{"id":"https://openalex.org/W2059554553","doi":"https://doi.org/10.1142/s0218127415500054","title":"Fuzzy Responses and Bifurcations of a Forced Duffing Oscillator with a Triple-Well Potential","display_name":"Fuzzy Responses and Bifurcations of a Forced Duffing Oscillator with a Triple-Well Potential","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2059554553","doi":"https://doi.org/10.1142/s0218127415500054","mag":"2059554553"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127415500054","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127415500054","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/A5042006886","display_name":"Ling Hong","orcid":"https://orcid.org/0000-0002-2837-9724"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ling Hong","raw_affiliation_strings":["State Key Laboratory for Strength and Vibration, Xi'an Jiaotong University, Xi'an 710049, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory for Strength and Vibration, Xi'an Jiaotong University, Xi'an 710049, P. R. China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072706004","display_name":"Jun Jiang","orcid":"https://orcid.org/0000-0003-4540-0270"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Jiang","raw_affiliation_strings":["State Key Laboratory for Strength and Vibration, Xi'an Jiaotong University, Xi'an 710049, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory for Strength and Vibration, Xi'an Jiaotong University, Xi'an 710049, P. R. China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017350937","display_name":"Jian\u2010Qiao Sun","orcid":"https://orcid.org/0000-0002-5441-7982"},"institutions":[{"id":"https://openalex.org/I156087764","display_name":"University of California, Merced","ror":"https://ror.org/00d9ah105","country_code":"US","type":"education","lineage":["https://openalex.org/I156087764"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jian-Qiao Sun","raw_affiliation_strings":["School of Engineering, University of California at Merced, Merced, CA 95344, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering, University of California at Merced, Merced, CA 95344, USA","institution_ids":["https://openalex.org/I156087764"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7663,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.85733203,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"25","issue":"01","first_page":"1550005","last_page":"1550005"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9287999868392944,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6936434507369995},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6666983366012573},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5635083913803101},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37222886085510254},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3514575660228729},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1898447573184967},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08407524228096008}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6936434507369995},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6666983366012573},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5635083913803101},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37222886085510254},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3514575660228729},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1898447573184967},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08407524228096008},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127415500054","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127415500054","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":33,"referenced_works":["https://openalex.org/W193172831","https://openalex.org/W593463051","https://openalex.org/W1968639412","https://openalex.org/W1989065092","https://openalex.org/W1995580872","https://openalex.org/W1997497643","https://openalex.org/W1998436997","https://openalex.org/W2001933015","https://openalex.org/W2003184377","https://openalex.org/W2006532376","https://openalex.org/W2007162114","https://openalex.org/W2010104284","https://openalex.org/W2014338223","https://openalex.org/W2020508693","https://openalex.org/W2024857351","https://openalex.org/W2025475113","https://openalex.org/W2025649014","https://openalex.org/W2027963054","https://openalex.org/W2044371775","https://openalex.org/W2047878675","https://openalex.org/W2049600235","https://openalex.org/W2051761453","https://openalex.org/W2058572562","https://openalex.org/W2073945649","https://openalex.org/W2074972654","https://openalex.org/W2079123443","https://openalex.org/W2082503639","https://openalex.org/W2091298827","https://openalex.org/W2091657382","https://openalex.org/W2092677482","https://openalex.org/W2111473560","https://openalex.org/W2165510765","https://openalex.org/W2262607245"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Responses":[0],"and":[1,84,104,127,168,178,231,273],"bifurcations":[2],"of":[3,16,28,37,46,69,88,118,125,137,147,150,157,164,176,181,188,234,256,271],"a":[4,34,53,97,195,209],"forced":[5],"triple-well":[6],"potential":[7,159,251],"system":[8],"with":[9,140,202,260],"fuzzy":[10,39,48,61,70,73,94,151,183,189,275],"uncertainty":[11],"are":[12,131,215,221,277],"studied":[13],"by":[14,77,133],"means":[15],"the":[17,29,38,43,60,66,81,102,106,115,119,122,134,138,141,148,158,174,182,186,199,229,235],"Fuzzy":[18],"Generalized":[19],"Cell":[20],"Mapping":[21],"(FGCM)":[22],"method.":[23],"A":[24,72,93],"rigorous":[25],"mathematical":[26],"foundation":[27],"FGCM":[30,51,120,139],"is":[31,75,111,239],"established":[32],"as":[33,242],"discrete":[35],"representation":[36],"master":[40,62],"equation":[41,63],"for":[42,57],"possibility":[44,86,225],"transition":[45],"continuous":[47],"processes.":[49],"The":[50,108,129,212,253],"offers":[52],"very":[54],"effective":[55],"approach":[56],"solutions":[58],"to":[59,208,228,265],"based":[64,113],"on":[65,114,173,223],"min\u2013max":[67,142,236],"operator":[68],"logic.":[71],"response":[74,109],"characterized":[76],"its":[78,85],"topology":[79,103,110],"in":[80,101,105,198],"state":[82,200],"space":[83,201],"measure":[87],"membership":[89,204],"distribution":[90],"functions":[91],"(MDFs).":[92],"bifurcation":[95],"implies":[96],"sudden":[98],"change":[99],"both":[100],"MDFs.":[107],"obtained":[112],"qualitative":[116],"analysis":[117,136],"involving":[121],"Boolean":[123],"operation":[124],"0":[126],"1.":[128],"MDFs":[130,180,193,220,247,258],"determined":[132],"quantitative":[135],"calculations.":[143],"With":[144],"an":[145],"increase":[146],"intensity":[149,187],"noise,":[152],"noise-induced":[153],"escape":[154],"from":[155],"each":[156],"wells":[160],"defines":[161],"two":[162],"types":[163],"bifurcations,":[165],"namely":[166],"catastrophe":[167],"explosion.":[169],"This":[170],"paper":[171],"focuses":[172],"evolution":[175],"transient":[177,246,257],"steady-state":[179,192,219],"response.":[184],"As":[185],"noise":[190,276],"increases,":[191],"cover":[194],"bigger":[196],"area":[197],"higher":[203],"values":[205],"spreading":[206],"out":[207],"larger":[210],"area.":[211],"previous":[213],"conjectures":[214],"further":[216],"confirmed":[217],"that":[218,241],"dependent":[222],"initial":[224],"distributions":[226],"due":[227],"nonsmooth":[230],"nonlinear":[232],"nature":[233],"operation.":[237],"It":[238],"found":[240],"time":[243],"goes":[244],"on,":[245],"spread":[248],"around":[249],"three":[250],"wells.":[252],"evolutionary":[254],"orientation":[255],"aligns":[259],"unstable":[261],"invariant":[262,267],"manifolds":[263],"leading":[264],"stable":[266],"sets.":[268],"Two":[269],"examples":[270],"additive":[272],"multiplicative":[274],"given.":[278]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}