{"id":"https://openalex.org/W2105153979","doi":"https://doi.org/10.1142/s0218127408020148","title":"GLOBAL TANGENCY AND TRANSVERSALITY OF PERIODIC FLOWS AND CHAOS IN A PERIODICALLY FORCED, DAMPED DUFFING OSCILLATOR","display_name":"GLOBAL TANGENCY AND TRANSVERSALITY OF PERIODIC FLOWS AND CHAOS IN A PERIODICALLY FORCED, DAMPED DUFFING OSCILLATOR","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2105153979","doi":"https://doi.org/10.1142/s0218127408020148","mag":"2105153979"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127408020148","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127408020148","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":true,"raw_author_name":"ALBERT C. J. LUO","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, Southern Illinois University at Edwardsville, Edwardsville IL 62026-1805, USA","Department of Mechanical and Industrial Engineering, Southern Illinois University at Edwardsville, Edwardsville, IL 62026-1805, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Southern Illinois University at Edwardsville, Edwardsville IL 62026-1805, USA","institution_ids":["https://openalex.org/I87547150"]},{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Southern Illinois University at Edwardsville, Edwardsville, IL 62026-1805, USA","institution_ids":["https://openalex.org/I87547150"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5076270155"],"corresponding_institution_ids":["https://openalex.org/I87547150"],"apc_list":null,"apc_paid":null,"fwci":4.7836,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.95259783,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"18","issue":"01","first_page":"1","last_page":"49"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","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/T11261","display_name":"Quantum chaos and dynamical systems","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/T10244","display_name":"Chaos control and synchronization","score":0.9975000023841858,"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":0.9819999933242798,"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/transversality","display_name":"Transversality","score":0.8592116832733154},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7012443542480469},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6353923082351685},{"id":"https://openalex.org/keywords/duffing-equation","display_name":"Duffing equation","score":0.5703586935997009},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.5067124962806702},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49483174085617065},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.46299630403518677},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.415621817111969},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.36706775426864624},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3649371266365051},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3064899444580078},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08858945965766907},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06597533822059631}],"concepts":[{"id":"https://openalex.org/C24167531","wikidata":"https://www.wikidata.org/wiki/Q2300767","display_name":"Transversality","level":2,"score":0.8592116832733154},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7012443542480469},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6353923082351685},{"id":"https://openalex.org/C132323500","wikidata":"https://www.wikidata.org/wiki/Q675387","display_name":"Duffing equation","level":3,"score":0.5703586935997009},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.5067124962806702},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49483174085617065},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.46299630403518677},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.415621817111969},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.36706775426864624},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3649371266365051},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3064899444580078},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08858945965766907},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06597533822059631},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/s0218127408020148","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127408020148","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":13,"referenced_works":["https://openalex.org/W150397081","https://openalex.org/W587386485","https://openalex.org/W1542389835","https://openalex.org/W1968141517","https://openalex.org/W1972517630","https://openalex.org/W1994006347","https://openalex.org/W2018895750","https://openalex.org/W2033459047","https://openalex.org/W2051907