{"id":"https://openalex.org/W1996163397","doi":"https://doi.org/10.1142/s0218127411029884","title":"CONDITIONS FOR APPEARANCE AND DISAPPEARANCE OF LIMIT CYCLES IN THE SHIMIZU\u2013MORIOKA SYSTEM","display_name":"CONDITIONS FOR APPEARANCE AND DISAPPEARANCE OF LIMIT CYCLES IN THE SHIMIZU\u2013MORIOKA SYSTEM","publication_year":2011,"publication_date":"2011-07-12","ids":{"openalex":"https://openalex.org/W1996163397","doi":"https://doi.org/10.1142/s0218127411029884","mag":"1996163397"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127411029884","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411029884","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/A5100614787","display_name":"Lingling Liu","orcid":"https://orcid.org/0000-0001-8165-0475"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"LINGLING LIU","raw_affiliation_strings":["Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China","Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R., China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China","institution_ids":["https://openalex.org/I24185976"]},{"raw_affiliation_string":"Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R., China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055507785","display_name":"Bo Gao","orcid":"https://orcid.org/0000-0002-5190-7337"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"BO GAO","raw_affiliation_strings":["Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China","Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R., China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R. China","institution_ids":["https://openalex.org/I24185976"]},{"raw_affiliation_string":"Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, P. R., China","institution_ids":["https://openalex.org/I24185976"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I24185976"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08590471,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":"09","first_page":"2489","last_page":"2503"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9991000294685364,"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":0.996999979019165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.8031840324401855},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7972646951675415},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.693981945514679},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.5852375030517578},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5549413561820984},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5253300666809082},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.5214701890945435},{"id":"https://openalex.org/keywords/lorenz-system","display_name":"Lorenz system","score":0.4331062436103821},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.3839437663555145},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3450871706008911},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3393072783946991},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3307808041572571},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13302206993103027},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10736039280891418},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0780608057975769}],"concepts":[{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.8031840324401855},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7972646951675415},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.693981945514679},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.5852375030517578},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5549413561820984},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5253300666809082},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.5214701890945435},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.4331062436103821},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.3839437663555145},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3450871706008911},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3393072783946991},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3307808041572571},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13302206993103027},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10736039280891418},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0780608057975769},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127411029884","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411029884","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1531715726","https://openalex.org/W1561704653","https://openalex.org/W1564263151","https://openalex.org/W1603340857","https://openalex.org/W1606340521","https://openalex.org/W1984861030","https://openalex.org/W1997194160","https://openalex.org/W2014509488","https://openalex.org/W2021696231","https://openalex.org/W2043122468","https://openalex.org/W2050454764","https://openalex.org/W2053227182","https://openalex.org/W2056525521","https://openalex.org/W2069436097","https://openalex.org/W2071673800","https://openalex.org/W2087984302","https://openalex.org/W2094255955","https://openalex.org/W2128563585","https://openalex.org/W2128978199","https://openalex.org/W2141394518","https://openalex.org/W2489426763","https://openalex.org/W4213264637","https://openalex.org/W4214513274"],"related_works":["https://openalex.org/W1987790493","https://openalex.org/W2153388945","https://openalex.org/W2038701038","https://openalex.org/W1975783007","https://openalex.org/W1996991127","https://openalex.org/W2382752082","https://openalex.org/W2115351049","https://openalex.org/W1988489950","https://openalex.org/W1986426368","https://openalex.org/W2363522146"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3],"the":[4,18,36,59,78],"Shimizu\u2013Morioka":[5],"system,":[6],"a":[7,29],"special":[8],"generalized":[9],"Lorenz":[10],"canonical":[11],"form.":[12],"Using":[13],"techniques":[14],"of":[15,20,39,52,63,80],"elimination":[16],"in":[17],"computation":[19,33],"algebraic":[21],"varieties":[22],"we":[23,92,109],"obtain":[24],"parameter-dependent":[25,68],"normal":[26,69],"forms":[27,70],"on":[28],"center":[30],"manifold.":[31],"Our":[32,67],"shows":[34],"that":[35],"maximal":[37],"number":[38,51],"limit":[40,53,85,100,118],"cycles":[41,54,86,101,119],"produced":[42,104],"from":[43,105],"Hopf":[44,106],"bifurcations":[45],"is":[46],"four":[47,84],"and":[48,83],"only":[49],"even":[50],"can":[55,102],"be":[56,103],"bifurcated":[57],"near":[58],"two":[60,82],"equilibria":[61],"because":[62],"[Formula:":[64],"see":[65],"text]-symmetry.":[66],"enable":[71],"us":[72],"to":[73],"give":[74,93,111],"parameter":[75],"conditions":[76,94,112],"for":[77,113],"cases":[79],"none,":[81],"separately.":[87],"Furthermore,":[88],"considering":[89],"exterior":[90],"perturbations,":[91],"under":[95,116],"which":[96,117],"one":[97],"or":[98,121],"three":[99],"bifurcations.":[107],"Moreover,":[108],"also":[110],"fold":[114],"bifurcations,":[115],"coincide":[120],"disappear.":[122],"Finally,":[123],"our":[124],"results":[125],"are":[126],"illustrated":[127],"by":[128],"numerical":[129],"simulations.":[130]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
