{"id":"https://openalex.org/W2980564742","doi":"https://doi.org/10.1142/s0218127419300313","title":"Global Dynamics and Synchronization in a Duopoly Game with Bounded Rationality and Consumer Surplus","display_name":"Global Dynamics and Synchronization in a Duopoly Game with Bounded Rationality and Consumer Surplus","publication_year":2019,"publication_date":"2019-10-01","ids":{"openalex":"https://openalex.org/W2980564742","doi":"https://doi.org/10.1142/s0218127419300313","mag":"2980564742"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127419300313","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419300313","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065456528","display_name":"Yinxia Cao","orcid":null},"institutions":[{"id":"https://openalex.org/I3133134087","display_name":"Lanzhou Jiaotong University","ror":"https://ror.org/03144pv92","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133134087"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yinxia Cao","raw_affiliation_strings":["School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, P. R. China","institution_ids":["https://openalex.org/I3133134087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041367076","display_name":"Wei Zhou","orcid":"https://orcid.org/0000-0002-4477-3940"},"institutions":[{"id":"https://openalex.org/I3133134087","display_name":"Lanzhou Jiaotong University","ror":"https://ror.org/03144pv92","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133134087"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Zhou","raw_affiliation_strings":["School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-4477-3940","affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, P. R. China","institution_ids":["https://openalex.org/I3133134087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077917968","display_name":"Tong Chu","orcid":"https://orcid.org/0000-0002-0200-772X"},"institutions":[{"id":"https://openalex.org/I90727586","display_name":"Zhejiang University of Finance and Economics","ror":"https://ror.org/055vj5234","country_code":"CN","type":"education","lineage":["https://openalex.org/I90727586"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tong Chu","raw_affiliation_strings":["School of Law, Zhejiang University of Finance and Economics, Hangzhou, Zhejiang 310018, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Law, Zhejiang University of Finance and Economics, Hangzhou, Zhejiang 310018, P. R. China","institution_ids":["https://openalex.org/I90727586"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112556374","display_name":"Chang Ying-xiang","orcid":null},"institutions":[{"id":"https://openalex.org/I3133134087","display_name":"Lanzhou Jiaotong University","ror":"https://ror.org/03144pv92","country_code":"CN","type":"education","lineage":["https://openalex.org/I3133134087"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yingxiang Chang","raw_affiliation_strings":["School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, P. R. China","institution_ids":["https://openalex.org/I3133134087"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":18.6626,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.99006465,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"29","issue":"11","first_page":"1930031","last_page":"1930031"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11043","display_name":"Merger and Competition Analysis","score":0.9739999771118164,"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/T11043","display_name":"Merger and Competition Analysis","score":0.9739999771118164,"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/T11031","display_name":"Game Theory and Applications","score":0.9527000188827515,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9301999807357788,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/mathematics","display_name":"Mathematics","score":0.7084333896636963},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.6909046173095703},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6544783711433411},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.47318506240844727},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.4521780014038086},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.41972553730010986},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35113877058029175},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11602750420570374},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1132257878780365}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7084333896636963},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.6909046173095703},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6544783711433411},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.47318506240844727},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4521780014038086},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.41972553730010986},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35113877058029175},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11602750420570374},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1132257878780365},{"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/s0218127419300313","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419300313","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6055618216","display_name":null,"funder_award_id":"2015029","funder_id":"https://openalex.org/F4320335475","funder_display_name":"Youth