{"id":"https://openalex.org/W3107596609","doi":"https://doi.org/10.1142/s0218127420502090","title":"Chaos Generated by a Class of 3D Three-Zone Piecewise Affine Systems with Coexisting Singular Cycles","display_name":"Chaos Generated by a Class of 3D Three-Zone Piecewise Affine Systems with Coexisting Singular Cycles","publication_year":2020,"publication_date":"2020-11-01","ids":{"openalex":"https://openalex.org/W3107596609","doi":"https://doi.org/10.1142/s0218127420502090","mag":"3107596609"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127420502090","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420502090","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/A5038706762","display_name":"Kai L\u00fc","orcid":"https://orcid.org/0000-0002-2010-1875"},"institutions":[{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kai Lu","raw_affiliation_strings":["School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, P. R. China","institution_ids":["https://openalex.org/I10535382"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028981621","display_name":"Wenjing Xu","orcid":"https://orcid.org/0000-0001-7071-6141"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenjing Xu","raw_affiliation_strings":["School of Science, Northwestern Polytechnical University, Xi\u2019an 710129, P. R. China","School of Science, Northwestern Polytechnical University, Xi'an 710129, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Northwestern Polytechnical University, Xi\u2019an 710129, P. R. China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"School of Science, Northwestern Polytechnical University, Xi'an 710129, P. R. China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080858709","display_name":"Qigui Yang","orcid":"https://orcid.org/0000-0002-3623-4947"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qigui Yang","raw_affiliation_strings":["School of Mathematics, South China University of Technology, Guangzhou 510000, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-3623-4947","affiliations":[{"raw_affiliation_string":"School of Mathematics, South China University of Technology, Guangzhou 510000, P. R. China","institution_ids":["https://openalex.org/I90610280"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080858709"],"corresponding_institution_ids":["https://openalex.org/I90610280"],"apc_list":null,"apc_paid":null,"fwci":1.1993,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.78725505,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"30","issue":"14","first_page":"2050209","last_page":"2050209"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9983999729156494,"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":0.9983999729156494,"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":0.9930999875068665,"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"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9781000018119812,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.9466276168823242},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7274259328842163},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6713792681694031},{"id":"https://openalex.org/keywords/heteroclinic-cycle","display_name":"Heteroclinic cycle","score":0.6491039395332336},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5522091388702393},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5506628155708313},{"id":"https://openalex.org/keywords/chaos","display_name":"CHAOS (operating system)","score":0.5183599591255188},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4777328670024872},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4439128041267395},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3740696310997009},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3670662045478821},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2895702123641968},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19585654139518738},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.18791472911834717},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07828620076179504},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.054463595151901245}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9466276168823242},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7274259328842163},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6713792681694031},{"id":"https://openalex.org/C142115181","wikidata":"https://www.wikidata.org/wiki/Q16948232","display_name":"Heteroclinic cycle","level":5,"score":0.6491039395332336},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5522091388702393},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5506628155708313},{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.5183599591255188},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4777328670024872},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4439128041267395},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3740696310997009},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3670662045478821},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2895702123641968},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19585654139518738},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.18791472911834717},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07828620076179504},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.054463595151901245},{"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127420502090","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420502090","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":[{"id":"https://openalex.org/G151301256","display_name":null,"funder_award_id":"2017A030312006","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G1775211613","display_name":null,"funder_award_id":"11671149","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5759887079","display_name":null,"funder_award_id":"201906290182","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1488048473","https://openalex.org/W1552277675","https://openalex.org/W1982233884","https://openalex.org/W1990853718","https://openalex.org/W2002782533","https://openalex.org/W2025459806","https://openalex.org/W2026653978","https://openalex.org/W2040704758","https://openalex.org/W2069436097","https://openalex.org/W2083531786","https://openalex.org/W2093351600","https://openalex.org/W2150927600","https://openalex.org/W2293773556","https://openalex.org/W2385406935","https://openalex.org/W2476121101","https://openalex.org/W2502596622","https://openalex.org/W2530719749","https://openalex.org/W2544167369","https://openalex.org/W2586746011","https://openalex.org/W2607357886","https://openalex.org/W2615011810","https://openalex.org/W2761348234","https://openalex.org/W2765499120","https://openalex.org/W2779306122","https://openalex.org/W2794646606","https://openalex.org/W2803715516","https://openalex.org/W2806531778","https://openalex.org/W2848018424","https://openalex.org/W2883016651","https://openalex.org/W2884884884","https://openalex.org/W2914536443","https://openalex.org/W2941630335","https://openalex.org/W2944418872","https://openalex.org/W2979320982","https://openalex.org/W2991150739","https://openalex.org/W2991215965","https://openalex.org/W3011950536","https://openalex.org/W3100468056","https://openalex.org/W3103998734","https://openalex.org/W4238307931","https://openalex.org/W4310301864"],"related_works":["https://openalex.org/W4226395615","https://openalex.org/W822127303","https://openalex.org/W2157317278","https://openalex.org/W3115753373","https://openalex.org/W2008693397","https://openalex.org/W1497977526","https://openalex.org/W2046598636","https://openalex.org/W2049546479","https://openalex.org/W1619079151","https://openalex.org/W2051721023"],"abstract_inverted_index":{"It":[0,64],"is":[1],"a":[2,54,78],"significant":[3],"and":[4,17,20,49,76],"challenging":[5],"task":[6],"to":[7,41,96],"detect":[8],"both":[9],"the":[10,24,31,44,67,83,88,98],"coexistence":[11,25,45],"of":[12,46,50,56,70],"singular":[13],"cycles,":[14,19],"mainly":[15],"homoclinic":[16,47],"heteroclinic":[18,51],"chaos":[21,71],"induced":[22],"by":[23,81],"in":[26,53],"nonsmooth":[27],"systems.":[28],"By":[29],"analyzing":[30,82],"dynamical":[32],"behaviors":[33],"on":[34],"manifolds,":[35],"this":[36],"paper":[37],"proposes":[38],"some":[39],"criteria":[40],"accurately":[42],"locate":[43],"cycles":[48,52],"class":[55],"three-dimensional":[57],"(3D)":[58],"piecewise":[59],"affine":[60],"systems":[61],"(PASs),":[62],"respectively.":[63],"further":[65],"establishes":[66],"existence":[68],"conditions":[69],"arising":[72],"from":[73],"such":[74],"coexistence,":[75],"presents":[77],"mathematical":[79],"proof":[80],"constructed":[84],"Poincar\u00e9":[85],"map.":[86],"Finally,":[87],"simulations":[89],"for":[90],"two":[91],"numerical":[92],"examples":[93],"are":[94],"provided":[95],"validate":[97],"established":[99],"results.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}