{"id":"https://openalex.org/W2028890652","doi":"https://doi.org/10.1109/ieem.2011.6117987","title":"Study on dynamical properties and simulation of a four-dimensional nonlinear discrete dynamics","display_name":"Study on dynamical properties and simulation of a four-dimensional nonlinear discrete dynamics","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2028890652","doi":"https://doi.org/10.1109/ieem.2011.6117987","mag":"2028890652"},"language":"en","primary_location":{"id":"doi:10.1109/ieem.2011.6117987","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ieem.2011.6117987","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Conference on Industrial Engineering and Engineering Management","raw_type":"proceedings-article"},"type":"conference-paper","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/A5072128915","display_name":"Jing Peng","orcid":"https://orcid.org/0000-0001-5490-6228"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]},{"id":"https://openalex.org/I95946905","display_name":"Hebei GEO University","ror":"https://ror.org/013x4kb81","country_code":"CN","type":"education","lineage":["https://openalex.org/I95946905"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Peng","raw_affiliation_strings":["School of Bussiness, Shijiazhuang University of Economics, Shijiazhuang, China","School of Management, Tianjin University, TJU, Tianjin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Bussiness, Shijiazhuang University of Economics, Shijiazhuang, China","institution_ids":["https://openalex.org/I95946905"]},{"raw_affiliation_string":"School of Management, Tianjin University, TJU, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Zehua Miao","orcid":null},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]},{"id":"https://openalex.org/I95946905","display_name":"Hebei GEO University","ror":"https://ror.org/013x4kb81","country_code":"CN","type":"education","lineage":["https://openalex.org/I95946905"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zehua Miao","raw_affiliation_strings":["School of Bussiness, Shijiazhuang University of Economics, Shijiazhuang, China","School of Manegement and Economics, Beijing Institute of Technology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Bussiness, Shijiazhuang University of Economics, Shijiazhuang, China","institution_ids":["https://openalex.org/I95946905"]},{"raw_affiliation_string":"School of Manegement and Economics, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090581016","display_name":"Luoping Zheng","orcid":"https://orcid.org/0000-0002-7101-355X"},"institutions":[{"id":"https://openalex.org/I95946905","display_name":"Hebei GEO University","ror":"https://ror.org/013x4kb81","country_code":"CN","type":"education","lineage":["https://openalex.org/I95946905"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Luoping Zheng","raw_affiliation_strings":["School of Bussiness, Shijiazhuang University of Economics, Shijiazhuang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Bussiness, Shijiazhuang University of Economics, Shijiazhuang, China","institution_ids":["https://openalex.org/I95946905"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":null,"first_page":"600","last_page":"604"},"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":0.9879000186920166,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9864000082015991,"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/oligopoly","display_name":"Oligopoly","score":0.6901001334190369},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.6883562803268433},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6620556116104126},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.5640375018119812},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5567182302474976},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5455361008644104},{"id":"https://openalex.org/keywords/bounded-rationality","display_name":"Bounded rationality","score":0.5320832133293152},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4998195171356201},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.49720409512519836},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.49000611901283264},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.4857923984527588},{"id":"https://openalex.org/keywords/complex-dynamics","display_name":"Complex dynamics","score":0.48283466696739197},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48188692331314087},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4716310501098633},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4656943082809448},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.4222012460231781},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3109211325645447},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.2734328508377075},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21828576922416687},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18684402108192444},{"id":"https://openalex.org/keywords/cournot-competition","display_name":"Cournot competition","score":0.08539581298828125}],"concepts":[{"id":"https://openalex.org/C121398111","wikidata":"https://www.wikidata.org/wiki/Q103639","display_name":"Oligopoly","level":3,"score":0.6901001334190369},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.6883562803268433},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6620556116104126},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.5640375018119812},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5567182302474976},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5455361008644104},{"id":"https://openalex.org/C58694771","wikidata":"https://www.wikidata.org/wiki/Q814385","display_name":"Bounded rationality","level":2,"score":0.5320832133293152},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4998195171356201},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.49720409512519836},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.49000611901283264},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.4857923984527588},{"id":"https://openalex.org/C126701199","wikidata":"https://www.wikidata.org/wiki/Q264224","display_name":"Complex dynamics","level":2,"score":0.48283466696739197},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48188692331314087},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4716310501098633},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4656943082809448},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.4222012460231781},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3109211325645447},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.2734328508377075},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21828576922416687},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18684402108192444},{"id":"https://openalex.org/C16520705","wikidata":"https://www.wikidata.org/wiki/Q601799","display_name":"Cournot competition","level":2,"score":0.08539581298828125},{"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},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ieem.2011.6117987","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ieem.2011.6117987","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Conference on Industrial Engineering and Engineering Management","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W207897951","https://openalex.org/W1976741659","https://openalex.org/W1982582947","https://openalex.org/W1984153198","https://openalex.org/W2003908419","https://openalex.org/W2006734637","https://openalex.org/W2009313082","https://openalex.org/W2016549420","https://openalex.org/W2019152861","https://openalex.org/W2022729218","https://openalex.org/W2023894595","https://openalex.org/W2035438233","https://openalex.org/W2036166961","https://openalex.org/W2050920251","https://openalex.org/W2057261694","https://openalex.org/W2066969234","https://openalex.org/W2156439224","https://openalex.org/W2265269832","https://openalex.org/W4253211883"],"related_works":["https://openalex.org/W1870109339","https://openalex.org/W3124328952","https://openalex.org/W2093264122","https://openalex.org/W2343007651","https://openalex.org/W36788","https://openalex.org/W2109235059","https://openalex.org/W4386731465","https://openalex.org/W4283744980","https://openalex.org/W3165288943","https://openalex.org/W2791213815"],"abstract_inverted_index":{"We":[0,52],"study":[1,15],"a":[2,24,38],"nonlinear":[3,40],"discrete":[4],"dynamic":[5],"game":[6,31],"model":[7,26],"of":[8,18,46,57,86,93,115,118],"an":[9],"oligopoly":[10],"market.":[11],"In":[12],"order":[13],"to":[14,131],"competition":[16],"process":[17],"the":[19,21,47,58,69,74,84,94,104,119,124,129],"players,":[20],"paper":[22],"considers":[23],"Bertrand":[25],"with":[27,32],"bounded":[28],"rationality.":[29],"A":[30],"four":[33],"oligopolies":[34],"is":[35,82],"modeled":[36],"by":[37,113],"four-dimensional":[39],"difference":[41],"equation":[42],"set.":[43],"The":[44,60],"stability":[45,92],"equilibrium":[48,96],"point":[49],"are":[50,63,133],"discussed.":[51,134],"demonstrate":[53],"rich":[54],"dynamical":[55],"behaviors":[56],"system.":[59,120],"chaotic":[61],"features":[62],"justified":[64],"numerically":[65],"via":[66],"bifurcation":[67,99],"diagrams,":[68],"maximal":[70],"Lyapunov":[71],"exponents":[72],"and":[73,97,100],"system's":[75],"sensitive":[76],"dependence":[77],"on":[78],"initial":[79],"conditions.":[80],"It":[81],"demonstrated":[83],"increasing":[85],"price":[87],"adjustment":[88],"parameters":[89],"might":[90,127],"change":[91],"Nash":[95],"cause":[98],"chaos.":[101],"Different":[102],"from":[103],"former":[105],"literatures,":[106],"we":[107],"find":[108],"that":[109,122],"chaos":[110,132],"maybe":[111],"caused":[112],"interaction":[114],"some":[116],"elements":[117],"On":[121],"basis,":[123],"main":[125],"factors":[126],"lead":[128],"system":[130]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
