{"id":"https://openalex.org/W3198038704","doi":"https://doi.org/10.1109/tcsii.2021.3108116","title":"Cluster Synchronization for Multi-Weighted and Directed Complex Networks via Pinning Control","display_name":"Cluster Synchronization for Multi-Weighted and Directed Complex Networks via Pinning Control","publication_year":2021,"publication_date":"2021-08-27","ids":{"openalex":"https://openalex.org/W3198038704","doi":"https://doi.org/10.1109/tcsii.2021.3108116","mag":"3198038704"},"language":"en","primary_location":{"id":"doi:10.1109/tcsii.2021.3108116","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2021.3108116","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 II: Express Briefs","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/A5027452592","display_name":"Jueqi Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jueqi Wang","raw_affiliation_strings":["Department of Computer Science and Technology and the Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology and the Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051541488","display_name":"Xiwei Liu","orcid":"https://orcid.org/0000-0003-3165-443X"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiwei Liu","raw_affiliation_strings":["Department of Computer Science and Technology and the Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology and the Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027452592"],"corresponding_institution_ids":["https://openalex.org/I116953780"],"apc_list":null,"apc_paid":null,"fwci":6.2124,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.9660301,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":"69","issue":"3","first_page":"1347","last_page":"1351"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"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":1.0,"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":0.9973000288009644,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9912999868392944,"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7477854490280151},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.6860663294792175},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.6503558158874512},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.5655609369277954},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.54902583360672},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5251438617706299},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5102901458740234},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4902696907520294},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4867701530456543},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.4795210659503937},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46452343463897705},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4117988348007202},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4024648070335388},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3580130338668823},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.25915277004241943},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1542542576789856},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11769089102745056},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1064608097076416},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09688854217529297},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.060360074043273926}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7477854490280151},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.6860663294792175},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.6503558158874512},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.5655609369277954},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.54902583360672},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5251438617706299},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5102901458740234},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4902696907520294},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4867701530456543},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.4795210659503937},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46452343463897705},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4117988348007202},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4024648070335388},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3580130338668823},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.25915277004241943},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1542542576789856},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11769089102745056},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1064608097076416},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09688854217529297},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.060360074043273926},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsii.2021.3108116","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2021.3108116","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 II: Express Briefs","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7027707469","display_name":null,"funder_award_id":"61673298","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8607042969","display_name":null,"funder_award_id":"62073243","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/F4320322449","display_name":"Tongji University","ror":"https://ror.org/03rc6as71"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W2041833126","https://openalex.org/W2054188778","https://openalex.org/W2068118500","https://openalex.org/W2145206324","https://openalex.org/W2556672803","https://openalex.org/W2588099484","https://openalex.org/W2752123807","https://openalex.org/W2762112322","https://openalex.org/W2765459685","https://openalex.org/W2788271979","https://openalex.org/W2888119068","https://openalex.org/W2888787571","https://openalex.org/W2905032080","https://openalex.org/W2948000482","https://openalex.org/W2990068480","https://openalex.org/W2991774807","https://openalex.org/W2995778623","https://openalex.org/W3003441677","https://openalex.org/W3004598589","https://openalex.org/W3024138322","https://openalex.org/W3126454014","https://openalex.org/W3201421046"],"related_works":["https://openalex.org/W1996375507","https://openalex.org/W2093513634","https://openalex.org/W2953241977","https://openalex.org/W1968407578","https://openalex.org/W2023658576","https://openalex.org/W2922390231","https://openalex.org/W1522710368","https://openalex.org/W3155076130","https://openalex.org/W4298325607","https://openalex.org/W2044668677"],"abstract_inverted_index":{"In":[0],"this":[1],"brief,":[2],"we":[3,71,100,139],"investigate":[4],"the":[5,18,31,39,47,118,130,133,142],"cluster":[6,134,152],"synchronization":[7,135,153],"of":[8,121,132],"multi-weighted":[9],"complex":[10],"networks":[11],"with":[12,107,144],"pinning":[13],"control.":[14],"We":[15,54],"assume":[16],"that":[17],"network":[19],"contains":[20],"multiple":[21,43],"coupling":[22,45,122,146],"matrices,":[23,46],"and":[24],"they":[25],"can":[26,72,101],"be":[27],"all":[28,111],"asymmetric":[29,44],"(including":[30],"symmetric":[32],"case),":[33],"which":[34],"is":[35,50,90,97,136,154],"more":[36],"practical":[37],"in":[38,80],"real":[40],"world.":[41],"For":[42],"Lyapunov":[48,105],"function":[49,106],"hard":[51],"to":[52,98,117,162],"design.":[53],"firstly":[55],"define":[56],"a":[57,76,103,108],"candidate":[58],"region":[59],"for":[60,151],"every":[61],"matrix.":[62],"Then":[63],"if":[64],"these":[65],"regions":[66],"are":[67,160],"not":[68],"too":[69],"far,":[70],"find":[73],"(at":[74],"least)":[75],"common":[77],"vector":[78,109],"lying":[79],"each":[81],"region.":[82],"This":[83],"method":[84],"has":[85],"geometrical":[86],"meaning,":[87],"so":[88],"it":[89],"different":[91],"from":[92],"previous":[93],"LMI":[94],"method.":[95],"That":[96],"say,":[99],"design":[102],"new":[104],"combining":[110],"normalized":[112],"left":[113],"eigenvectors":[114],"(NLEVec)":[115],"corresponding":[116],"zero":[119],"eigenvalue":[120],"matrices.":[123,147],"With":[124],"some":[125],"sufficient":[126],"conditions":[127],"presented":[128],"accordingly,":[129],"realization":[131],"guaranteed.":[137],"Especially,":[138],"carefully":[140],"discuss":[141],"case":[143],"three":[145],"The":[148],"adaptive":[149],"rule":[150],"also":[155],"designed.":[156],"Finally,":[157],"numerical":[158],"simulations":[159],"given":[161],"demonstrate":[163],"our":[164],"results\u2019":[165],"effectiveness.":[166]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":17},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}