{"id":"https://openalex.org/W2898544341","doi":"https://doi.org/10.1142/s0218127418300380","title":"Exploring the Dynamics of a Third-Order Phase-Locked Loop Model","display_name":"Exploring the Dynamics of a Third-Order Phase-Locked Loop Model","publication_year":2018,"publication_date":"2018-10-01","ids":{"openalex":"https://openalex.org/W2898544341","doi":"https://doi.org/10.1142/s0218127418300380","mag":"2898544341"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127418300380","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127418300380","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":true,"oa_status":"green","oa_url":"https://repositorio.udesc.br/handle/UDESC/6098","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018328761","display_name":"Cesar Manchein","orcid":"https://orcid.org/0000-0001-8786-3893"},"institutions":[{"id":"https://openalex.org/I164790352","display_name":"Universidade do Estado de Santa Catarina","ror":"https://ror.org/03ztsbk67","country_code":"BR","type":"education","lineage":["https://openalex.org/I164790352"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Cesar Manchein","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade Do Estado de Santa Catarina, Joinville, SC, 89219-710, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Do Estado de Santa Catarina, Joinville, SC, 89219-710, Brazil","institution_ids":["https://openalex.org/I164790352"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082376093","display_name":"Holokx A. Albuquerque","orcid":"https://orcid.org/0000-0001-8133-7606"},"institutions":[{"id":"https://openalex.org/I164790352","display_name":"Universidade do Estado de Santa Catarina","ror":"https://ror.org/03ztsbk67","country_code":"BR","type":"education","lineage":["https://openalex.org/I164790352"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Holokx A. Albuquerque","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade Do Estado de Santa Catarina, Joinville, SC, 89219-710, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Do Estado de Santa Catarina, Joinville, SC, 89219-710, Brazil","institution_ids":["https://openalex.org/I164790352"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003957478","display_name":"Luis Fernando Mello","orcid":"https://orcid.org/0000-0002-4989-3052"},"institutions":[{"id":"https://openalex.org/I8165072","display_name":"Universidade Federal de Itajub\u00e1","ror":"https://ror.org/00235nr42","country_code":"BR","type":"education","lineage":["https://openalex.org/I8165072"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Luis Fernando Mello","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, 37500-903 Itajub\u00e1, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-4989-3052","affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Computa\u00e7\u00e3o, Universidade Federal de Itajub\u00e1, 37500-903 Itajub\u00e1, Brazil","institution_ids":["https://openalex.org/I8165072"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018328761"],"corresponding_institution_ids":["https://openalex.org/I164790352"],"apc_list":null,"apc_paid":null,"fwci":0.7681,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.72252024,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"28","issue":"11","first_page":"1830038","last_page":"1830038"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9990000128746033,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9926000237464905,"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/parameter-space","display_name":"Parameter space","score":0.7657437324523926},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.7000402212142944},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.682440459728241},{"id":"https://openalex.org/keywords/phase-plane","display_name":"Phase plane","score":0.6371064186096191},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5695807337760925},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5130668878555298},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.5026180744171143},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4949738383293152},{"id":"https://openalex.org/keywords/phase-locked-loop","display_name":"Phase-locked loop","score":0.4897339344024658},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.44507819414138794},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4417263865470886},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4221288859844208},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.4190469980239868},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.41161590814590454},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3404879868030548},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28499287366867065},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.27102404832839966},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.15211758017539978},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12137386202812195},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08734485507011414}],"concepts":[{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.7657437324523926},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.7000402212142944},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.682440459728241},{"id":"https://openalex.org/C157626765","wikidata":"https://www.wikidata.org/wiki/Q2088081","display_name":"Phase plane","level":3,"score":0.6371064186096191},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5695807337760925},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5130668878555298},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.5026180744171143},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4949738383293152},{"id":"https://openalex.org/C12707504","wikidata":"https://www.wikidata.org/wiki/Q52637","display_name":"Phase-locked