{"id":"https://openalex.org/W4388961834","doi":"https://doi.org/10.1142/s0218127423501729","title":"Limit Cycles from Perturbed Center on the Invariant Algebraic Surface of Unified Lorenz-Type System","display_name":"Limit Cycles from Perturbed Center on the Invariant Algebraic Surface of Unified Lorenz-Type System","publication_year":2023,"publication_date":"2023-11-01","ids":{"openalex":"https://openalex.org/W4388961834","doi":"https://doi.org/10.1142/s0218127423501729"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127423501729","doi":"https://doi.org/10.1142/s0218127423501729","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423501729","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,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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"},"volume":null,"type":"article","is_traditional":true,"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/A5100384007","display_name":"Yuming Chen","orcid":"https://orcid.org/0000-0001-6619-9962","observed_orcids":["https://orcid.org/0000-0001-6619-9962","https://orcid.org/0009-0001-4404-9143"]},"institutions":[{"id":"https://openalex.org/I4210119042","display_name":"Gannan Normal University","ror":"https://ror.org/02jf7e446","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210119042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuming Chen","raw_affiliation_strings":["Department of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, P. R. China"],"raw_orcid":"https://orcid.org/0000-0001-6619-9962","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, P. R. China","institution_ids":["https://openalex.org/I4210119042"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080858709","display_name":"Qigui Yang","orcid":"https://orcid.org/0000-0002-3623-4947","observed_orcids":["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":false,"raw_author_name":"Qigui Yang","raw_affiliation_strings":["School of Mathematics, South China University of Technology, Guangzhou 510640, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, South China University of Technology, Guangzhou 510640, P. R. China","institution_ids":["https://openalex.org/I90610280"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.344,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.41248441,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"33","issue":"14","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.8920999765396118,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.8920999765396118,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.09549999982118607,"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":0.005499999970197678,"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/limit-cycles","display_name":"limit cycles","score":0.8859999775886536},{"id":"https://openalex.org/keywords/invariant-algebraic-surfaces","display_name":"invariant algebraic surfaces","score":0.949999988079071},{"id":"https://openalex.org/keywords/center-manifold","display_name":"center manifold","score":0.7480000257492065},{"id":"https://openalex.org/keywords/method-of-averaging","display_name":"averaging method","score":0.8360000252723694},{"id":"https://openalex.org/keywords/bifurcation","display_name":"bifurcation","score":0.5609999895095825},{"id":"https://openalex.org/keywords/limit-cycle-stability","display_name":"limit cycle stability","score":0.8029999732971191},{"id":"https://openalex.org/keywords/three-dimensional-chaotic-system","display_name":"three-dimensional chaotic system","score":0.871999979019165}],"concepts":[{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.7943360805511475},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.708549439907074},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6829777956008911},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6345952749252319},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6232731938362122},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5906593203544617},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5707215666770935},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.5572900772094727},{"id":"https://openalex.org/C69653121","wikidata":"https://www.wikidata.org/wiki/Q1434805","display_name":"Algebraic surface","level":3,"score":0.5066476464271545},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.4538877308368683},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.44787201285362244},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43224218487739563},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.41967490315437317},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.344889760017395},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.18741893768310547},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17078104615211487},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12315025925636292},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.09263339638710022},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.09199753403663635},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07440969347953796},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.073496013879776},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0643797218799591},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"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:10.1142/s0218127423501729","doi":"https://doi.org/10.1142/s0218127423501729","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423501729","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,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1932396371","display_name":null,"funder_award_id":"12261005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1558736232","https://openalex.org/W1596321532","https://openalex.org/W1966709319","https://openalex.org/W1979416304","https://openalex.org/W1983674368","https://openalex.org/W1992299830","https://openalex.org/W2000168901","https://openalex.org/W2003158098","https://openalex.org/W2019143828","https://openalex.org/W2029750936","https://openalex.org/W2030838868","https://openalex.org/W2032192133","https://openalex.org/W2035013249","https://openalex.org/W2036870441","https://openalex.org/W2069436097","https://openalex.org/W2079776726","https://openalex.org/W2083531786","https://openalex.org/W2093351600","https://openalex.org/W2106154524","https://openalex.org/W2131762088","https://openalex.org/W2141394518","https://openalex.org/W2148489408","https://openalex.org/W2158334808","https://openalex.org/W3016221005","https://openalex.org/W3018925682","https://openalex.org/W3025401191","https://openalex.org/W3039212132","https://openalex.org/W3041070869","https://openalex.org/W3081720511","https://openalex.org/W3131326656"],"related_works":["https://openalex.org/W2061562820","https://openalex.org/W2093351600","https://openalex.org/W2950461812","https://openalex.org/W1976271680","https://openalex.org/W2089636745","https://openalex.org/W2027442439","https://openalex.org/W4200066376","https://openalex.org/W4387955689","https://openalex.org/W2609736742","https://openalex.org/W2621862725"],"abstract_inverted_index":{"For":[0],"a":[1],"three-dimensional":[2],"chaotic":[3,62],"system,":[4,112],"little":[5],"seems":[6],"to":[7,35,108,178],"be":[8],"known":[9],"about":[10],"the":[11,18,37,48,53,71,77,83,92,102,109,122,131,135,140,143,155,163,167,180],"perturbation":[12,84,118],"of":[13,52,85,105,119,121,139,145,158,170],"invariant":[14,49,86,136],"algebraic":[15,50,87,137],"surface":[16,51,138],"and":[17,28,44,142],"center":[19,42,73,80,97,133],"on":[20,47,70,95,134],"this":[21,96,146],"surface.":[22],"This":[23,31],"question":[24],"is":[25,33,125,149,176],"very":[26],"interesting":[27],"worth":[29],"investigating.":[30],"paper":[32],"devoted":[34],"analyzing":[36],"limit":[38,127,147],"cycles":[39],"from":[40,82,130],"perturbed":[41,132],"(trivial":[43],"nontrivial":[45],"equilibria)":[46],"unified":[54],"Lorenz-type":[55],"system":[56,94],"(ULTS),":[57],"which":[58],"contains":[59],"some":[60],"common":[61],"systems":[63],"as":[64,89,91,151],"its":[65],"particular":[66],"cases.":[67],"First,":[68],"based":[69],"parameter-dependent":[72],"manifold,":[74],"we":[75,113,161],"obtain":[76],"approximate":[78],"two-dimensional":[79,93,111],"manifold":[81],"surface,":[88],"well":[90],"manifold.":[98],"Second,":[99],"by":[100],"applying":[101],"averaging":[103,156,168],"method":[104,157,169],"third":[106,171],"order":[107],"above":[110],"show":[114,162],"that":[115],"under":[116],"suitable":[117],"parameters":[120],"ULTS,":[123,141],"there":[124],"one":[126],"cycle":[128,148],"bifurcating":[129],"stability":[144],"determined":[150],"well.":[152],"By":[153],"using":[154],"fourth":[159],"order,":[160],"same":[164],"results":[165],"with":[166],"order.":[172],"Finally,":[173],"numerical":[174],"simulation":[175],"used":[177],"verify":[179],"theoretical":[181],"analyses.":[182]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2023-11-24T00:00:00"}