{"id":"https://openalex.org/W2808504306","doi":"https://doi.org/10.1109/tcyb.2018.2839648","title":"Synchronization Analysis of Two-Time-Scale Nonlinear Complex Networks With Time-Scale-Dependent Coupling","display_name":"Synchronization Analysis of Two-Time-Scale Nonlinear Complex Networks With Time-Scale-Dependent Coupling","publication_year":2018,"publication_date":"2018-06-14","ids":{"openalex":"https://openalex.org/W2808504306","doi":"https://doi.org/10.1109/tcyb.2018.2839648","mag":"2808504306","pmid":"https://pubmed.ncbi.nlm.nih.gov/29994284"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2018.2839648","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2018.2839648","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5020014838","display_name":"Wu\u2010Hua Chen","orcid":"https://orcid.org/0000-0002-7381-1969"},"institutions":[{"id":"https://openalex.org/I150807315","display_name":"Guangxi University","ror":"https://ror.org/02c9qn167","country_code":"CN","type":"education","lineage":["https://openalex.org/I150807315"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wu-Hua Chen","raw_affiliation_strings":["College of Mathematics and Information Science, Guangxi University, Nanning, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Guangxi University, Nanning, China","institution_ids":["https://openalex.org/I150807315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047674009","display_name":"Yunli Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I150807315","display_name":"Guangxi University","ror":"https://ror.org/02c9qn167","country_code":"CN","type":"education","lineage":["https://openalex.org/I150807315"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunli Liu","raw_affiliation_strings":["College of Mathematics and Information Science, Guangxi University, Nanning, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Guangxi University, Nanning, China","institution_ids":["https://openalex.org/I150807315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108050907","display_name":"Wei Xing Zheng","orcid":"https://orcid.org/0000-0002-0572-5938"},"institutions":[{"id":"https://openalex.org/I63525965","display_name":"Western Sydney University","ror":"https://ror.org/03t52dk35","country_code":"AU","type":"education","lineage":["https://openalex.org/I63525965"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Wei Xing Zheng","raw_affiliation_strings":["School of Computing, Engineering and Mathematics, Western Sydney University, Sydney, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"School of Computing, Engineering and Mathematics, Western Sydney University, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I63525965"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5020014838"],"corresponding_institution_ids":["https://openalex.org/I150807315"],"apc_list":null,"apc_paid":null,"fwci":3.1371,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.92381548,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"49","issue":"9","first_page":"3255","last_page":"3267"},"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":0.9997000098228455,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9922999739646912,"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/nonlinear-system","display_name":"Nonlinear system","score":0.631484866142273},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6060941815376282},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.5346801280975342},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.5341856479644775},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.5290569067001343},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4857195019721985},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4219841957092285},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4202847182750702},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3871835768222809},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37182068824768066},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3609165549278259},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18009185791015625},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1593705415725708},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07827204465866089},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07155779004096985}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.631484866142273},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6060941815376282},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.5346801280975342},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.5341856479644775},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.5290569067001343},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4857195019721985},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4219841957092285},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4202847182750702},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3871835768222809},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37182068824768066},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3609165549278259},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18009185791015625},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1593705415725708},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07827204465866089},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07155779004096985},{"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcyb.2018.2839648","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2018.2839648","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},{"id":"pmid:29994284","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29994284","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on