed":[30],"strong":[31],"revival":[32],"endogenous":[37],"business":[38],"models.":[40],"inability":[42],"predict":[44],"behavior":[46,171],"dynamical":[48,251],"presence":[52],"chaos":[54,59],"suggests":[55],"application":[57,215],"control":[60,219],"methods,":[61],"when":[62],"we":[63,75,116,167],"are":[64],"more":[65],"interested":[66],"obtaining":[68],"regular":[69,206],"behavior.":[70],"In":[71],"present":[73],"article,":[74],"a":[77,86,108,205,217],"specific":[78],"model":[80,139,177],"from":[81,173],"literature.":[83],"More":[84],"precisely,":[85],"system":[87,153],"three":[89],"ordinary":[90,255],"differential":[91,256],"equations":[92],"gather":[93],"variables":[95],"profits,":[97],"reinvestments":[98],"and":[99,121,160,186,246],"financial":[100],"flow":[101],"borrowings":[103],"structure":[106],"firm.":[109],"Firstly,":[110],"using":[111],"results":[112],"symbolic":[114],"characterize":[117],"topological":[119],"entropy":[120],"parameter":[123,154],"space":[124],"ordering":[125],"kneading":[127],"sequences,":[128],"associated":[129],"with":[130],"one-dimensional":[131],"maps":[132],"that":[133,169],"reproduce":[134],"significant":[135],"aspects":[136],"dynamics.":[140],"analysis":[142],"variation":[145],"this":[147],"numerical":[148,247],"invariant,":[149],"some":[151],"realistic":[152],"region,":[155],"allows":[156],"us":[157],"quantify":[159],"distinguish":[162],"different":[163],"regimes.":[165],"Finally,":[166],"show":[168],"complicated":[170],"arising":[172],"firm":[176],"can":[178,189,240],"be":[179,190,241],"controlled":[180],"without":[181],"changing":[182],"its":[183],"original":[184],"properties":[185],"dynamics":[188],"turned":[191],"into":[192,204],"desired":[194],"attracting":[195],"time":[196],"periodic":[197],"motion":[198],"(a":[199],"stable":[200],"steady":[201],"state":[202],"or":[203],"cycle).":[207],"orbit":[209],"stabilization":[210],"is":[211],"illustrated":[212],"by":[213,223,243,254],"feedback":[218],"technique":[220],"initially":[221],"developed":[222],"Romeiras":[224],"et":[225],"al.":[226],"[1992].":[227],"This":[228],"work":[229],"provides":[230],"another":[231],"illustration":[232],"how":[234],"our":[235],"understanding":[236],"models":[239],"enhanced":[242],"theoretical":[245],"investigation":[248],"modeled":[253],"equations.":[257]},"counts_by_year":[{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}