{"id":"https://openalex.org/W3114767154","doi":"https://doi.org/10.1142/s0218127420502405","title":"Breaking and Sustaining Bifurcations in SN-Invariant Equidistant Economy","display_name":"Breaking and Sustaining Bifurcations in SN-Invariant Equidistant Economy","publication_year":2020,"publication_date":"2020-12-28","ids":{"openalex":"https://openalex.org/W3114767154","doi":"https://doi.org/10.1142/s0218127420502405","mag":"3114767154"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127420502405","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420502405","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/10400.14/31703","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077442961","display_name":"Hiroki Aizawa","orcid":"https://orcid.org/0000-0002-0929-6325"},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]},{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP","PT"],"is_corresponding":false,"raw_author_name":"H. Aizawa","raw_affiliation_strings":["Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan","CEF.UP, University of Porto, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"CEF.UP, University of Porto, Portugal","institution_ids":["https://openalex.org/I182534213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031616318","display_name":"Kiyohiro Ikeda","orcid":"https://orcid.org/0000-0002-0291-4346"},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]},{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP","PT"],"is_corresponding":false,"raw_author_name":"K. Ikeda","raw_affiliation_strings":["Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan","CEF.UP, University of Porto, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"CEF.UP, University of Porto, Portugal","institution_ids":["https://openalex.org/I182534213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038050327","display_name":"Minoru Osawa","orcid":"https://orcid.org/0000-0001-9067-5375"},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]},{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP","PT"],"is_corresponding":false,"raw_author_name":"M. Osawa","raw_affiliation_strings":["Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan","CEF.UP, University of Porto, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"CEF.UP, University of Porto, Portugal","institution_ids":["https://openalex.org/I182534213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085403280","display_name":"Jos\u00e9 M. Gaspar","orcid":"https://orcid.org/0000-0002-5443-3683"},"institutions":[{"id":"https://openalex.org/I182534213","display_name":"Universidade do Porto","ror":"https://ror.org/043pwc612","country_code":"PT","type":"education","lineage":["https://openalex.org/I182534213"]},{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]},{"id":"https://openalex.org/I25169866","display_name":"Universidade Cat\u00f3lica Portuguesa","ror":"https://ror.org/03b9snr86","country_code":"PT","type":"education","lineage":["https://openalex.org/I25169866"]}],"countries":["JP","PT"],"is_corresponding":true,"raw_author_name":"J. M. Gaspar","raw_affiliation_strings":["CEGE and Cat\u00f3lica Porto Business School, Universidade Cat\u00f3lica Portuguesa, CEF.UP, University of Porto, Portugal","Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CEGE and Cat\u00f3lica Porto Business School, Universidade Cat\u00f3lica Portuguesa, CEF.UP, University of Porto, Portugal","institution_ids":["https://openalex.org/I25169866","https://openalex.org/I182534213"]},{"raw_affiliation_string":"Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan","institution_ids":["https://openalex.org/I201537933"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5085403280"],"corresponding_institution_ids":["https://openalex.org/I182534213","https://openalex.org/I201537933","https://openalex.org/I25169866"],"apc_list":null,"apc_paid":null,"fwci":1.553,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.90856684,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"30","issue":"16","first_page":"2050240","last_page":"2050240"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.996999979019165,"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/T12137","display_name":"Economic theories and models","score":0.996999979019165,"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/T11014","display_name":"Regional Economics and Spatial Analysis","score":0.9883999824523926,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9815999865531921,"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/equidistant","display_name":"Equidistant","score":0.892325758934021},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.8113503456115723},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.71375572681427},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6317648887634277},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.5370458960533142},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.488883912563324},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.4637492299079895},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3827345073223114},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3222699761390686},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23461413383483887},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1452455222606659},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.13469228148460388},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06587386131286621}],"concepts":[{"id":"https://openalex.org/C158245278","wikidata":"https://www.wikidata.org/wiki/Q4386982","display_name":"Equidistant","level":2,"score":0.892325758934