{"id":"https://openalex.org/W2523506647","doi":"https://doi.org/10.1137/15m1017752","title":"Characterization and Computation of Partial Synchronization Manifolds for Diffusive Delay-Coupled Systems","display_name":"Characterization and Computation of Partial Synchronization Manifolds for Diffusive Delay-Coupled Systems","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2523506647","doi":"https://doi.org/10.1137/15m1017752","mag":"2523506647"},"language":"en","primary_location":{"id":"doi:10.1137/15m1017752","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1017752","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/handle/123456789/548014","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029166882","display_name":"Erik Steur","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"E. Steur","raw_affiliation_strings":["Dynamics and Control"],"affiliations":[{"raw_affiliation_string":"Dynamics and Control","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035925529","display_name":"Hakk\u0131 Ula\u015f \u00dcnal","orcid":"https://orcid.org/0000-0001-8979-4625"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]},{"id":"https://openalex.org/I4210091745","display_name":"Eski\u015fehir City Hospital","ror":"https://ror.org/00czdkn85","country_code":"TR","type":"healthcare","lineage":["https://openalex.org/I1303077703","https://openalex.org/I4210091745"]},{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]},{"id":"https://openalex.org/I133743585","display_name":"Anadolu University","ror":"https://ror.org/05nz37n09","country_code":"TR","type":"education","lineage":["https://openalex.org/I133743585"]}],"countries":["BE","NL","TR"],"is_corresponding":false,"raw_author_name":"H. U. \u00dcnal","raw_affiliation_strings":["Department of Electrical and Electronics Engineering, Anadolu University, Eskise-hir 26555, Turkey","Laboratory for Perceptual Dynamics, Faculty of Psychology and Educational Sci-ences, KU Leuven, Tiensestraat 102, Box 3711, Leuven,B-3000, Belgium","Department of Mechanical Engineering and Institute for Complex and Molec-ular Systems, Eindhoven University of Technology, P.O. Box. 513, 5600 MB, Eindhoven, the Netherlands","Department of Computer Science, KU Leuven, Heverlee 3001, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronics Engineering, Anadolu University, Eskise-hir 26555, Turkey","institution_ids":["https://openalex.org/I133743585","https://openalex.org/I4210091745"]},{"raw_affiliation_string":"Laboratory for Perceptual Dynamics, Faculty of Psychology and Educational Sci-ences, KU Leuven, Tiensestraat 102, Box 3711, Leuven,B-3000, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Department of Mechanical Engineering and Institute for Complex and Molec-ular Systems, Eindhoven University of Technology, P.O. Box. 513, 5600 MB, Eindhoven, the Netherlands","institution_ids":["https://openalex.org/I83019370"]},{"raw_affiliation_string":"Department of Computer Science, KU Leuven, Heverlee 3001, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017565153","display_name":"Cees van Leeuwen","orcid":"https://orcid.org/0000-0002-4441-2440"},"institutions":[{"id":"https://openalex.org/I133743585","display_name":"Anadolu University","ror":"https://ror.org/05nz37n09","country_code":"TR","type":"education","lineage":["https://openalex.org/I133743585"]},{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]},{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]},{"id":"https://openalex.org/I4210091745","display_name":"Eski\u015fehir City Hospital","ror":"https://ror.org/00czdkn85","country_code":"TR","type":"healthcare","lineage":["https://openalex.org/I1303077703","https://openalex.org/I4210091745"]}],"countries":["BE","NL","TR"],"is_corresponding":false,"raw_author_name":"C. van Leeuwen","raw_affiliation_strings":["Department of Electrical and Electronics Engineering, Anadolu University, Eskise-hir 26555, Turkey","Laboratory for Perceptual Dynamics, Faculty of Psychology and Educational Sci-ences, KU Leuven, Tiensestraat 102, Box 3711, Leuven,B-3000, Belgium","Department of Computer Science, KU Leuven, Heverlee 3001, Belgium","Department of Mechanical Engineering and Institute for Complex and Molec-ular Systems, Eindhoven University of Technology, P.O. Box. 513, 5600 MB, Eindhoven, the Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronics Engineering, Anadolu University, Eskise-hir 26555, Turkey","institution_ids":["https://openalex.org/I133743585","https://openalex.org/I4210091745"]},{"raw_affiliation_string":"Laboratory for Perceptual Dynamics, Faculty of Psychology and Educational Sci-ences, KU Leuven, Tiensestraat 102, Box 3711, Leuven,B-3000, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Department of Computer Science, KU Leuven, Heverlee 3001, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Department of Mechanical Engineering and Institute for Complex and Molec-ular Systems, Eindhoven University of Technology, P.O. Box. 513, 5600 MB, Eindhoven, the Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008378186","display_name":"Wim Michiels","orcid":"https://orcid.org/0000-0002-0877-0080"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"W. Michiels","raw_affiliation_strings":["Research not related to TU/e