loop","level":3,"score":0.4897339344024658},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.44507819414138794},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4417263865470886},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4221288859844208},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4190469980239868},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.41161590814590454},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3404879868030548},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28499287366867065},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27102404832839966},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.15211758017539978},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12137386202812195},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08734485507011414},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127418300380","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127418300380","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"},{"id":"pmh:oai:repositorio.udesc.br:UDESC/6098","is_oa":true,"landing_page_url":"https://repositorio.udesc.br/handle/UDESC/6098","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"instacron:UDESC","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:repositorio.udesc.br:UDESC/6098","is_oa":true,"landing_page_url":"https://repositorio.udesc.br/handle/UDESC/6098","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"instacron:UDESC","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5067002747","display_name":null,"funder_award_id":"88881.119020/2016-01","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"}],"funders":[{"id":"https://openalex.org/F4320310522","display_name":"Texas Christian University","ror":"https://ror.org/054b0b564"},{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320323349","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa e Inova\u00e7\u00e3o do Estado de Santa Catarina","ror":"https://ror.org/0503xdx77"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1818408676","https://openalex.org/W1964976653","https://openalex.org/W1981640378","https://openalex.org/W1985400384","https://openalex.org/W1988855581","https://openalex.org/W1991829357","https://openalex.org/W1994101970","https://openalex.org/W1998709706","https://openalex.org/W2003762982","https://openalex.org/W2007305479","https://openalex.org/W2021200242","https://openalex.org/W2030497467","https://openalex.org/W2050887107","https://openalex.org/W2060665231","https://openalex.org/W2061212285","https://openalex.org/W2066205711","https://openalex.org/W2072998188","https://openalex.org/W2089415436","https://openalex.org/W2090062370","https://openalex.org/W2092361954","https://openalex.org/W2114661612","https://openalex.org/W2120949553","https://openalex.org/W2152254020","https://openalex.org/W2154331325","https://openalex.org/W2199804412","https://openalex.org/W2292587277","https://openalex.org/W2338889714","https://openalex.org/W2412276656","https://openalex.org/W2509686129","https://openalex.org/W2593614124","https://openalex.org/W2736683621","https://openalex.org/W2769002207","https://openalex.org/W3098158272","https://openalex.org/W3100607886","https://openalex.org/W3101726342","https://openalex.org/W4206651839","https://openalex.org/W4237591246","https://openalex.org/W4247794243"],"related_works":["https://openalex.org/W4389303746","https://openalex.org/W2115371521","https://openalex.org/W2562509657","https://openalex.org/W1168863844","https://openalex.org/W2618142611","https://openalex.org/W4280554182","https://openalex.org/W2144002436","https://openalex.org/W2171160532","https://openalex.org/W2394617381","https://openalex.org/W2095454919"],"abstract_inverted_index":{"We":[0,151],"study":[1],"the":[2,6,42,52,63,79,117,130,154,158,184],"dynamics":[3,133],"and":[4,36,68,87,144,170],"characterize":[5],"bifurcation":[7,43],"structure":[8],"of":[9,28,51,119],"a":[10,17,112,164],"phase-locked":[11],"loop":[12],"(PLL)":[13],"device":[14],"modeled":[15],"by":[16,111],"third-order":[18],"autonomous":[19],"differential":[20],"equation":[21],"with":[22],"sinusoidal":[23],"phase":[24],"detector.":[25],"The":[26],"development":[27],"this":[29],"work":[30],"was":[31],"performed":[32],"using":[33,57],"rigorous":[34],"analysis":[35,41],"numerical":[37,59,145],"experiments.":[38],"Through":[39],"theoretical":[40,143],"structures":[44,100],"related":[45],"to":[46,167,182],"two":[47,84,89],"fundamental":[48],"equilibrium":[49],"points":[50],"system":[53],"are":[54,95,109],"described.":[55],"By":[56],"extensive":[58],"experiments":[60],"we":[61],"investigate":[62],"intricate":[64],"organization":[65],"between":[66],"periodic":[67,99],"chaotic":[69,126,185],"domains":[70],"in":[71,104],"parameter":[72,76,105,138,159],"space":[73],"(named":[74],"here":[75],"plane":[77,160],"as":[78],"PLL":[80,174],"model":[81],"has":[82],"only":[83],"control":[85,137],"parameters)":[86],"obtain":[88],"following":[90],"remarkable":[91],"findings:":[92],"(i)":[93],"there":[94],"self-organized":[96],"generic":[97],"stable":[98],"along":[101],"specific":[102],"directions":[103],"plane,":[106],"whose":[107],"periods":[108],"defined":[110],"mathematical":[113],"rule":[114],"and,":[115],"(ii)":[116],"existence":[118],"transient":[120],"chaos":[121],"phenomenon":[122],"responsible":[123],"for":[124,134,177],"long":[125],"temporal":[127],"evolution":[128],"preceding":[129],"asymptotic":[131],"(periodic)":[132],"some":[135],"particular":[136],"pairs":[139],"is":[140],"characterized.":[141],"Our":[142],"results":[146],"present":[147,155],"an":[148],"astonishing":[149],"concordance.":[150],"believe":[152],"that":[153],"study,":[156],"specially":[157],"analysis,":[161],"may":[162],"have":[163],"great":[165],"importance":[166],"experimental":[168],"studies":[169],"general":[171],"applications":[172],"involving":[173],"devices":[175],"when,":[176],"example,":[178],"one":[179],"would":[180],"like":[181],"avoid":[183],"regimes.":[186]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}