{"id":"https://openalex.org/W2161202377","doi":"https://doi.org/10.1142/s0218127414501582","title":"Existence of Chaotic Invariant Set in a Class of 4-Dimensional Piecewise Linear Dynamical Systems","display_name":"Existence of Chaotic Invariant Set in a Class of 4-Dimensional Piecewise Linear Dynamical Systems","publication_year":2014,"publication_date":"2014-12-01","ids":{"openalex":"https://openalex.org/W2161202377","doi":"https://doi.org/10.1142/s0218127414501582","mag":"2161202377"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127414501582","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414501582","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/A5091408092","display_name":"Song-Mei Huan","orcid":"https://orcid.org/0000-0002-4574-6805"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Song-Mei Huan","raw_affiliation_strings":["School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049130877","display_name":"Xiao\u2010Song Yang","orcid":"https://orcid.org/0000-0002-4789-8335"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao-Song Yang","raw_affiliation_strings":["School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China","institution_ids":["https://openalex.org/I47720641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I47720641"],"apc_list":null,"apc_paid":null,"fwci":2.2302,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.87425069,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"24","issue":"12","first_page":"1450158","last_page":"1450158"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9980000257492065,"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":0.9962000250816345,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.8590013384819031},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.7453286647796631},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7393235564231873},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.7298797965049744},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6483049988746643},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.613937258720398},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5608571171760559},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5096402168273926},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5075193643569946},{"id":"https://openalex.org/keywords/heteroclinic-orbit","display_name":"Heteroclinic orbit","score":0.486417293548584},{"id":"https://openalex.org/keywords/topological-entropy","display_name":"Topological entropy","score":0.4734470546245575},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3795836567878723},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3206353783607483},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.31466618180274963},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.15651515126228333},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12722304463386536},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12365639209747314},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.07797542214393616}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.8590013384819031},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.7453286647796631},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7393235564231873},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.7298797965049744},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6483049988746643},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.613937258720398},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5608571171760559},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5096402168273926},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5075193643569946},{"id":"https://openalex.org/C184481792","wikidata":"https://www.wikidata.org/wiki/Q1992087","display_name":"Heteroclinic orbit","level":5,"score":0.486417293548584},{"id":"https://openalex.org/C2780350623","wikidata":"https://www.wikidata.org/wiki/Q3055355","display_name":"Topological entropy","level":2,"score":0.4734470546245575},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3795836567878723},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3206353783607483},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.31466618180274963},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.15651515126228333},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12722304463386536},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12365639209747314},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.07797542214393616},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127414501582","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414501582","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":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W126935648","https://openalex.org/W629413978","https://openalex.org/W1552277675","https://openalex.org/W1582770960","https://openalex.org/W1964873435","https://openalex.org/W1967520985","https://openalex.org/W1968084142","https://openalex.org/W1972807647","https://openalex.org/W1979881100","https://openalex.org/W1980228211","https://openalex.org/W1982233884","https://openalex.org/W1982805533","https://openalex.org/W1982943962","https://openalex.org/W2001362577","https://openalex.org/W2001555961","https://openalex.org/W2001944982","https://openalex.org/W2008393500","https://openalex.org/W2016035284","https://openalex.org/W2019383201","https://openalex.org/W2026267947","https://openalex.org/W2032086631","https://openalex.org/W2035651162","https://openalex.org/W2037024940","https://openalex.org/W2051631404","https://openalex.org/W2053658423","https://openalex.org/W2054208173","https://openalex.org/W2057325994","https://openalex.org/W2058345837","https://openalex.org/W2060720651","https://openalex.org/W2064867536","https://openalex.org/W2092046534","https://openalex.org/W2092680287","https://openalex.org/W2095978105","https://openalex.org/W2104953567","https://openalex.org/W2109088611","https://openalex.org/W2118384094","https://openalex.org/W2121642303","https://openalex.org/W2123042723","https://openalex.org/W2125605829","https://openalex.org/W2145346322","https://openalex.org/W2148863923","https://openalex.org/W2162820017","https://openalex.org/W2182274314","https://openalex.org/W2318352476","https://openalex.org/W2476121101","https://openalex.org/W3140194025","https://openalex.org/W4294967943"],"related_works":["https://openalex.org/W1497977526","https://openalex.org/W2008693397","https://openalex.org/W2151523878","https://openalex.org/W2018591892","https://openalex.org/W3192909774","https://openalex.org/W2009763826","https://openalex.org/W2157138821","https://openalex.org/W2350473807","https://openalex.org/W3142626835","https://openalex.org/W1999123830"],"abstract_inverted_index":{"For":[0],"a":[1,41],"class":[2],"of":[3,15,27,35],"4-dim":[4],"piecewise":[5],"linear":[6],"dynamical":[7],"systems,":[8],"some":[9],"sufficient":[10],"conditions":[11],"for":[12],"the":[13,25,36],"existence":[14,26],"homoclinic":[16],"orbit":[17],"and":[18],"chaotic":[19,28,48],"invariant":[20,29],"set":[21,30],"are":[22],"provided.":[23],"Especially,":[24],"is":[31,50],"proved":[32],"in":[33],"terms":[34],"constructed":[37],"Poincar\u00e9":[38],"map":[39],"with":[40,47],"topological":[42],"horseshoe.":[43],"A":[44],"numerical":[45],"example":[46],"attractor":[49],"provided":[51],"to":[52],"illustrate":[53],"our":[54],"main":[55],"result.":[56]},"counts_by_year":[{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
