{"id":"https://openalex.org/W4390865692","doi":"https://doi.org/10.1109/tcns.2024.3395836","title":"Analysis and Control of Multi-Time-Scale Modular Directed Heterogeneous Networks","display_name":"Analysis and Control of Multi-Time-Scale Modular Directed Heterogeneous Networks","publication_year":2024,"publication_date":"2024-05-01","ids":{"openalex":"https://openalex.org/W4390865692","doi":"https://doi.org/10.1109/tcns.2024.3395836"},"language":"en","primary_location":{"id":"doi:10.1109/tcns.2024.3395836","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcns.2024.3395836","pdf_url":null,"source":{"id":"https://openalex.org/S2502544478","display_name":"IEEE Transactions on Control of Network Systems","issn_l":"2325-5870","issn":["2325-5870","2372-2533"],"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 Control of Network Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-04266142/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050406436","display_name":"Anes Lazri","orcid":"https://orcid.org/0009-0001-4872-381X"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Anes Lazri","raw_affiliation_strings":["L2S, CNRS, University of Paris-Saclay, Gif-sur-Yvette, France","L2S, CNRS, Univ Paris-Saclay, France"],"raw_orcid":"https://orcid.org/0009-0001-4872-381X","affiliations":[{"raw_affiliation_string":"L2S, CNRS, University of Paris-Saclay, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I277688954"]},{"raw_affiliation_string":"L2S, CNRS, Univ Paris-Saclay, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I277688954"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036042991","display_name":"Elena Panteley","orcid":"https://orcid.org/0000-0002-4565-9138"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210087640","display_name":"London Rebuilding Society","ror":"https://ror.org/001fg0044","country_code":"GB","type":"nonprofit","lineage":["https://openalex.org/I4210087640"]}],"countries":["FR","GB"],"is_corresponding":false,"raw_author_name":"Elena Panteley","raw_affiliation_strings":["L2S, CNRS, University of Paris-Saclay, Gif-sur-Yvette, France","L2SCNRS"],"raw_orcid":"https://orcid.org/0000-0002-4565-9138","affiliations":[{"raw_affiliation_string":"L2S, CNRS, University of Paris-Saclay, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I277688954"]},{"raw_affiliation_string":"L2SCNRS","institution_ids":["https://openalex.org/I4210087640"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090052067","display_name":"Antonio Lor\u0131\u0301a","orcid":"https://orcid.org/0000-0003-4223-9397"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210087640","display_name":"London Rebuilding Society","ror":"https://ror.org/001fg0044","country_code":"GB","type":"nonprofit","lineage":["https://openalex.org/I4210087640"]}],"countries":["FR","GB"],"is_corresponding":false,"raw_author_name":"Antonio Lor\u00eda","raw_affiliation_strings":["L2S, CNRS, University of Paris-Saclay, Gif-sur-Yvette, France","L2SCNRS"],"raw_orcid":"https://orcid.org/0000-0003-4223-9397","affiliations":[{"raw_affiliation_string":"L2S, CNRS, University of Paris-Saclay, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I277688954"]},{"raw_affiliation_string":"L2SCNRS","institution_ids":["https://openalex.org/I4210087640"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":0.2086,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50712544,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"12","issue":"1","first_page":"661","last_page":"672"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9984999895095825,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9984999895095825,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9889000058174133,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9817000031471252,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.6861819624900818},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.6367440223693848},{"id":"https://openalex.org/keywords/nonlinear-dynamical-systems","display_name":"Nonlinear dynamical systems","score":0.6238003969192505},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5911155343055725},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.5833526253700256},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5486180186271667},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5364051461219788},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5251231789588928},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5228546261787415},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4655251204967499},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.446661114692688},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4397476017475128},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.42138415575027466},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3887025713920593},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3559637665748596},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12386897206306458},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11104792356491089}],"concepts":[{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.6861819624900818},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.6367440223693848},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.6238003969192505},