{"id":"https://openalex.org/W2010379616","doi":"https://doi.org/10.1109/tac.2012.2228053","title":"Synchronization of Coupled Discrete-Time Harmonic Oscillators With Rational Frequency","display_name":"Synchronization of Coupled Discrete-Time Harmonic Oscillators With Rational Frequency","publication_year":2012,"publication_date":"2012-11-16","ids":{"openalex":"https://openalex.org/W2010379616","doi":"https://doi.org/10.1109/tac.2012.2228053","mag":"2010379616"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2012.2228053","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2228053","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5103153702","display_name":"Xingping Wang","orcid":"https://orcid.org/0000-0003-2311-0889"},"institutions":[{"id":"https://openalex.org/I4210162215","display_name":"Naval Aeronautical and Astronautical University","ror":"https://ror.org/02j2yhq26","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210162215"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xingping Wang","raw_affiliation_strings":["Naval Aeronautical and Astronautical University, Institute of Systems Science and Mathematics, Yantai, PR, China","Inst. of Syst. Sci. & Math., Naval Aeronaut. & Astronaut. Univ., Yantai, China"],"affiliations":[{"raw_affiliation_string":"Naval Aeronautical and Astronautical University, Institute of Systems Science and Mathematics, Yantai, PR, China","institution_ids":["https://openalex.org/I4210162215"]},{"raw_affiliation_string":"Inst. of Syst. Sci. & Math., Naval Aeronaut. & Astronaut. Univ., Yantai, China","institution_ids":["https://openalex.org/I4210162215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102049960","display_name":"Zhaolin Cheng","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhaolin Cheng","raw_affiliation_strings":["Shandong University, School of Mathematics and System Sciences, Jinan, PR, China","[Sch. of Math. & Syst. Sci., Shandong Univ., Jinan, China]"],"affiliations":[{"raw_affiliation_string":"Shandong University, School of Mathematics and System Sciences, Jinan, PR, China","institution_ids":["https://openalex.org/I154099455"]},{"raw_affiliation_string":"[Sch. of Math. & Syst. Sci., Shandong Univ., Jinan, China]","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103153702"],"corresponding_institution_ids":["https://openalex.org/I4210162215"],"apc_list":null,"apc_paid":null,"fwci":1.0638,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.77715877,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"58","issue":"6","first_page":"1573","last_page":"1579"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998999834060669,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9997000098228455,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9995999932289124,"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/topology","display_name":"Topology (electrical circuits)","score":0.8121848106384277},{"id":"https://openalex.org/keywords/synchronizing","display_name":"Synchronizing","score":0.7673896551132202},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.746524453163147},{"id":"https://openalex.org/keywords/synchronization-networks","display_name":"Synchronization networks","score":0.6833740472793579},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5600247383117676},{"id":"https://openalex.org/keywords/product-topology","display_name":"Product topology","score":0.5465093851089478},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.494431734085083},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4870634377002716},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.45277315378189087},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3612448573112488},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.158888041973114},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09147018194198608},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.069129079580307}],"concepts":[{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.8121848106384277},{"id":"https://openalex.org/C162932704","wikidata":"https://www.wikidata.org/wiki/Q1058791","display_name":"Synchronizing","level":3,"score":0.7673896551132202},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.746524453163147},{"id":"https://openalex.org/C111097370","wikidata":"https://www.wikidata.org/wiki/Q10969923","display_name":"Synchronization networks","level":4,"score":0.6833740472793579},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5600247383117676},{"id":"https://openalex.org/C123222754","wikidata":"https://www.wikidata.org/wiki/Q1070472","display_name":"Product topology","level":2,"score":0.5465093851089478},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.494431734085083},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4870634377002716},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.45277315378189087},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3612448573112488},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.158888041973114},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09147018194198608},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.069129079580307},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2012.2228053","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2228053","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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":25,"referenced_works":["https://openalex.org/W111157985","https://openalex.org/W1488435683","https://openalex.org/W1614210333","https://openalex.org/W1630241696","https://openalex.org/W1904869745","https://openalex.org/W1988095001","https://openalex.org/W2038158348","https://openalex.org/W2093627340","https://openalex.org/W2098974515","https://openalex.org/W2099175737","https://openalex.org/W2101426918","https://openalex.org/W2114482313","https://openalex.org/W2125668987","https://openalex.org/W2128928412","https://openalex.org/W2140380216","https://openalex.org/W2141070320","https://openalex.org/W2154953441","https://openalex.org/W2160549945","https://openalex.org/W2160932744","https://openalex.org/W2164761327","https://openalex.org/W2165744313","https://openalex.org/W2172498959","https://openalex.org/W2316342622","https://openalex.org/W2526182054","https://openalex.org/W4238591275"],"related_works":["https://openalex.org/W2116519977","https://openalex.org/W1981446230","https://openalex.org/W2365128652","https://openalex.org/W2356659732","https://openalex.org/W2315567295","https://openalex.org/W1581301957","https://openalex.org/W3202423486","https://openalex.org/W2071365237","https://openalex.org/W2356421920","https://openalex.org/W2114908129"],"abstract_inverted_index":{"This":[0],"technical":[1],"note":[2],"studies":[3],"the":[4,25,30,40,54,67,69,109,120,123],"synchronization":[5,70,106],"of":[6,20,33,71,80,97,101,122],"coupled":[7,72,110],"discrete-time":[8],"harmonic":[9],"oscillators":[10,73],"with":[11],"rational":[12],"frequency":[13,45],"under":[14],"switching":[15],"topology.":[16],"The":[17],"remarkable":[18],"feature":[19],"this":[21],"problem":[22],"is":[23,74,116],"that":[24,27,49],"conditions":[26],"merely":[28],"involve":[29],"connectivity":[31],"structure":[32],"topology":[34,47,55],"does":[35],"not":[36],"suffice":[37],"for":[38,108],"synchronizing":[39],"oscillators.":[41,111],"We":[42],"propose":[43],"a":[44,91,98,105,113],"dependent":[46],"condition":[48],"indicates":[50],"in":[51],"what":[52],"way":[53],"switches,":[56],"and":[57],"introduce":[58],"firmly":[59],"nonexpansive":[60],"mapping":[61],"(FNM)":[62],"from":[63],"functional":[64],"analysis.":[65],"Under":[66],"condition,":[68],"related":[75],"to":[76,118],"an":[77],"infinite":[78,95],"product":[79,96],"FNMs,":[81],"which":[82],"share":[83],"only":[84],"one":[85],"zero":[86],"common":[87],"fixed":[88],"point.":[89],"By":[90],"convergence":[92],"result":[93,107],"on":[94],"finite":[99],"number":[100],"FNM,":[102],"we":[103],"present":[104],"Finally,":[112],"simulation":[114],"example":[115],"given":[117],"illustrate":[119],"effectiveness":[121],"result.":[124]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}