乐胖代购免代理版

{"id":"https://openalex.org/W2088409980","doi":"https://doi.org/10.1142/s0218127406016525","title":"COMPLEX DYNAMICS IN PENDULUM EQUATION WITH PARAMETRIC AND EXTERNAL EXCITATIONS I","display_name":"COMPLEX DYNAMICS IN PENDULUM EQUATION WITH PARAMETRIC AND EXTERNAL EXCITATIONS I","publication_year":2006,"publication_date":"2006-10-01","ids":{"openalex":"https://openalex.org/W2088409980","doi":"https://doi.org/10.1142/s0218127406016525","mag":"2088409980"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127406016525","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5109193106","display_name":"Zhujun Jing","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"ZHUJUN JING","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, P. R. China","Department of Mathematics, Hunan Normal University, Hunan, Changsha 410081, P. R. China"],"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, P. R. China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Department of Mathematics, Hunan Normal University, Hunan, Changsha 410081, P. R. China","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037915634","display_name":"Jianping Yang","orcid":"https://orcid.org/0000-0001-5431-3457"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JIANPING YANG","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, P. R. China","Graduate School of the Chinese Academy of Sciences, Beijing 100039, P. R. China"],"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, P. R. China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Graduate School of the Chinese Academy of Sciences, Beijing 100039, P. R. China","institution_ids":["https://openalex.org/I19820366"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.062,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":14,"citation_normalized_percentile":{"value":0.679653,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":84,"max":85},"biblio":{"volume":"16","issue":"10","first_page":"2887","last_page":"2902"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9988,"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":0.9988,"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":0.9972,"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/T13126","display_name":"Scientific Research and Discoveries","score":0.9731,"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/chaotic-hysteresis","display_name":"Chaotic hysteresis","score":0.46693793},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.45004472},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.4393261},{"id":"https://openalex.org/keywords/control-of-chaos","display_name":"Control of chaos","score":0.42156672},{"id":"https://openalex.org/keywords/kapitzas-pendulum","display_name":"Kapitza's pendulum","score":0.41280916}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.70076925},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.6245208},{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.55026114},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.53656334},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.50287},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.48388562},{"id":"https://openalex.org/C207219937","wikidata":"https://www.wikidata.org/wiki/Q5072841","display_name":"Chaotic hysteresis","level":5,"score":0.46693793},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.46609226},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.45004472},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.4393261},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4321053},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.42468226},{"id":"https://openalex.org/C95518870","wikidata":"https://www.wikidata.org/wiki/Q49315702","display_name":"Control of chaos","level":5,"score":0.42156672},{"id":"https://openalex.org/C152442685","wikidata":"https://www.wikidata.org/wiki/Q4286430","display_name":"Kapitza's pendulum","level":5,"score":0.41280916},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40780684},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2696525},{"id":"https://openalex.org/C167183279","wikidata":"https://www.wikidata.org/wiki/Q1243208","display_name":"Double pendulum","level":4,"score":0.2583412},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.25478864},{"id":"https://openalex.org/C192921069","wikidata":"https://www.wikidata.org/wiki/Q550134","display_name":"Inverted