{"id":"https://openalex.org/W2924620096","doi":"https://doi.org/10.1109/tcsi.2019.2899879","title":"Bipartite Synchronization and Convergence Analysis for Network of Harmonic Oscillator Systems With Signed Graph and Time Delay","display_name":"Bipartite Synchronization and Convergence Analysis for Network of Harmonic Oscillator Systems With Signed Graph and Time Delay","publication_year":2019,"publication_date":"2019-03-19","ids":{"openalex":"https://openalex.org/W2924620096","doi":"https://doi.org/10.1109/tcsi.2019.2899879","mag":"2924620096"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2019.2899879","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2019.2899879","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078689543","display_name":"Qiang Song","orcid":"https://orcid.org/0000-0001-9635-1355"},"institutions":[{"id":"https://openalex.org/I199305430","display_name":"Nantong University","ror":"https://ror.org/02afcvw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I199305430"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qiang Song","raw_affiliation_strings":["School of Electrical Engineering, Institute of Systems Science, Nantong University, Nantong, China"],"raw_orcid":"https://orcid.org/0000-0001-9635-1355","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Institute of Systems Science, Nantong University, Nantong, China","institution_ids":["https://openalex.org/I199305430"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100398912","display_name":"Guoping L\u00fc","orcid":"https://orcid.org/0000-0002-6815-4554"},"institutions":[{"id":"https://openalex.org/I199305430","display_name":"Nantong University","ror":"https://ror.org/02afcvw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I199305430"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guoping Lu","raw_affiliation_strings":["School of Electrical Engineering, Institute of Systems Science, Nantong University, Nantong, China"],"raw_orcid":"https://orcid.org/0000-0002-6815-4554","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Institute of Systems Science, Nantong University, Nantong, China","institution_ids":["https://openalex.org/I199305430"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040088510","display_name":"Guanghui Wen","orcid":"https://orcid.org/0000-0003-0070-8597"},"institutions":[{"id":"https://openalex.org/I82951845","display_name":"RMIT University","ror":"https://ror.org/04ttjf776","country_code":"AU","type":"education","lineage":["https://openalex.org/I82951845"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Guanghui Wen","raw_affiliation_strings":["School of Engineering, RMIT University, Melbourne, VIC, Australia"],"raw_orcid":"https://orcid.org/0000-0003-0070-8597","affiliations":[{"raw_affiliation_string":"School of Engineering, RMIT University, Melbourne, VIC, Australia","institution_ids":["https://openalex.org/I82951845"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017808266","display_name":"Jinde Cao","orcid":"https://orcid.org/0000-0003-3133-7119"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinde Cao","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-3133-7119","affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100453036","display_name":"Fang Liu","orcid":"https://orcid.org/0000-0002-0430-4381"},"institutions":[{"id":"https://openalex.org/I4210131125","display_name":"Huanghuai University","ror":"https://ror.org/02k92ks68","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210131125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fang Liu","raw_affiliation_strings":["Henan International Joint Laboratory of Behavior Optimization Control for Smart Robots, School of Information Engineering, Huanghuai University, Zhumadian, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Henan International Joint Laboratory of Behavior Optimization Control for Smart Robots, School of Information Engineering, Huanghuai University, Zhumadian, China","institution_ids":["https://openalex.org/I4210131125"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5078689543"],"corresponding_institution_ids":["https://openalex.org/I199305430"],"apc_list":null,"apc_paid":null,"fwci":7.4285,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.9745679,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"66","issue":"7","first_page":"2723","last_page":"2734"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","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"}},{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9983000159263611,"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/bipartite-graph","display_name":"Bipartite graph","score":0.6783192157745361},{"id":"https://openalex.org/keywords/signed-graph","display_name":"Signed graph","score":0.6616731286048889},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.6529881954193115},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.640536367893219},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5955421924591064},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5760550498962402},{"id":"https://openalex.org/keywords/synchronization-networks","display_name":"Synchronization networks","score":0.48692405223846436},{"id":"https://openalex.org/keywords/harmonic-oscillator","display_name":"Harmonic oscillator","score":0.4371947646141052},{"id":"https://openalex.org/keywords/algebraic-connectivity","display_name":"Algebraic connectivity","score":0.4354058504104614},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.43302640318870544},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.4311069846153259},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.39496278762817383},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3946501612663269},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3226093649864197},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23523807525634766},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2213086187839508}],"concepts":[{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6783192157745361},{"id":"https://openalex.org/C2779773260","wikidata":"https://www.wikidata.org/wiki/Q11246292","display_name":"Signed graph","level":3,"score":0.6616731286048889},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.6529881954193115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.640536367893219},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5955421924591064},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5760550498962402},{"id":"https://openalex.org/C111097370","wikidata":"https://www.wikidata.org/wiki/Q10969923","display_name":"Synchronization networks","level":4,"score":0.48692405223846436},{"id":"https://openalex.org/C40934718","wikidata":"https://www.wikidata.org/wiki/Q190070","display_name":"Harmonic oscillator","level":2,"score":0.4371947646141052},{"id":"https://openalex.org/C7948225","wikidata":"https://www.wikidata.org/wiki/Q4723998","display_name":"Algebraic