{"id":"https://openalex.org/W4386754610","doi":"https://doi.org/10.3390/sym15091751","title":"Modelling a Market Society with Stochastically Varying Money Exchange Frequencies","display_name":"Modelling a Market Society with Stochastically Varying Money Exchange Frequencies","publication_year":2023,"publication_date":"2023-09-13","ids":{"openalex":"https://openalex.org/W4386754610","doi":"https://doi.org/10.3390/sym15091751"},"language":"en","primary_location":{"id":"doi:10.3390/sym15091751","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15091751","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1751/pdf?version=1694591428","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/9/1751/pdf?version=1694591428","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072155586","display_name":"Maria Letizia Bertotti","orcid":"https://orcid.org/0000-0001-6086-8395"},"institutions":[{"id":"https://openalex.org/I171543936","display_name":"Free University of Bozen-Bolzano","ror":"https://ror.org/012ajp527","country_code":"IT","type":"education","lineage":["https://openalex.org/I171543936"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Maria Letizia Bertotti","raw_affiliation_strings":["Faculty of Engineering, Free University of Bozen-Bolzano, 39100 Bolzano, Italy"],"raw_orcid":"https://orcid.org/0000-0001-6086-8395","affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Free University of Bozen-Bolzano, 39100 Bolzano, Italy","institution_ids":["https://openalex.org/I171543936"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085854765","display_name":"Bruno Carbonaro","orcid":"https://orcid.org/0000-0001-7102-6011"},"institutions":[{"id":"https://openalex.org/I197809005","display_name":"University of Campania \"Luigi Vanvitelli\"","ror":"https://ror.org/02kqnpp86","country_code":"IT","type":"education","lineage":["https://openalex.org/I197809005"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Bruno Carbonaro","raw_affiliation_strings":["Department of Mathematics and Physics, University of Campania \u201cL. Vanvitelli\u201d, 81100 Caserta, Italy","Department of Mathematics and Physics, University of Campania \"L. Vanvitelli\", 81100 Caserta, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, University of Campania \u201cL. Vanvitelli\u201d, 81100 Caserta, Italy","institution_ids":["https://openalex.org/I197809005"]},{"raw_affiliation_string":"Department of Mathematics and Physics, University of Campania \"L. Vanvitelli\", 81100 Caserta, Italy","institution_ids":["https://openalex.org/I197809005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043488166","display_name":"Marco Menale","orcid":"https://orcid.org/0000-0001-8822-3038"},"institutions":[{"id":"https://openalex.org/I197809005","display_name":"University of Campania \"Luigi Vanvitelli\"","ror":"https://ror.org/02kqnpp86","country_code":"IT","type":"education","lineage":["https://openalex.org/I197809005"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Menale","raw_affiliation_strings":["Department of Mathematics and Physics, University of Campania \u201cL. Vanvitelli\u201d, 81100 Caserta, Italy","Department of Mathematics and Physics, University of Campania \"L. Vanvitelli\", 81100 Caserta, Italy"],"raw_orcid":"https://orcid.org/0000-0001-8822-3038","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, University of Campania \u201cL. Vanvitelli\u201d, 81100 Caserta, Italy","institution_ids":["https://openalex.org/I197809005"]},{"raw_affiliation_string":"Department of Mathematics and Physics, University of Campania \"L. Vanvitelli\", 81100 Caserta, Italy","institution_ids":["https://openalex.org/I197809005"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072155586"],"corresponding_institution_ids":["https://openalex.org/I171543936"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2288,"currency":"EUR","value_usd":2467},"fwci":2.2077,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.92115406,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"15","issue":"9","first_page":"1751","last_page":"1751"},"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":0.9991000294685364,"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":0.9991000294685364,"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":0.9929999709129333,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9282000064849854,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.7909043431282043},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6349532604217529},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6138041615486145},{"id":"https://openalex.org/keywords/state-variable","display_name":"State variable","score":0.5187828540802002},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.47151482105255127},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.46056634187698364},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4556967318058014},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.44202956557273865},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.4347003102302551},{"id":"https://openalex.org/keywords/complex-system","display_name":"Complex