{"id":"https://openalex.org/W2948689568","doi":"https://doi.org/10.1142/s0218127419500603","title":"Constructing a New 3D Chaotic System with Any Number of Equilibria","display_name":"Constructing a New 3D Chaotic System with Any Number of Equilibria","publication_year":2019,"publication_date":"2019-05-01","ids":{"openalex":"https://openalex.org/W2948689568","doi":"https://doi.org/10.1142/s0218127419500603","mag":"2948689568"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127419500603","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419500603","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/A5080858709","display_name":"Qigui Yang","orcid":"https://orcid.org/0000-0002-3623-4947"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qigui Yang","raw_affiliation_strings":["School of Mathematical Sciences, South China University of Technology, Guangzhou, Guangdong 510641, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-3623-4947","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, South China University of Technology, Guangzhou, Guangdong 510641, P. R. China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028016895","display_name":"Xinmei Qiao","orcid":null},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinmei Qiao","raw_affiliation_strings":["School of Mathematical Sciences, South China University of Technology, Guangzhou, Guangdong 510641, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, South China University of Technology, Guangzhou, Guangdong 510641, P. R. China","institution_ids":["https://openalex.org/I90610280"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080858709"],"corresponding_institution_ids":["https://openalex.org/I90610280"],"apc_list":null,"apc_paid":null,"fwci":2.3036,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.88936488,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"29","issue":"05","first_page":"1950060","last_page":"1950060"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9997000098228455,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9973000288009644,"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":0.993399977684021,"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/attractor","display_name":"Attractor","score":0.8332241773605347},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.7593934535980225},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6251125335693359},{"id":"https://openalex.org/keywords/lorenz-system","display_name":"Lorenz system","score":0.4799256920814514},{"id":"https://openalex.org/keywords/crisis","display_name":"Crisis","score":0.47956985235214233},{"id":"https://openalex.org/keywords/chaotic-hysteresis","display_name":"Chaotic hysteresis","score":0.4740966260433197},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.448081910610199},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43892142176628113},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.39073941111564636},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3044961392879486},{"id":"https://openalex.org/keywords/synchronization-of-chaos","display_name":"Synchronization of chaos","score":0.2962974011898041},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27232420444488525},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.22043290734291077},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18839234113693237},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15255188941955566},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.14380517601966858},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.09626820683479309}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.8332241773605347},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.7593934535980225},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6251125335693359},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.4799256920814514},{"id":"https://openalex.org/C78302928","wikidata":"https://www.wikidata.org/wiki/Q5185947","display_name":"Crisis","level":4,"score":0.47956985235214233},{"id":"https://openalex.org/C207219937","wikidata":"https://www.wikidata.org/wiki/Q5072841","display_name":"Chaotic hysteresis","level":5,"score":0.4740966260433197},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.448081910610199},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43892142176628113},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.39073941111564636},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3044961392879486},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.2962974011898041},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27232420444488525},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.22043290734291077},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18839234113693237},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15255188941955566},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.14380517601966858},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.09626820683479309},{"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},{"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/s0218127419500603","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419500603","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/G1088879481","display_name":null,"funder_award_id":"61527811","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G151301256","display_name":null,"funder_award_id":"2017A030312006","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W297325920","https://openalex.org/W766633888","https://openalex.org/W1427684937","https://openalex.org/W1558736232","https://openalex.org/W1596321532","https://openalex.org/W1967008192","https://openalex.org/W1967332757","https://openalex.org/W1990987436","https://openalex.org/W1994859578","https://openalex.org/W2028923894","https://openalex.org/W2036870441","https://openalex.org/W2037908232","https://openalex.org/W2042868976","https://openalex.org/W2065766143","https://openalex.org/W2069436097","https://openalex.org/W2073077943","https://openalex.org/W2083531786","https://openalex.org/W2084854524","https://openalex.org/W2086533323","https://openalex.org/W2089876099","https://openalex.org/W2092680287","https://openalex.org/W2093351600","https://openalex.org/W2139425917","https://openalex.org/W2141394518","https://openalex.org/W2150927600","https://openalex.org/W2157551165","https://openalex.org/W2465672619","https://openalex.org/W2560829432","https://openalex.org/W2594650004","https://openalex.org/W2779306122","https://openalex.org/W2806531778","https://openalex.org/W2964079314","https://openalex.org/W4292283611","https://openalex.org/W4294967943"],"related_works":["https://openalex.org/W2185766792","https://openalex.org/W2001163940","https://openalex.org/W2802455359","https://openalex.org/W2319716479","https://openalex.org/W2082884906","https://openalex.org/W2410336490","https://openalex.org/W3037847165","https://openalex.org/W2379488025","https://openalex.org/W2565482338","https://openalex.org/W2780885364"],"abstract_inverted_index":{"In":[0],"the":[1,21,24,74,103,122,149,161,184,201,206,211],"chaotic":[2,42,55,80,87,137,150,162,185,216],"polynomial":[3],"Lorenz-type":[4],"systems":[5],"(including":[6],"Lorenz,":[7],"Chen,":[8],"L\u00fc":[9],"and":[10,13,20,63,105,114,168,174,179,208],"Yang":[11],"systems)":[12],"R\u00f6ssler":[14],"system,":[15,81],"their":[16,108],"equilibria":[17,26,94,109,142,167,212],"are":[18,27,110,128],"unstable":[19,154,158,169,176,181],"number":[22,49,92,104,207],"of":[23,50,68,77,93,107,200,210,213],"hyperbolic":[25],"no":[28,58,141],"more":[29],"than":[30],"three.":[31],"This":[32,116],"paper":[33],"shows":[34],"how":[35],"to":[36,73],"construct":[37],"a":[38,66,70,79,86,135],"simple":[39],"analytic":[40],"(nonpolynomial)":[41],"system":[43,56,88,117],"that":[44,85,124],"can":[45,95],"have":[46],"any":[47,90],"preassigned":[48,91],"equilibria.":[51,193],"A":[52],"special":[53],"3D":[54],"with":[57,89,140,153,165,188,205],"equilibrium":[59],"is":[60,83,118],"first":[61],"presented":[62],"discussed.":[64],"Using":[65],"methodology":[67],"adding":[69],"constant":[71],"controller":[72],"third":[75],"equation":[76],"such":[78],"it":[82],"shown":[84],"be":[96],"generated.":[97],"Two":[98],"complete":[99],"mathematical":[100],"characterizations":[101],"for":[102],"stability":[106,209],"further":[111],"rigorously":[112],"derived":[113],"studied.":[115],"very":[119],"interesting":[120],"in":[121],"sense":[123],"some":[125,214],"complex":[126],"dynamics":[127],"found,":[129],"revealing":[130],"many":[131,190],"amazing":[132],"properties:":[133],"(i)":[134],"hidden":[136],"attractor":[138,151,163,186],"exists":[139],"or":[143],"only":[144],"one":[145,172],"stable":[146,166,173,178],"equilibrium;":[147],"(ii)":[148],"coexists":[152,164,187],"equilibria,":[155,170],"including":[156,171],"two/five":[157],"equilibria;":[159,182],"(iii)":[160],"two":[175],"equilibria/94":[177],"93":[180],"(iv)":[183],"infinitely":[189],"nonhyperbolic":[191],"isolated":[192],"These":[194],"results":[195],"reveal":[196],"an":[197],"intrinsic":[198],"relationship":[199],"global":[202],"dynamical":[203],"behaviors":[204],"unusual":[215],"systems.":[217]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}