021},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.8113503456115723},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.71375572681427},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6317648887634277},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.5370458960533142},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.488883912563324},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.4637492299079895},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3827345073223114},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3222699761390686},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23461413383483887},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1452455222606659},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.13469228148460388},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06587386131286621},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127420502405","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420502405","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:repositorio.ucp.pt:10400.14/31703","is_oa":true,"landing_page_url":"http://hdl.handle.net/10400.14/31703","pdf_url":null,"source":{"id":"https://openalex.org/S4306401375","display_name":"Reposit\u00f3rio Institucional da Universidade Cat\u00f3lica Portuguesa (Universidade Cat\u00f3lica Portuguesa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I25169866","host_organization_name":"Universidade Cat\u00f3lica Portuguesa","host_organization_lineage":["https://openalex.org/I25169866"],"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":null,"raw_type":"journal article"}],"best_oa_location":{"id":"pmh:oai:repositorio.ucp.pt:10400.14/31703","is_oa":true,"landing_page_url":"http://hdl.handle.net/10400.14/31703","pdf_url":null,"source":{"id":"https://openalex.org/S4306401375","display_name":"Reposit\u00f3rio Institucional da Universidade Cat\u00f3lica Portuguesa (Universidade Cat\u00f3lica Portuguesa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I25169866","host_organization_name":"Universidade Cat\u00f3lica Portuguesa","host_organization_lineage":["https://openalex.org/I25169866"],"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":null,"raw_type":"journal article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth","score":0.4000000059604645}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1567092208","https://openalex.org/W1618519913","https://openalex.org/W1965778005","https://openalex.org/W1968115548","https://openalex.org/W1986769726","https://openalex.org/W1996259624","https://openalex.org/W2028798910","https://openalex.org/W2030439670","https://openalex.org/W2033661690","https://openalex.org/W2074928114","https://openalex.org/W2146040615","https://openalex.org/W2168699659","https://openalex.org/W2487249630","https://openalex.org/W2735007081","https://openalex.org/W2803861565","https://openalex.org/W2898187704","https://openalex.org/W2955699151","https://openalex.org/W2972494483","https://openalex.org/W3013001495","https://openalex.org/W3022035939","https://openalex.org/W3121519629","https://openalex.org/W3122692461","https://openalex.org/W3123620848","https://openalex.org/W3124212237","https://openalex.org/W3124813244","https://openalex.org/W4243592922","https://openalex.org/W4253859505"],"related_works":["https://openalex.org/W4245057904","https://openalex.org/W2106448822","https://openalex.org/W2319243846","https://openalex.org/W3151296820","https://openalex.org/W2995910379","https://openalex.org/W2962916793","https://openalex.org/W2361894068","https://openalex.org/W2387129305","https://openalex.org/W3114767154","https://openalex.org/W2997160749"],"abstract_inverted_index":{"This":[0],"paper":[1],"elucidates":[2],"the":[3,18,44,57,68,71,82,132,167],"bifurcation":[4,42,72,152],"mechanism":[5,88,153],"of":[6,20,30,40,43,59,70,77,89,98,107,116,134,146,157,163,169],"an":[7,78],"equidistant":[8,79],"economy":[9,80],"in":[10,166],"spatial":[11,65,117,170],"economics.":[12,171],"To":[13],"this":[14,31],"end,":[15],"we":[16,34],"derive":[17],"rules":[19],"secondary":[21],"and":[22,148,154],"further":[23],"bifurcations":[24,90],"as":[25,144],"a":[26,139],"major":[27],"theoretical":[28,151],"contribution":[29],"paper.":[32],"Then":[33],"combine":[35],"them":[36,108],"with":[37],"pre-existing":[38],"results":[39],"direct":[41],"symmetric":[45],"group":[46],"[Formula:":[47],"see":[48],"text]":[49],"[Elmhirst,":[50],"2004].":[51],"Particular":[52],"attention":[53],"is":[54,94,101],"devoted":[55],"to":[56,103],"existence":[58],"invariant":[60,135],"solutions":[61],"which":[62,142],"retain":[63],"their":[64],"distributions":[66],"when":[67],"value":[69],"parameter":[73],"changes.":[74],"Invariant":[75],"patterns":[76,93],"under":[81],"replicator":[83],"dynamics":[84],"are":[85,109,126],"obtained.":[86],"The":[87,96,150],"from":[91],"these":[92],"elucidated.":[95],"stability":[97],"bifurcating":[99,124,129],"branches":[100,125],"analyzed":[102],"demonstrate":[104],"that":[105,121],"most":[106],"unstable":[110],"immediately":[111],"after":[112],"bifurcation.":[113],"Numerical":[114],"analysis":[115],"economic":[118],"models":[119],"confirms":[120],"almost":[122],"all":[123],"unstable.":[127],"Direct":[128],"curves":[130,133],"connect":[131],"solutions,":[136],"thereby":[137],"creating":[138],"mesh-like":[140],"network,":[141],"appears":[143],"threads":[145],"warp":[147],"weft.":[149],"numerical":[155],"examples":[156],"networks":[158],"advanced":[159],"herein":[160],"might":[161],"be":[162],"great":[164],"assistance":[165],"study":[168]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}