{"id":"https://openalex.org/W3133691361","doi":"https://doi.org/10.1142/s0218127421500322","title":"On Periodic Solutions of a Time-Delayed, Discontinuous System with a Hyperbola Switching Control Law","display_name":"On Periodic Solutions of a Time-Delayed, Discontinuous System with a Hyperbola Switching Control Law","publication_year":2021,"publication_date":"2021-02-01","ids":{"openalex":"https://openalex.org/W3133691361","doi":"https://doi.org/10.1142/s0218127421500322","mag":"3133691361"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127421500322","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421500322","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/A5101961040","display_name":"Liping Li","orcid":"https://orcid.org/0000-0002-8400-3959"},"institutions":[{"id":"https://openalex.org/I3018263800","display_name":"Huzhou University","ror":"https://ror.org/04mvpxy20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3018263800"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liping Li","raw_affiliation_strings":["Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, P. R. China","institution_ids":["https://openalex.org/I3018263800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076270155","display_name":"Albert C. J. Luo","orcid":"https://orcid.org/0000-0001-8208-6108"},"institutions":[{"id":"https://openalex.org/I87547150","display_name":"Southern Illinois University Edwardsville","ror":"https://ror.org/04cqs5j56","country_code":"US","type":"education","lineage":["https://openalex.org/I2801502357","https://openalex.org/I87547150"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Albert C. J. Luo","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, IL 62026-1805, USA"],"raw_orcid":"https://orcid.org/0000-0001-8208-6108","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, IL 62026-1805, USA","institution_ids":["https://openalex.org/I87547150"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076270155"],"corresponding_institution_ids":["https://openalex.org/I87547150"],"apc_list":null,"apc_paid":null,"fwci":1.6891,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.82600494,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"31","issue":"02","first_page":"2150032","last_page":"2150032"},"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":0.9997000098228455,"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":0.9997000098228455,"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":0.9973000288009644,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9828000068664551,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6900189518928528},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6286977529525757},{"id":"https://openalex.org/keywords/hyperbola","display_name":"Hyperbola","score":0.5723183155059814},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5487998127937317},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.46961671113967896},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.463024765253067},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45850756764411926},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.44123610854148865},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.20558014512062073},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2044019103050232},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1811378300189972},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17977765202522278}],"concepts":[{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6900189518928528},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6286977529525757},{"id":"https://openalex.org/C145050668","wikidata":"https://www.wikidata.org/wiki/Q165301","display_name":"Hyperbola","level":2,"score":0.5723183155059814},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5487998127937317},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.46961671113967896},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.463024765253067},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45850756764411926},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.44123610854148865},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.20558014512062073},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2044019103050232},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1811378300189972},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17977765202522278},{"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/s0218127421500322","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127421500322","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":[{"score":0.7799999713897705,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G662644295","display_name":null,"funder_award_id":"61473332","funder_id":"https://openalex.org/F4320315254","funder_display_name":"Innovative Research Group Project of the National Natural Science Foundation of China"},{"id":"https://openalex.org/G8798792812","display_name":null,"funder_award_id":"11571106","funder_id":"https://openalex.org/F4320315254","funder_display_name":"Innovative Research Group Project of the National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320315254","display_name":"Innovative Research Group Project of the National Natural Science Foundation of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1269033259","https://openalex.org/W1542389835","https://openalex.org/W1552094772","https://openalex.org/W1593811304","https://openalex.org/W1964094519","https://openalex.org/W1973538380","https://openalex.org/W1990042683","https://openalex.org/W1995439076","https://openalex.org/W1995524463","https://openalex.org/W2013256170","https://openalex.org/W2016609461","https://openalex.org/W2050416508","https://openalex.org/W2072652000","https://openalex.org/W2078205729","https://openalex.org/W2087066713","https://openalex.org/W2088458865","https://openalex.org/W2108996927","https://openalex.org/W2126543121","https://openalex.org/W2128449512","https://openalex.org/W2155124529","https://openalex.org/W2159590762","https://openalex.org/W2484469314","https://openalex.org/W2564554664","https://openalex.org/W2883595324","https://openalex.org/W3037567238","https://openalex.org/W4206225272","https://openalex.org/W4293078920","https://openalex.org/W4300220933"],"related_works":["https://openalex.org/W4250831671","https://openalex.org/W2230606337","https://openalex.org/W2089869689","https://openalex.org/W4388681848","https://openalex.org/W2078952919","https://openalex.org/W2945666329","https://openalex.org/W2617651062","https://openalex.org/W2330535098","https://openalex.org/W2377513064","https://openalex.org/W2952544653"],"abstract_inverted_index":{"In":[0],"this":[1,43],"paper,":[2],"the":[3,21,26,36,104,115,129,133,141,146,171],"existence":[4],"of":[5,8,32,52,61,106,126],"periodic":[6,107,143],"motions":[7,83,108,127],"a":[9,14,33,65,86],"discontinuous":[10,45,88,135,148,160,173],"delayed":[11],"system":[12,89],"with":[13,109],"hyperbolic":[15],"switching":[16,37,80,116,130],"boundary":[17,38,131],"is":[18],"investigated.":[19],"From":[20],"delay-related":[22],"[Formula:":[23],"see":[24],"text]-function,":[25],"crossing,":[27],"sliding":[28,112],"and":[29,58,78,92,137,163],"grazing":[30],"conditions":[31,125],"flow":[34],"to":[35,122,139,169],"are":[39,49,71,90,101],"first":[40],"developed.":[41],"For":[42],"time-delayed":[44,134,147,159,172],"dynamical":[46,161,174],"system,":[47],"there":[48],"17":[50],"classes":[51],"generic":[53,69],"mappings":[54,63,70],"in":[55,64,75,84,132,158],"phase":[56],"plane":[57],"66":[59],"types":[60],"local":[62],"delay":[66,87],"duration.":[67],"The":[68],"determined":[72],"by":[73],"subsystems":[74],"three":[76],"domains":[77],"two":[79],"boundaries.":[81],"Periodic":[82],"such":[85,167],"constructed":[91],"predicted":[93],"analytically":[94],"from":[95],"specific":[96,142],"mapping":[97],"structures.":[98],"Three":[99],"examples":[100],"given":[102],"for":[103,145],"illustration":[105],"or":[110],"without":[111],"motion":[113],"on":[114],"boundary.":[117],"This":[118,150],"paper":[119],"shows":[120],"how":[121,138],"develop":[123],"switchability":[124],"at":[128],"systems":[136],"construct":[140],"solutions":[144],"systems.":[149,175],"study":[151],"can":[152,165],"help":[153],"us":[154],"understand":[155],"complex":[156],"dynamics":[157],"systems,":[162],"one":[164],"use":[166],"analysis":[168],"control":[170]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
