{"id":"https://openalex.org/W2124484443","doi":"https://doi.org/10.1142/s0218127413500867","title":"ASYMMETRIC PERIODIC MOTIONS WITH CHAOS IN A SOFTENING DUFFING OSCILLATOR","display_name":"ASYMMETRIC PERIODIC MOTIONS WITH CHAOS IN A SOFTENING DUFFING OSCILLATOR","publication_year":2013,"publication_date":"2013-05-01","ids":{"openalex":"https://openalex.org/W2124484443","doi":"https://doi.org/10.1142/s0218127413500867","mag":"2124484443"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127413500867","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413500867","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/A5076270155","display_name":"Albert C. J. Luo","orcid":"https://orcid.org/0000-0001-8208-6108"},"institutions":[{"id":"https://openalex.org/I87547150","display_name":"Southern Illinois University Edwardsville","ror":"https://ror.org/04cqs5j56","country_code":"US","type":"education","lineage":["https://openalex.org/I2801502357","https://openalex.org/I87547150"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"ALBERT C. J. LUO","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA","Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA","institution_ids":["https://openalex.org/I87547150"]},{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA#TAB#","institution_ids":["https://openalex.org/I87547150"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020274098","display_name":"Jianzhe Huang","orcid":"https://orcid.org/0000-0002-5945-6235"},"institutions":[{"id":"https://openalex.org/I87547150","display_name":"Southern Illinois University Edwardsville","ror":"https://ror.org/04cqs5j56","country_code":"US","type":"education","lineage":["https://openalex.org/I2801502357","https://openalex.org/I87547150"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"JIANZHE HUANG","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA","Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA","institution_ids":["https://openalex.org/I87547150"]},{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA#TAB#","institution_ids":["https://openalex.org/I87547150"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2482,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.88558395,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"23","issue":"05","first_page":"1350086","last_page":"1350086"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9979000091552734,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9957000017166138,"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/duffing-equation","display_name":"Duffing equation","score":0.8395465016365051},{"id":"https://openalex.org/keywords/softening","display_name":"Softening","score":0.6898916959762573},{"id":"https://openalex.org/keywords/harmonic-balance","display_name":"Harmonic balance","score":0.5276509523391724},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5119005441665649},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.5104852914810181},{"id":"https://openalex.org/keywords/harmonic-oscillator","display_name":"Harmonic oscillator","score":0.49508824944496155},{"id":"https://openalex.org/keywords/anharmonicity","display_name":"Anharmonicity","score":0.47008681297302246},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.46394988894462585},{"id":"https://openalex.org/keywords/periodic-function","display_name":"Periodic function","score":0.43090352416038513},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3846290707588196},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3754922151565552},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3671652674674988},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08133071660995483}],"concepts":[{"id":"https://openalex.org/C132323500","wikidata":"https://www.wikidata.org/wiki/Q675387","display_name":"Duffing equation","level":3,"score":0.8395465016365051},{"id":"https://openalex.org/C2781098093","wikidata":"https://www.wikidata.org/wiki/Q85787439","display_name":"Softening","level":2,"score":0.6898916959762573},{"id":"https://openalex.org/C121758426","wikidata":"https://www.wikidata.org/wiki/Q5659248","display_name":"Harmonic balance","level":3,"score":0.5276509523391724},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5119005441665649},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.5104852914810181},{"id":"https://openalex.org/C40934718","wikidata":"https://www.wikidata.org/wiki/Q190070","display_name":"Harmonic oscillator","level":2,"score":0.49508824944496155},{"id":"https://openalex.org/C147724859","wikidata":"https://www.wikidata.org/wiki/Q545228","display_name":"Anharmonicity","level":2,"score":0.47008681297302246},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.46394988894462585},{"id":"https://openalex.org/C98644592","wikidata":"https://www.wikidata.org/wiki/Q184743","display_name":"Periodic function","level":2,"score":0.43090352416038513},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3846290707588196},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3754922151565552},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3671652674674988},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08133071660995483}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127413500867","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413500867","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1546721432","https://openalex.org/W1979400963","https://openalex.org/W1986177202","https://openalex.org/W1987882966","https://openalex.org/W2000293654","https://openalex.org/W2018895750","https://openalex.org/W2020336658","https://openalex.org/W2032215782","https://openalex.org/W2056010807","https://openalex.org/W2059266872","https://openalex.org/W2065325403","https://openalex.org/W2068003521","https://openalex.org/W2071623546","https://openalex.org/W2103317247","https://openalex.org/W2119368478","https://openalex.org/W2325936659","https://openalex.org/W3134182129"],"related_works":["https://openalex.org/W2755606167","https://openalex.org/W2071623546","https://openalex.org/W1615069852","https://openalex.org/W2059266872","https://openalex.org/W2500762073","https://openalex.org/W2072026997","https://openalex.org/W2090432991","https://openalex.org/W2042117772","https://openalex.org/W2077274631","https://openalex.org/W2124484443"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"asymmetric":[3,39,54,71,77,90],"periodic":[4,29,40,55,93,109],"motions":[5,30,41,56,64,79,94,110],"in":[6,42,65,95,122],"a":[7,116],"periodically":[8],"forced,":[9],"softening":[10,24,44,67,97,124],"Duffing":[11,25,45,68,98,125],"oscillator":[12,99],"are":[13,47,100,111],"presented":[14],"analytically":[15,50],"through":[16],"the":[17,23,27,43,62,66,73,96,123],"generalized":[18],"harmonic":[19],"balance":[20],"method.":[21],"For":[22,70],"oscillator,":[26],"symmetric":[28,63],"with":[31],"jumping":[32],"phenomena":[33],"were":[34],"understood":[35],"very":[36],"well.":[37],"However,":[38],"oscillators":[46],"not":[48],"investigated":[49],"yet,":[51],"and":[52,88,91,102,107],"such":[53],"possess":[57],"much":[58],"richer":[59],"dynamics":[60],"than":[61],"oscillator.":[69,126],"motions,":[72],"bifurcation":[74],"tree":[75],"from":[76],"period-1":[78],"to":[80],"chaos":[81],"is":[82],"discussed":[83],"comprehensively.":[84],"The":[85],"corresponding,":[86],"unstable":[87,108],"stable,":[89],"symmetric,":[92],"presented,":[101],"numerical":[103],"illustrations":[104],"of":[105,119],"stable":[106],"completed.":[112],"This":[113],"investigation":[114],"provides":[115],"better":[117],"picture":[118],"complex":[120],"motion":[121]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