workplace (outside TU/e employment)"],"affiliations":[{"raw_affiliation_string":"Research not related to TU/e workplace (outside TU/e employment)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5029166882"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5932,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.73617531,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"15","issue":"4","first_page":"1874","last_page":"1915"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9995999932289124,"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"}},"topics":[{"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9980000257492065,"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":0.9961000084877014,"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/synchronization","display_name":"Synchronization (alternating current)","score":0.6285930871963501},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.591947615146637},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.509096086025238},{"id":"https://openalex.org/keywords/synchronization-networks","display_name":"Synchronization networks","score":0.4899138808250427},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.45756274461746216},{"id":"https://openalex.org/keywords/invariant-manifold","display_name":"Invariant manifold","score":0.4296427369117737},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.4214169681072235},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36945149302482605},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19679588079452515}],"concepts":[{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.6285930871963501},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.591947615146637},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.509096086025238},{"id":"https://openalex.org/C111097370","wikidata":"https://www.wikidata.org/wiki/Q10969923","display_name":"Synchronization networks","level":4,"score":0.4899138808250427},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.45756274461746216},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.4296427369117737},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.4214169681072235},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36945149302482605},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19679588079452515},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1137/15m1017752","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1017752","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/dc861236-c264-4548-a12a-d51e90e76eb7","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/dc861236-c264-4548-a12a-d51e90e76eb7","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Steur, E, \u00dcnal, H U, van Leeuwen, C & Michiels, W 2016, 'Characterization and Computation of Partial Synchronization Manifolds for Diffusive Delay-Coupled Systems', SIAM Journal on Applied Dynamical Systems, vol. 15, no. 4, pp. 1874-1915. https://doi.org/10.1137/15M1017752","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/548014","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/548014","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"SIAM Journal on Applied Dynamical Systems, vol. 15 (4), (1874-1915)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:855135","is_oa":false,"landing_page_url":"http://library.tue.nl/csp/dare/LinkToRepository.csp?recordnumber=855135","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:1536-0040","raw_type":"Article / Letter to the editor"},{"id":"pmh:885136","is_oa":false,"landing_page_url":"http://library.tue.nl/csp/dare/LinkToRepository.csp?recordnumber=885136","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:1536-0040","raw_type":"Article / Letter to the editor"},{"id":"pmh:oai:library.tue.nl:855135","is_oa":false,"landing_page_url":"http://repository.tue.nl/855135","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:1536-0040","raw_type":"Article / Letter to the editor"},{"id":"pmh:oai:library.tue.nl:885136","is_oa":false,"landing_page_url":"http://repository.tue.nl/885136","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:1536-0040","raw_type":"Article / Letter to the editor"},{"id":"pmh:oai:zenodo.org:3500610","is_oa":true,"landing_page_url":"https://zenodo.org/record/3500610","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:tue:oai:pure.tue.nl:publications/dc861236-c264-4548-a12a-d51e90e76eb7","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/dc861236-c264-4548-a12a-d51e90e76eb7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Applied Dynamical Systems, 15(4), 1874 - 1915. Society for Industrial and Applied Mathematics (SIAM)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/548014","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/548014","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"SIAM Journal on Applied Dynamical Systems, vol. 15 (4), (1874-1915)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2547934977","display_name":null,"funder_award_id":"UCoCoS","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6483651114","display_name":null,"funder_award_id":"grant agreement 675080","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320322681","display_name":"Onderzoeksraad, KU