{"id":"https://openalex.org/W4252876441","doi":"https://doi.org/10.1142/s0218127410028276","title":"SUDDEN OCCURRENCE OF CHAOS-II IN NONSMOOTH MAPS","display_name":"SUDDEN OCCURRENCE OF CHAOS-II IN NONSMOOTH MAPS","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W4252876441","doi":"https://doi.org/10.1142/s0218127410028276"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127410028276","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127410028276","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/A5109722769","display_name":"Gaogao Dong","orcid":"https://orcid.org/0000-0003-4425-7724"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"GAOGAO DONG","raw_affiliation_strings":["Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang Jiangsu, 212013, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang Jiangsu, 212013, P. R. China","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100345572","display_name":"Lixin Tian","orcid":"https://orcid.org/0000-0002-4550-2472"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"LIXIN TIAN","raw_affiliation_strings":["Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang Jiangsu, 212013, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang Jiangsu, 212013, P. R. China","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003154913","display_name":"Jun Xia","orcid":"https://orcid.org/0009-0008-6635-5572"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JUN XIA","raw_affiliation_strings":["Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang Jiangsu, 212013, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang Jiangsu, 212013, P. R. China","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003209414","display_name":"Song Zheng","orcid":"https://orcid.org/0000-0003-2382-4435"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"SONG ZHENG","raw_affiliation_strings":["Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang Jiangsu, 212013, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang Jiangsu, 212013, P. R. China","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100742778","display_name":"Ruijin Du","orcid":"https://orcid.org/0000-0002-1530-7676"},"institutions":[{"id":"https://openalex.org/I126924076","display_name":"Chongqing Normal University","ror":"https://ror.org/01dcw5w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I126924076"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"RUIJIN DU","raw_affiliation_strings":["College of Mathematics and Computer Science, Chongqing Normal University, Chongqing, 401331, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Computer Science, Chongqing Normal University, Chongqing, 401331, P. R. China","institution_ids":["https://openalex.org/I126924076"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2355,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62659847,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"20","issue":"12","first_page":"4159","last_page":"4174"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9987999796867371,"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":0.9987999796867371,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9940999746322632,"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/chaos","display_name":"CHAOS (operating system)","score":0.8466416597366333},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6258798837661743},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6059612035751343},{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.556424081325531},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5054233074188232},{"id":"https://openalex.org/keywords/control-of-chaos","display_name":"Control of chaos","score":0.48243269324302673},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.47834107279777527},{"id":"https://openalex.org/keywords/sudden-death","display_name":"Sudden death","score":0.417726069688797},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3456900715827942},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.31815075874328613},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.26502543687820435},{"id":"https://openalex.org/keywords/synchronization-of-chaos","display_name":"Synchronization of chaos","score":0.24279287457466125},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.2051546573638916},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18755275011062622},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12413915991783142},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10407862067222595},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0864909291267395}],"concepts":[{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.8466416597366333},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6258798837661743},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6059612035751343},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.556424081325531},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5054233074188232},{"id":"https://openalex.org/C95518870","wikidata":"https://www.wikidata.org/wiki/Q49315702","display_name":"Control of chaos","level":5,"score":0.48243269324302673},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.47834107279777527},{"id":"https://openalex.org/C2993353509","wikidata":"https://www.wikidata.org/wiki/Q411867","display_name":"Sudden death","level":2,"score":0.417726069688797},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3456900715827942},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.31815075874328613},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.26502543687820435},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.24279287457466125},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2051546573638916},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18755275011062622},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12413915991783142},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10407862067222595},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0864909291267395},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C164705383","wikidata":"https://www.wikidata.org/wiki/Q10379","display_name":"Cardiology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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/s0218127410028276","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127410028276","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":20,"referenced_works":["https://openalex.org/W1967755877","https://openalex.org/W1970500498","https://openalex.org/W1975889601","https://openalex.org/W1978769092","https://openalex.org/W1985732103","https://openalex.org/W2004659685","https://openalex.org/W2016397389","https://openalex.org/W2017540121","https://openalex.org/W2021020784","https://openalex.org/W2039817925","https://openalex.org/W2045184052","https://openalex.org/W2067017955","https://openalex.org/W2081128244","https://openalex.org/W2084403515","https://openalex.org/W2092187455","https://openalex.org/W2102892532","https://openalex.org/W2151268547","https://openalex.org/W2168711358","https://openalex.org/W2953154342","https://openalex.org/W4239883234"],"related_works":["https://openalex.org/W2028445092","https://openalex.org/W1581278046","https://openalex.org/W2390824390","https://openalex.org/W2052017700","https://openalex.org/W2360213031","https://openalex.org/W2371341827","https://openalex.org/W2370852778","https://openalex.org/W2028196466","https://openalex.org/W4247599920","https://openalex.org/W2011681983"],"abstract_inverted_index":{"Different":[0],"ways":[1,21],"to":[2,22,51],"chaos":[3],"show":[4],"different":[5,98],"features.":[6],"The":[7,43,85],"study":[8],"of":[9,12,31,41,46,55,58,70,75,87,109,113],"Sudden":[10,29,39,44,56,111],"Occurrence":[11,30,40,45,57,112],"Chaos":[13],"has":[14],"generated":[15],"much":[16],"interest":[17],"in":[18,81],"exploring":[19],"new":[20],"chaos.":[23],"In":[24],"this":[25],"novel":[26],"way,":[27],"the":[28,52,82,100],"Chaos-II":[32,47,114],"indicates":[33],"more":[34],"comprehensive":[35],"dynamical":[36],"behaviors":[37],"than":[38],"Chaos.":[42],"not":[48,79],"only":[49],"belongs":[50],"previous":[53,83],"category":[54],"Chaos,":[59],"but":[60],"also":[61],"includes":[62],"inverse":[63,88],"period-doubling":[64,89],"band":[65,91],"splitting,":[66],"and":[67],"a":[68],"series":[69],"\"band-gaps\"":[71],"by":[72,115],"successive":[73],"splitting":[74,90],"bands,":[76],"which":[77,95],"do":[78],"appear":[80],"case.":[84],"constant":[86],"is":[92,96],"first":[93,101],"calculated,":[94],"completely":[97],"from":[99],"Feigenbaum":[102],"constant.":[103],"Furthermore,":[104],"we":[105],"give":[106],"some":[107],"examples":[108],"m-period":[110],"regulating":[116],"periodic":[117],"parameter":[118],"m.":[119]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}