Science Foundation of Lanzhou Jiaotong University"}],"funders":[{"id":"https://openalex.org/F4320335475","display_name":"Youth Science Foundation of Lanzhou Jiaotong University","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W13521166","https://openalex.org/W85446323","https://openalex.org/W746781411","https://openalex.org/W1578751306","https://openalex.org/W1873051372","https://openalex.org/W1986521498","https://openalex.org/W2005878741","https://openalex.org/W2009313082","https://openalex.org/W2021883117","https://openalex.org/W2022155489","https://openalex.org/W2022891194","https://openalex.org/W2035222139","https://openalex.org/W2035731514","https://openalex.org/W2044664527","https://openalex.org/W2050920251","https://openalex.org/W2062957830","https://openalex.org/W2094372694","https://openalex.org/W2120537934","https://openalex.org/W2135402841","https://openalex.org/W2138890315","https://openalex.org/W2153453045","https://openalex.org/W2161137744","https://openalex.org/W2179943225","https://openalex.org/W2228432980","https://openalex.org/W2263547296","https://openalex.org/W2293358305","https://openalex.org/W2301321055","https://openalex.org/W2515822818","https://openalex.org/W2524056771","https://openalex.org/W2544246901","https://openalex.org/W2605783304","https://openalex.org/W2618208446","https://openalex.org/W2621046272","https://openalex.org/W2767249390","https://openalex.org/W2770097487","https://openalex.org/W2782167235","https://openalex.org/W2897844789","https://openalex.org/W3103143917","https://openalex.org/W3121489036","https://openalex.org/W4233040091"],"related_works":["https://openalex.org/W3104914783","https://openalex.org/W2313198288","https://openalex.org/W1965923678","https://openalex.org/W2953601251","https://openalex.org/W2105088728","https://openalex.org/W3119049163","https://openalex.org/W4200398452","https://openalex.org/W1585510467","https://openalex.org/W2530518784","https://openalex.org/W2551321485"],"abstract_inverted_index":{"Based":[0],"on":[1,224,238],"the":[2,20,23,26,29,34,38,47,50,55,70,78,86,94,100,107,130,139,143,150,155,160,164,182,185,192,195,214,222,225,229,232,239,242,246,250,256,259],"oligopoly":[3],"game":[4],"theory,":[5,158],"a":[6,60,207],"dynamic":[7],"duopoly":[8],"Cournot":[9],"model":[10],"with":[11,96],"bounded":[12],"rationality":[13],"and":[14,25,33,135,146,163,228],"consumer":[15,233],"surplus":[16,234],"is":[17,57,67,83,91,104,113,127,169,197,204,211,235,253],"established.":[18],"On":[19,46],"one":[21],"hand,":[22,49],"type":[24],"stability":[27,35],"of":[28,37,54,62,81,109,132,142,149,175,181,184,194,221,231,241,258],"boundary":[30],"equilibrium":[31,40],"points":[32,98],"conditions":[36],"Nash":[39],"point":[41],"are":[42,152],"discussed":[43,254],"in":[44,99],"detail.":[45],"other":[48,136],"potential":[51],"complex":[52],"dynamics":[53,148],"system":[56,151,196,223],"demonstrated":[58],"by":[59,106,154,206],"set":[61],"2D":[63,101],"bifurcation":[64,71,87,102,219],"diagrams.":[65],"It":[66,112,126,168],"found":[68,115,129],"that":[69,93,116,171,191],"diagrams":[72,103],"have":[73],"beautiful":[74],"fractal":[75],"structures":[76],"when":[77],"adjustment":[79,226],"speed":[80,227],"production":[82],"taken":[84],"as":[85],"parameter.":[88],"And":[89,202,245],"it":[90,187,203],"verified":[92],"area":[95],"scattered":[97],"caused":[105],"coexistence":[108,131],"multiple":[110],"attractors.":[111,125,137],"also":[114],"there":[117],"may":[118,178],"be":[119,189],"two,":[120],"three":[121],"or":[122],"four":[123],"coexisting":[124],"even":[128],"Milnor":[133],"attractor":[134],"Moreover,":[138],"topological":[140],"structure":[141],"attracting":[144],"basin":[145],"global":[147,176],"investigated":[153],"noninvertible":[156],"map":[157,209],"using":[159],"critical":[161],"curve":[162,220],"transverse":[165],"Lyapunov":[166],"exponent.":[167],"concluded":[170,190],"two":[172],"different":[173],"types":[174],"bifurcations":[177],"occur.":[179],"Because":[180],"symmetry":[183],"system,":[186],"can":[188],"diagonal":[193,252],"an":[198],"invariant":[199,251],"one-dimensional":[200,208],"submanifold.":[201],"controlled":[205],"which":[210],"equivalent":[212],"to":[213],"classical":[215],"Logistic":[216,243],"map.":[217,244],"The":[218],"weight":[230],"obtained":[236],"based":[237],"properties":[240],"synchronization":[247],"phenomenon":[248],"along":[249],"at":[255],"end":[257],"paper.":[260]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":12}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}