connectivity","level":4,"score":0.4354058504104614},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43302640318870544},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.4311069846153259},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.39496278762817383},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3946501612663269},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3226093649864197},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23523807525634766},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2213086187839508},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tcsi.2019.2899879","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2019.2899879","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","raw_type":"journal-article"},{"id":"pmh:oai:alma.61RMIT_INST:11247322630001341","is_oa":false,"landing_page_url":"https://doi.org/10.1109/TCSI.2019.2899879","pdf_url":null,"source":{"id":"https://openalex.org/S4306402074","display_name":"RMIT Research Repository (RMIT University Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I82951845","host_organization_name":"RMIT University","host_organization_lineage":["https://openalex.org/I82951845"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/27480690","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/27480690","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1888779397","display_name":null,"funder_award_id":"61573201","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1922400327","display_name":null,"funder_award_id":"182102410067","funder_id":"https://openalex.org/F4320323845","funder_display_name":"Natural Science Foundation of Henan Province"},{"id":"https://openalex.org/G2169118838","display_name":null,"funder_award_id":"172102210212","funder_id":"https://openalex.org/F4320323845","funder_display_name":"Natural Science Foundation of Henan Province"},{"id":"https://openalex.org/G3083055430","display_name":null,"funder_award_id":"182102310625","funder_id":"https://openalex.org/F4320323845","funder_display_name":"Natural Science Foundation of Henan Province"},{"id":"https://openalex.org/G4585534567","display_name":null,"funder_award_id":"61833005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4741143070","display_name":null,"funder_award_id":"61673104","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8363503722","display_name":null,"funder_award_id":"DE180101268","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G8929467201","display_name":null,"funder_award_id":"61773155","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323845","display_name":"Natural Science Foundation of Henan Province","ror":null},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W261461018","https://openalex.org/W941796482","https://openalex.org/W950821216","https://openalex.org/W1509185796","https://openalex.org/W1533970237","https://openalex.org/W1630241696","https://openalex.org/W1967509640","https://openalex.org/W1979472936","https://openalex.org/W1988095001","https://openalex.org/W2013925402","https://openalex.org/W2032858129","https://openalex.org/W2038561575","https://openalex.org/W2061378078","https://openalex.org/W2061901927","https://openalex.org/W2072694395","https://openalex.org/W2075175322","https://openalex.org/W2077616895","https://openalex.org/W2083759184","https://openalex.org/W2083787309","https://openalex.org/W2099175737","https://openalex.org/W2100757047","https://openalex.org/W2101426918","https://openalex.org/W2107396783","https://openalex.org/W2128226330","https://openalex.org/W2143843955","https://openalex.org/W2150495686","https://openalex.org/W2160549945","https://openalex.org/W2268931211","https://openalex.org/W2286576976","https://openalex.org/W2287281329","https://openalex.org/W2343734929","https://openalex.org/W2405538611","https://openalex.org/W2460207227","https://openalex.org/W2473140891","https://openalex.org/W2537120359","https://openalex.org/W2547596511","https://openalex.org/W2588573379","https://openalex.org/W2592442839","https://openalex.org/W2596337367","https://openalex.org/W2609230518","https://openalex.org/W2625711953","https://openalex.org/W2765956954","https://openalex.org/W2770416798","https://openalex.org/W2783148609","https://openalex.org/W2790967000","https://openalex.org/W2886232339","https://openalex.org/W2899510315","https://openalex.org/W3101538765","https://openalex.org/W4285719527","https://openalex.org/W6739083902"],"related_works":["https://openalex.org/W4205812024","https://openalex.org/W2290309487","https://openalex.org/W2806168309","https://openalex.org/W2998654349","https://openalex.org/W2994336805","https://openalex.org/W2679948989","https://openalex.org/W4214697242","https://openalex.org/W4315628389","https://openalex.org/W2014217492","https://openalex.org/W2350484011"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"the":[3,31,46,65,91,96,99,109,115,132,137,144,149,155],"distributed":[4],"control":[5],"problem":[6],"for":[7],"a":[8,23,119,124],"network":[9,49,110],"of":[10,34,78,148],"harmonic":[11,37],"oscillator":[12],"systems":[13],"with":[14,143],"delayed":[15],"velocity":[16],"coupling":[17,79],"and":[18,60,73,81,139],"signed":[19,48,92,100,150],"graph":[20,67,101],"topology":[21],"containing":[22],"directed":[24],"spanning":[25],"tree.":[26],"In":[27,122],"sharp":[28],"contrast":[29],"to":[30,86,114,118,129],"dynamical":[32],"behaviors":[33],"traditional":[35],"coupled":[36],"oscillators":[38],"over":[39],"unsigned":[40],"graphs,":[41],"it":[42,105],"is":[43,68,102,106,127,158],"found":[44],"that":[45,98,108],"considered":[47],"can":[50],"exhibit":[51],"some":[52,71,161],"more":[53],"interesting":[54],"behaviors,":[55],"including":[56],"bipartite":[57,88],"synchronization,":[58],"stabilization,":[59],"convergent":[61],"behavior.":[62],"First,":[63],"when":[64],"underlying":[66],"structurally":[69,103],"balanced,":[70],"necessary":[72],"sufficient":[74],"conditions":[75],"in":[76,90],"terms":[77],"strength":[80],"time":[82],"delay":[83],"are":[84],"established":[85],"achieve":[87],"synchronization":[89],"network.":[93],"Then,":[94],"under":[95],"assumption":[97],"unbalanced,":[104],"shown":[107],"state":[111],"converges":[112],"either":[113],"origin":[116],"or":[117],"nontrivial":[120],"trajectory.":[121],"particular,":[123],"novel":[125],"approach":[126],"developed":[128],"explicitly":[130],"determine":[131],"converged":[133],"trajectory":[134],"based":[135],"on":[136],"left":[138],"right":[140],"eigenvectors":[141],"associated":[142],"simple":[145],"zero":[146],"eigenvalue":[147],"graph's":[151],"Laplacian":[152],"matrix.":[153],"Finally,":[154],"theoretical":[156],"analysis":[157],"illustrated":[159],"by":[160],"numerical":[162],"examples.":[163]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":3}],"updated_date":"2026-04-24T08:23:43.765630","created_date":"2025-10-10T00:00:00"}