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5911155343055725},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.5833526253700256},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5486180186271667},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5364051461219788},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5251231789588928},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5228546261787415},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4655251204967499},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.446661114692688},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4397476017475128},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.42138415575027466},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3887025713920593},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3559637665748596},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12386897206306458},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11104792356491089},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcns.2024.3395836","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcns.2024.3395836","pdf_url":null,"source":{"id":"https://openalex.org/S2502544478","display_name":"IEEE Transactions on Control of Network Systems","issn_l":"2325-5870","issn":["2325-5870","2372-2533"],"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 Control of Network Systems","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04266142v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04266142","pdf_url":"https://hal.science/hal-04266142/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"IEEE Transactions on Control of Network Systems, 2024, pp.1-11. &#x27E8;10.1109/TCNS.2024.3395836&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04266142v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04266142","pdf_url":"https://hal.science/hal-04266142/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"IEEE Transactions on Control of Network Systems, 2024, pp.1-11. &#x27E8;10.1109/TCNS.2024.3395836&#x27E9;","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4390865692.pdf","grobid_xml":"https://content.openalex.org/works/W4390865692.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1590821414","https://openalex.org/W1979813760","https://openalex.org/W1993650658","https://openalex.org/W2002494248","https://openalex.org/W2015385256","https://openalex.org/W2030205386","https://openalex.org/W2086264532","https://openalex.org/W2128226330","https://openalex.org/W2142189574","https://openalex.org/W2150116043","https://openalex.org/W2179502718","https://openalex.org/W2180822344","https://openalex.org/W2326883828","https://openalex.org/W2343609308","https://openalex.org/W2533982193","https://openalex.org/W2571108256","https://openalex.org/W2571527988","https://openalex.org/W2887463190","https://openalex.org/W2912352567","https://openalex.org/W2963372344","https://openalex.org/W2964198956","https://openalex.org/W2981624099","https://openalex.org/W4292198410","https://openalex.org/W4292411591","https://openalex.org/W4301823516","https://openalex.org/W4382936367","https://openalex.org/W4387914451","https://openalex.org/W6855174922"],"related_works":["https://openalex.org/W4391062601","https://openalex.org/W2074717584","https://openalex.org/W4250831671","https://openalex.org/W2050258033","https://openalex.org/W2931186781","https://openalex.org/W2592826714","https://openalex.org/W4390075452","https://openalex.org/W2090738527","https://openalex.org/W3124821244","https://openalex.org/W3174433017"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,16,21,26,46,59,76,80,89,101,105,108,112,134,139],"collective":[3],"behavior":[4],"of":[5,23,35],"heterogeneous":[6],"nonlinear":[7],"systems,":[8],"interconnected":[9],"over":[10],"generic":[11],"directed":[12],"graphs":[13],"and":[14,87,120],"in":[15,29,132],"scenario":[17],"that,":[18],"due":[19],"to":[20,85,137],"nature":[22],"their":[24],"interconnections,":[25],"agents":[27,36],"self-organize":[28],"modules.":[30],"These":[31],"are":[32,38,49],"sub-networks":[33],"composed":[34],"that":[37,71,107,130],"densely":[39],"connected":[40],"with":[41,66],"a":[42,67,115],"strong":[43],"coupling,":[44],"while":[45],"modules":[47,90],"themselves":[48],"sparsely":[50],"interconnected.":[51],"As":[52],"we":[53,95,126],"show,":[54],"beyond":[55],"certain":[56],"coupling":[57],"thresholds,":[58],"systems":[60,83],"within":[61],"each":[62,86,121],"module":[63],"synchronize":[64,91],"rapidly":[65],"weighted-average":[68],"dynamical":[69,82],"system":[70,122],"evolves":[72],"more":[73],"slowly":[74],"than":[75],"individual":[77],"systems.":[78],"Then,":[79],"average":[81,109,135],"corresponding":[84],"all":[88],"among":[92],"themselves.":[93],"Furthermore,":[94],"establish":[96],"global":[97],"asymptotic":[98],"stability":[99],"for":[100],"overall":[102],"network":[103],"under":[104],"conditions":[106],"dynamics":[110,136],"admit":[111],"origin":[113,140],"as":[114],"globally":[116,141],"asymptotically":[117,142],"stable":[118],"equilibrium":[119],"be":[123],"semi-passive.":[124],"Finally,":[125],"explore":[127],"stabilization":[128],"techniques":[129],"consist":[131],"controlling":[133],"make":[138],"stable.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}