pendulum","level":3,"score":0.21131587},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.14654765},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10022816},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","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/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127406016525","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_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":35,"referenced_works":["https://openalex.org/W126935648","https://openalex.org/W1528672889","https://openalex.org/W1552040624","https://openalex.org/W1606202192","https://openalex.org/W1632660198","https://openalex.org/W1638842865","https://openalex.org/W186186683","https://openalex.org/W1948009307","https://openalex.org/W1966257363","https://openalex.org/W1968529879","https://openalex.org/W1974760971","https://openalex.org/W1985249099","https://openalex.org/W2021773575","https://openalex.org/W2043767790","https://openalex.org/W2054120189","https://openalex.org/W2058236317","https://openalex.org/W2078988381","https://openalex.org/W2085386447","https://openalex.org/W2086478588","https://openalex.org/W2089400660","https://openalex.org/W2089876099","https://openalex.org/W2114385471","https://openalex.org/W2119596659","https://openalex.org/W2293007794","https://openalex.org/W2489691424","https://openalex.org/W3041070869","https://openalex.org/W3123094903","https://openalex.org/W3127727104","https://openalex.org/W4230976146","https://openalex.org/W4231409469","https://openalex.org/W4252959020","https://openalex.org/W4294967943","https://openalex.org/W564911608","https://openalex.org/W637047068","https://openalex.org/W950991549"],"related_works":["https://openalex.org/W4312884869","https://openalex.org/W2239100685","https://openalex.org/W2143334025","https://openalex.org/W2080921990","https://openalex.org/W2049767790","https://openalex.org/W2035379472","https://openalex.org/W2021742636","https://openalex.org/W2021345684","https://openalex.org/W1980307432","https://openalex.org/W179003357"],"abstract_inverted_index":{"Pendulum":[0],"equation":[1],"with":[2,142,160],"parametric":[3,123,210],"and":[4,11,45,49,66,83,103,125,148,164,175,206],"external":[5,120],"excitations":[6],"is":[7,140],"investigated":[8],"in":[9,43,86,134],"(I)":[10],"(II).":[12],"In":[13,185,220],"(I),":[14],"by":[15,199],"applying":[16],"Melnikov's":[17],"method,":[18],"we":[19,187,222],"prove":[20],"the":[21,69,74,135,143,171,190,225],"criterion":[22],"of":[23,25,36,41,94,98,110,137,146,151,156,209],"existence":[24],"chaos":[26,111,126,159],"under":[27,228],"periodic":[28,91,95,130,162,197],"perturbation.":[29,230],"The":[30],"numerical":[31],"simulations,":[32],"including":[33,73,170],"bifurcation":[34,39,51],"diagram":[35,40],"fixed":[37],"points,":[38],"system":[42,191],"three-":[44],"two-dimensional":[46],"space,":[47],"homoclinic":[48],"heteroclinic":[50],"surface,":[52],"Maximum":[53],"Lyapunov":[54],"exponent,":[55],"phase":[56],"portraits,":[57],"Poincar\u00e9":[58],"map,":[59],"are":[60],"plotted":[61],"to":[62,67,79,129,196],"illustrate":[63],"theoretical":[64],"analysis,":[65],"expose":[68],"complex":[70,161,226],"dynamical":[71],"behaviors":[72],"period-n":[75],"(n":[76],"=":[77],"2":[78],"6,":[80],"10,":[81],"15":[82],"20)":[84],"orbits":[85],"different":[87],"chaotic":[88,168,177,179,194],"regions,":[89],"interlocking":[90],"orbits,":[92,105,131],"symmetry-breaking":[93],"orbit,":[96],"cascade":[97],"period-doubling":[99,107],"bifurcations":[100],"from":[101],"period-5":[102],"-10":[104],"reverse":[106],"bifurcation,":[108],"onset":[109],"which":[112,139,212],"occurs":[113],"more":[114,172],"than":[115,173],"once":[116],"for":[117],"a":[118,217],"given":[119],"frequency":[121,124,207],"or":[122],"suddenly":[127],"converting":[128],"sudden":[132],"jump":[133],"size":[136],"attractors":[138,169],"associated":[141],"transverse":[144],"intersection":[145],"stable":[147],"unstable":[149],"manifolds":[150],"perturbed":[152],"saddle,":[153],"hopping":[154],"behavior":[155],"chaos,":[157],"transient":[158],"windows":[163],"interior":[165],"crisis,":[166],"varied":[167],"three-band":[174],"eight-band":[176],"attractors,":[178],"attractor":[180],"after":[181],"strange":[182],"nonchaotic":[183],"attractor.":[184],"particular,":[186],"observe":[188],"that":[189],"can":[192,213],"leave":[193],"region":[195],"motion":[198],"adjusting":[200],"damping":[201],"\u03b4,":[202],"spring":[203],"constant":[204],"\u03b1":[205],"\u03a9":[208],"excitation":[211],"be":[214],"considered":[215],"as":[216],"control":[218],"strategy.":[219],"(II),":[221],"will":[223],"investigate":[224],"dynamics":[227],"quasi-periodic":[229]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2088409980","counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-01-17T18:07:46.708055","created_date":"2016-06-24"}