cybernetics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1743199603","display_name":null,"funder_award_id":"61633011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4183255768","display_name":null,"funder_award_id":"2015GXNSFAA139003","funder_id":"https://openalex.org/F4320322768","funder_display_name":"Natural Science Foundation of Guangxi Province"},{"id":"https://openalex.org/G4647966911","display_name":null,"funder_award_id":"61573111","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G61038381","display_name":null,"funder_award_id":"DP120104986","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320322768","display_name":"Natural Science Foundation of Guangxi Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W150604082","https://openalex.org/W261461018","https://openalex.org/W607068030","https://openalex.org/W1671909755","https://openalex.org/W1966364372","https://openalex.org/W1992381023","https://openalex.org/W1992435968","https://openalex.org/W1997974219","https://openalex.org/W2002349705","https://openalex.org/W2004117240","https://openalex.org/W2006002535","https://openalex.org/W2012378616","https://openalex.org/W2017878009","https://openalex.org/W2018959247","https://openalex.org/W2028821684","https://openalex.org/W2039661201","https://openalex.org/W2042187707","https://openalex.org/W2044140943","https://openalex.org/W2056598937","https://openalex.org/W2058766213","https://openalex.org/W2068118500","https://openalex.org/W2075720166","https://openalex.org/W2080208605","https://openalex.org/W2124676026","https://openalex.org/W2129934604","https://openalex.org/W2141066375","https://openalex.org/W2141070320","https://openalex.org/W2141541004","https://openalex.org/W2153765205","https://openalex.org/W2160821152","https://openalex.org/W2163618991","https://openalex.org/W2224855903","https://openalex.org/W2259261597","https://openalex.org/W2338393438","https://openalex.org/W2343397127","https://openalex.org/W2514447902","https://openalex.org/W2556264647","https://openalex.org/W2600743521","https://openalex.org/W2609122333","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2380573388","https://openalex.org/W2369636957","https://openalex.org/W2029465934","https://openalex.org/W4231087120","https://openalex.org/W2757394160","https://openalex.org/W2069173628","https://openalex.org/W2975999490","https://openalex.org/W3125812129","https://openalex.org/W3215671869","https://openalex.org/W2291158962"],"abstract_inverted_index":{"In":[0,142],"this":[1,16,143],"paper,":[2],"a":[3,107,176],"time-scale-dependent":[4,37,189],"coupling":[5,20,39,65,190],"scheme":[6],"for":[7,146],"two-time-scale":[8,60,72,167],"nonlinear":[9],"complex":[10],"networks":[11],"is":[12,41,52,90,119,169,192],"proposed.":[13],"According":[14],"to":[15,24,92,133],"scheme,":[17],"the":[18,25,44,47,63,67,75,94,112,122,127,137,162,165,184,187],"inner":[19,38],"matrices":[21,40],"are":[22,32,152],"related":[23],"fast":[26,76],"dynamics":[27,77],"of":[28,49,56,59,87,96,111,126,136,139,158,164,178,186],"individual":[29,71],"subsystems,":[30],"but":[31],"no":[33],"longer":[34],"time-scale-independent.":[35],"Designing":[36],"motivated":[42],"by":[43,174],"fact":[45],"that":[46,74,121,161],"difference":[48],"time":[50],"scales":[51],"an":[53],"essential":[54],"feature":[55],"modular":[57],"architecture":[58],"systems.":[61],"Under":[62],"novel":[64],"framework,":[66],"previous":[68],"assumption":[69],"on":[70],"subsystems":[73],"must":[78],"be":[79,83,131,134,172],"exponentially":[80],"stable":[81],"can":[82,130,171],"removed.":[84],"The":[85,154],"idea":[86],"time-scale":[88],"separation":[89],"employed":[91],"analyze":[93],"stability":[95],"synchronization":[97,128,151],"error":[98,129],"systems":[99],"via":[100],"weighted":[101],"\u03b5":[102,116,140,159,179],"-dependent":[103,180],"Lyapunov":[104],"functions.":[105],"For":[106],"given":[108],"upper":[109,156],"bound":[110,157],"singular":[113],"perturbation":[114],"parameter":[115],",":[117],"it":[118],"proved":[120],"exponential":[123,150],"decay":[124],"rate":[125],"guaranteed":[132],"independent":[135],"value":[138],".":[141],"way,":[144],"criteria":[145],"local":[147],"and":[148],"global":[149],"established.":[153],"allowable":[155],"such":[160],"synchronizability":[163],"considered":[166],"network":[168],"retained":[170],"obtained":[173],"solving":[175],"set":[177],"matrix":[181],"inequalities.":[182],"Finally,":[183],"efficiency":[185],"proposed":[188],"strategy":[191],"demonstrated":[193],"through":[194],"numerical":[195],"simulations.":[196]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}