system","score":0.4208945631980896},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.4197857081890106},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3177288770675659},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.270841509103775},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09640464186668396},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08953103423118591},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08716046810150146},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08420747518539429}],"concepts":[{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.7909043431282043},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6349532604217529},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6138041615486145},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.5187828540802002},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.47151482105255127},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.46056634187698364},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4556967318058014},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.44202956557273865},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.4347003102302551},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.4208945631980896},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.4197857081890106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3177288770675659},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.270841509103775},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09640464186668396},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08953103423118591},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08716046810150146},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08420747518539429},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym15091751","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15091751","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1751/pdf?version=1694591428","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:unibz.it:11303868630001241","is_oa":true,"landing_page_url":"https://www.mdpi.com/2073-8994/15/9/1751","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1751/pdf","source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:4aa4406583244559a9b6cf7cd5ebdf97","is_oa":false,"landing_page_url":"https://doaj.org/article/4aa4406583244559a9b6cf7cd5ebdf97","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 9, p 1751 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/9/1751/","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15091751","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15091751","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15091751","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1751/pdf?version=1694591428","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320325400","display_name":"Libera Universit\u00e0 di Bolzano","ror":"https://ror.org/012ajp527"},{"id":"https://openalex.org/F4320334080","display_name":"Gruppo Nazionale per la Fisica Matematica","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4386754610.pdf"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W71165104","https://openalex.org/W592485236","https://openalex.org/W1581231885","https://openalex.org/W1784105272","https://openalex.org/W2005004598","https://openalex.org/W2020126051","https://openalex.org/W2031849821","https://openalex.org/W2132858596","https://openalex.org/W2143240768","https://openalex.org/W3015030207","https://openalex.org/W3100339217","https://openalex.org/W3156949233","https://openalex.org/W4313017177","https://openalex.org/W6651720505"],"related_works":["https://openalex.org/W2487162673","https://openalex.org/W2793211469","https://openalex.org/W2949152769","https://openalex.org/W4372354731","https://openalex.org/W2942366970","https://openalex.org/W2807634898","https://openalex.org/W1518014891","https://openalex.org/W2606182810","https://openalex.org/W2091347336","https://openalex.org/W1529028091"],"abstract_inverted_index":{"We":[0,18],"propose":[1],"and":[2,95,99,114,131,165],"examine":[3],"a":[4,15,23,47,158],"model":[5],"expressed":[6],"by":[7,35,53,146],"stochastic":[8],"differential":[9],"equations":[10,55],"for":[11,132,157],"the":[12,28,36,58,62,68,77,80,93,105,109,111,115],"evolution":[13,44],"of":[14,30,38,45,64,71,76,97,118,162],"complex":[16],"system.":[17,78],"refer":[19],"in":[20,26,61,108],"particular":[21],"to":[22,92,123,137,152],"market":[24],"society,":[25],"which":[27],"state":[29,66,122],"each":[31,65],"individual":[32],"is":[33,51],"identified":[34],"amount":[37],"money":[39,89],"at":[40,82],"his/her":[41],"disposal.":[42],"The":[43],"such":[46],"system":[48],"over":[49],"time":[50],"described":[52],"suitable":[54],"that":[56],"link":[57],"instantaneous":[59],"changes":[60],"probability":[63],"with":[67],"probable":[69],"outcomes":[70],"pairwise":[72,85],"interactions":[73,86],"between":[74],"elements":[75],"In":[79,101],"context":[81],"hand,":[83],"these":[84],"simply":[87],"represent":[88],"exchanges,":[90],"due":[91],"sales":[94],"purchases":[96],"goods":[98],"services.":[100],"this":[102],"paper,":[103],"unlike":[104],"usual":[106],"method":[107],"literature,":[110],"interaction":[112],"frequencies":[113],"consequent":[116],"probabilities":[117],"passing":[119],"from":[120],"one":[121],"another":[124],"are":[125,135],"not":[126],"considered":[127],"as":[128,143],"assigned":[129],"once":[130],"all":[133],"but":[134],"supposed":[136],"be":[138],"randomly":[139],"variable.":[140],"This":[141],"choice,":[142],"also":[144],"shown":[145],"several":[147],"numerical":[148],"simulations,":[149],"seems":[150],"likely":[151],"have":[153],"fruitful":[154],"consequences,":[155],"especially":[156],"more":[159],"realistic":[160],"representation":[161],"economic":[163],"issues":[164],"phenomena.":[166]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}