Leuven","ror":"https://ror.org/05f950310"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1976666676","https://openalex.org/W1996272580","https://openalex.org/W2009143060","https://openalex.org/W2010465263","https://openalex.org/W2010900209","https://openalex.org/W2016650848","https://openalex.org/W2031356502","https://openalex.org/W2036997036","https://openalex.org/W2045425785","https://openalex.org/W2048419276","https://openalex.org/W2052427582","https://openalex.org/W2072210701","https://openalex.org/W2077668039","https://openalex.org/W2083694019","https://openalex.org/W2090679648","https://openalex.org/W2095993878","https://openalex.org/W2102899117","https://openalex.org/W2106674032","https://openalex.org/W2108185322","https://openalex.org/W2117880560","https://openalex.org/W2119077806","https://openalex.org/W2128995499","https://openalex.org/W2129270652","https://openalex.org/W2140380216","https://openalex.org/W2141451487","https://openalex.org/W2149971042","https://openalex.org/W2154563705","https://openalex.org/W2157540413","https://openalex.org/W2157586156","https://openalex.org/W2169632627","https://openalex.org/W3100746818","https://openalex.org/W4241364206"],"related_works":["https://openalex.org/W2063663506","https://openalex.org/W1586366284","https://openalex.org/W2297311436","https://openalex.org/W2969606317","https://openalex.org/W153843616","https://openalex.org/W2397248170","https://openalex.org/W2050769472","https://openalex.org/W3118528670","https://openalex.org/W2527776493","https://openalex.org/W2288531340"],"abstract_inverted_index":{"Sometimes":[0],"a":[1,7,80,107,115,214,268,279,328,336,374],"network":[2,59,221,307],"of":[3,9,15,20,26,43,52,57,60,70,101,106,114,128,238,254,278,282,316,327],"dynamical":[4],"systems":[5,318,341,379],"shows":[6],"form":[8],"incomplete":[10,27],"synchronization,":[11],"characterized":[12,73],"by":[13,74,79],"synchronization":[14,28,32,37,45,66,97,149,216,228,274,297,330],"some":[16],"but":[17,311],"not":[18,168,242,312,373],"all":[19,154,354],"its":[21],"component":[22],"systems.":[23,61],"This":[24],"type":[25],"is":[29,38,140,167,189,206,222,368],"called":[30],"partial":[31,44,65,96,148,215,227,273,296,329],"or":[33,202,372],"cluster":[34],"synchronization.":[35],"Partial":[36],"associated":[39,284],"with":[40,175,261],"the":[41,54,58,88,104,112,124,129,135,144,160,164,187,192,195,204,219,231,236,239,248,252,259,306,314,317,320,325,340,343,360,382],"existence":[42,93,145,270,301],"manifolds,":[46],"which":[47,246,303],"are":[48,151,198,322,349,384],"linear":[49,75],"invariant":[50,102],"subspaces":[51],"$\\mathcal{C}$,":[53],"state":[55],"space":[56],"We":[62,90,118,332],"focus":[63],"on":[64,305,313,339],"manifolds":[67,98,150,229,275],"in":[68,87,99,276],"networks":[69,256],"identical":[71],"systems,":[72],"diffusive":[76],"coupling":[77,130,367,375],"described":[78],"weighted":[81],"graph,":[82],"and":[83,111,132,194,308,364],"allowing":[84],"for":[85,95,147,153,159,218,230,272,294,324],"time-delay":[86],"coupling.":[89],"present":[91],"equivalent":[92,223,300],"criteria":[94,355],"terms":[100,277],"spaces,":[103],"block-structure":[105],"reordered":[108],"adjacency":[109],"matrix,":[110],"solvability":[113],"Sylvester":[116],"equation.":[117],"emphasize":[119],"decomposable":[120,255],"networks,":[121],"according":[122,133,190,207,257],"to":[123,134,191,208,224,235,258],"rational":[125],"dependency":[126],"structure":[127,310],"weights,":[131,260,265],"delay":[136,210,309],"values,":[137,211],"respectively.":[138],"It":[139],"obvious":[141],"that":[142,185,334,359],"if":[143,186,203],"conditions":[146,348],"satisfied":[152],"subnetworks":[155,240],"simultaneously,":[156],"they":[157],"hold":[158],"original":[161,220],"network,":[162],"yet":[163],"converse":[165],"result":[166],"always":[169],"true,":[170],"as":[171,179,351],"we":[172,183,266,288],"shall":[173],"illustrate":[174],"an":[176,283],"example.":[177],"Furthermore,":[178],"our":[180],"main":[181],"results,":[182],"show":[184,333],"decomposition":[188,205],"weights":[193,197],"basis":[196,264],"rationally":[199,262],"independent":[200,263],"numbers,":[201],"different":[209],"then":[212],"finding":[213,225],"manifold":[217],"common":[226],"subnetworks,":[232],"i.e.,":[233,370],"restricting":[234],"analysis":[237,249],"does":[241],"impose":[243],"any":[244],"conservatism,":[245],"simplifies":[247],"significantly.":[250],"For":[251],"case":[253],"provide":[267],"fourth":[269],"criterion":[271],"balanced":[280],"coloring":[281],"multigraph.":[285],"In":[286,353],"addition,":[287],"briefly":[289],"describe":[290],"publicly":[291],"available":[292],"software":[293],"detecting":[295],"manifolds.":[298],"Our":[299],"criteria,":[302],"depend":[304],"dynamics":[315],"at":[319,342],"nodes,":[321,344],"sufficient":[323],"presence":[326],"manifold.":[331],"under":[335],"mild":[337],"assumption":[338],"namely,":[345],"left-invertibility,":[346],"these":[347],"necessary":[350],"well.":[352],"it":[356],"turns":[357],"out":[358],"distinction":[361],"between":[362,377],"noninvasive":[363],"invasive":[365],"delayed":[366],"important,":[369],"whether":[371],"term":[376],"two":[378],"vanishes":[380],"whenever":[381],"latter":[383],"synchronized.":[385]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}