816","https://openalex.org/W2089876099","https://openalex.org/W2160163816","https://openalex.org/W4206225272","https://openalex.org/W4212928962"],"related_works":["https://openalex.org/W125373334","https://openalex.org/W4250831671","https://openalex.org/W2230606337","https://openalex.org/W1979172495","https://openalex.org/W2089869689","https://openalex.org/W4388681848","https://openalex.org/W2078952919","https://openalex.org/W2945666329","https://openalex.org/W2617651062","https://openalex.org/W2330535098"],"abstract_inverted_index":{"This":[0,70],"paper":[1,71],"presents":[2,72],"how":[3],"to":[4,24,48,58,81,105,129,156,256,338,419,462,483],"apply":[5],"a":[6,25,31,53,196,238,243,392,455],"newly":[7],"developed":[8,285],"general":[9],"theory":[10,501],"for":[11,51,174,195,202,250,286,381,454,510],"the":[12,43,49,62,73,76,82,87,91,100,111,123,132,143,153,159,171,192,208,214,220,226,251,257,270,279,294,303,313,320,326,340,346,359,399,411,421,436,452,459,463,470,475,479,485,491,499,504,511,522],"global":[13,38,77,175,252,274,289,300,347,460,486,512],"transversality":[14,41,78,176,253,461,487,513],"and":[15,40,45,79,177,205,217,254,261,269,273,288,325,361,365,408,442,474,514,519],"tangency":[16,39,80,178,255,348,515],"of":[17,42,64,86,122,134,161,179,299,312,342,349,376,388,413,423,432,447,458,488,521],"flows":[18,204,291,351,378,434],"in":[19,66,95,136,163,168,207,302,352,390],"n-dimensional":[20],"nonlinear":[21,27,54,67,96,112,137,164,181,210],"dynamical":[22,28,68,97,113,138,165,182,211],"systems":[23,98,114,183],"2-D":[26,180,209],"system":[29,55],"(i.e.":[30,191,334,430],"periodically":[32,232],"forced,":[33,233],"damped":[34,234,304,314],"Duffing":[35,235,305,315,393],"oscillator).":[36],"The":[37,119,186,246,266,281,296,329,371,403,425,444,465,493,507],"periodic":[44,203,290,350,377,384],"chaotic":[46,107,433],"motions":[47],"separatrix":[50,83,239,258,453,471,480],"such":[52,353,391],"are":[56,84,184,259,276,284,307,317,395,417,449,496,516],"discussed":[57],"help":[59],"us":[60],"understand":[61],"complexity":[63,160,422],"chaos":[65,135,162,206,301,389,448,489],"systems.":[69,139,166,212],"concept":[74],"that":[75],"independent":[85,520],"Melnikov":[88,124,221,505],"function":[89,125,222],"(or":[90],"energy":[92,102,193,405],"increment).":[93],"Chaos":[94],"makes":[99],"exact":[101],"increment":[103,190,333,375,429],"quantity":[104,189,229,332,374,428],"be":[106,127],"no":[108],"matter":[109],"if":[110],"have":[115],"separatrices":[116],"or":[117],"not.":[118],"simple":[120],"zero":[121,380],"cannot":[126],"used":[128],"simply":[130],"determine":[131],"existence":[133],"Through":[140],"this":[141,169],"paper,":[142,170],"expectation":[144],"is":[145,200,223,240,336,356,366,379,440,472,481],"that,":[146],"from":[147,225,498],"now":[148],"on,":[149],"one":[150],"can":[151],"use":[152],"alternative":[154],"aspect":[155],"look":[157],"into":[158],"Therefore,":[167],"analytical":[172,248,494],"conditions":[173,249,495,509],"presented.":[185],"first":[187,227,330,372,426],"integral":[188,228,331,373,427],"increment)":[194],"certain":[197],"time":[198],"interval":[199],"achieved":[201],"Under":[213],"perturbation":[215],"assumptions":[216],"convergent":[218],"conditions,":[219],"recovered":[224],"increment.":[230],"A":[231],"oscillator":[236,306,316,355,394],"with":[237],"investigated":[241],"as":[242],"sampled":[244],"problem.":[245],"corresponding":[247,271],"obtained":[260,497],"verified":[262,367],"by":[263,358,368],"numerical":[264,369],"simulations.":[265,370],"switching":[267,327,445,466,476],"planes":[268,446],"local":[272,287],"mappings":[275],"defined":[277],"on":[278,451,469,478,490],"separatrix.":[280,295,464,492],"mapping":[282,297,323,401,415,438],"structures":[283,298],"passing":[292],"through":[293,319,398],"also":[308],"discussed.":[309],"Bifurcation":[310],"scenarios":[311],"presented":[318,337,418,450,473],"traditional":[321],"Poincar\u00e9":[322,400,414,437],"section":[324],"planes.":[328],"L-function)":[335,431],"observe":[339,420],"periodicity":[341],"flows.":[343],"In":[344],"addition,":[345],"an":[354],"measured":[357],"G-function":[360,407,477],"G":[362],"(1)":[363],"-function,":[364],"their":[382],"complete":[383],"cycles.":[385],"Numerical":[386],"simulations":[387],"carried":[396],"out":[397],"sections.":[402],"conservative":[404],"distribution,":[406],"L-function":[409],"along":[410],"displacement":[412],"points":[416,439],"chaos.":[424],"at":[435],"nonzero":[441],"chaotic.":[443],"better":[456],"understanding":[457],"point":[467],"distribution":[468],"given":[482],"show":[484],"new":[500,508],"rather":[502],"than":[503],"method.":[506],"more":[517],"accurate":[518],"small":[523],"parameters.":[524]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
