{"id":"https://openalex.org/W2962846557","doi":"https://doi.org/10.1137/16m106861x","title":"Center manifolds of coupled cell networks","display_name":"Center manifolds of coupled cell networks","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2962846557","doi":"https://doi.org/10.1137/16m106861x","mag":"2962846557"},"language":"en","primary_location":{"id":"pmh:oai:research.vu.nl:openaire/35ddeca2-587e-43ef-8a85-aab0b2d61f9c","is_oa":true,"landing_page_url":"https://research.vu.nl/en/publications/35ddeca2-587e-43ef-8a85-aab0b2d61f9c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Rink, B W, Nijholt, E C & Sanders, J A 2017, 'Center manifolds of coupled cell networks', SIAM Journal on Mathematical Analysis, vol. 49, no. 5, pp. 4117-4148. https://doi.org/10.1137/16M106861X","raw_type":"info:eu-repo/semantics/publishedVersion"},"type":"article","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.vu.nl/en/publications/35ddeca2-587e-43ef-8a85-aab0b2d61f9c","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Rink, B.W.","orcid":null},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Rink, B.W.","raw_affiliation_strings":["Department of Mathematics, VU University Amsterdam, 1081 HV Amsterdam, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, VU University Amsterdam, 1081 HV Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I865915315"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Nijholt, E.C.","orcid":null},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Nijholt, E.C.","raw_affiliation_strings":["Department of Mathematics, VU University Amsterdam, 1081 HV Amsterdam, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, VU University Amsterdam, 1081 HV Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I865915315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059159255","display_name":"Jan A. Sanders","orcid":"https://orcid.org/0000-0003-0499-9889"},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Sanders, J.A.","raw_affiliation_strings":["Department of Mathematics, VU University Amsterdam, 1081 HV Amsterdam, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, VU University Amsterdam, 1081 HV Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I865915315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I865915315"],"apc_list":null,"apc_paid":null,"fwci":1.2354,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.79771212,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9976000189781189,"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"}},"topics":[{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9976000189781189,"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"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9937000274658203,"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":0.98580002784729,"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/mathematics","display_name":"Mathematics","score":0.836790919303894},{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.7972846031188965},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.7022002935409546},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.5508442521095276},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5300882458686829},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5121364593505859},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4759996831417084},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4725368022918701},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.46096253395080566},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4571797847747803},{"id":"https://openalex.org/keywords/vector-bundle","display_name":"Vector bundle","score":0.43975016474723816},{"id":"https://openalex.org/keywords/fundamental-group","display_name":"Fundamental group","score":0.41692185401916504},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3237857222557068},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1717020571231842},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14199531078338623},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1305408477783203}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.836790919303894},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.7972846031188965},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.7022002935409546},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.5508442521095276},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5300882458686829},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5121364593505859},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4759996831417084},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4725368022918701},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.46096253395080566},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4571797847747803},{"id":"https://openalex.org/C95857938","wikidata":"https://www.wikidata.org/wiki/Q658429","display_name":"Vector bundle","level":2,"score":0.43975016474723816},{"id":"https://openalex.org/C159876591","wikidata":"https://www.wikidata.org/wiki/Q662830","display_name":"Fundamental group","level":2,"score":0.41692185401916504},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3237857222557068},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1717020571231842},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14199531078338623},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1305408477783203},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","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":2,"locations":[{"id":"pmh:oai:research.vu.nl:openaire/35ddeca2-587e-43ef-8a85-aab0b2d61f9c","is_oa":true,"landing_page_url":"https://research.vu.nl/en/publications/35ddeca2-587e-43ef-8a85-aab0b2d61f9c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Rink, B W, Nijholt, E C & Sanders, J A 2017, 'Center manifolds of coupled cell networks', SIAM Journal on Mathematical Analysis, vol. 49, no. 5, pp. 4117-4148. https://doi.org/10.1137/16M106861X","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research.vu.nl:publications/35ddeca2-587e-43ef-8a85-aab0b2d61f9c","is_oa":true,"landing_page_url":"https://hdl.handle.net/1871.1/35ddeca2-587e-43ef-8a85-aab0b2d61f9c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"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":"Rink, B W, Nijholt, E C & Sanders, J A 2017, 'Center manifolds of coupled cell networks', SIAM Journal on Mathematical Analysis, vol. 49, no. 5, pp. 4117-4148. https://doi.org/10.1137/16M106861X","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:research.vu.nl:openaire/35ddeca2-587e-43ef-8a85-aab0b2d61f9c","is_oa":true,"landing_page_url":"https://research.vu.nl/en/publications/35ddeca2-587e-43ef-8a85-aab0b2d61f9c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Rink, B W, Nijholt, E C & Sanders, J A 2017, 'Center manifolds of coupled cell networks', SIAM Journal on Mathematical Analysis, vol. 49, no. 5, pp. 4117-4148. https://doi.org/10.1137/16M106861X","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1989296467","https://openalex.org/W1992394023","https://openalex.org/W2007648542","https://openalex.org/W2012152080","https://openalex.org/W2029537795","https://openalex.org/W2036153627","https://openalex.org/W2038801293","https://openalex.org/W2045425785","https://openalex.org/W2097457784","https://openalex.org/W2118742026","https://openalex.org/W2129270652","https://openalex.org/W2157540413","https://openalex.org/W2168679843","https://openalex.org/W2175370996","https://openalex.org/W2591909761","https://openalex.org/W2962946421","https://openalex.org/W4248079659","https://openalex.org/W4251718542","https://openalex.org/W4252804454"],"related_works":["https://openalex.org/W3148895720","https://openalex.org/W2393913406","https://openalex.org/W30258475","https://openalex.org/W2356579025","https://openalex.org/W2736697936","https://openalex.org/W3211835374","https://openalex.org/W2548611373","https://openalex.org/W4300892325","https://openalex.org/W4313905118","https://openalex.org/W1496877660"],"abstract_inverted_index":{"Dynamical":[0],"systems":[1],"with":[2,96],"a":[3,11,60,68],"network":[4],"structure":[5],"can":[6,26],"display":[7],"anomalous":[8],"bifurcations":[9,91],"as":[10,29],"generic":[12,90],"phenomenon.":[13],"As":[14],"an":[15],"explanation":[16],"for":[17,42,70],"this":[18,63,83],"it":[19],"has":[20],"been":[21],"noted":[22],"that":[23],"homogeneous":[24],"networks":[25,31,45,76,95],"be":[27],"realized":[28],"quotient":[30],"of":[32,38,51,55,59],"so-called":[33],"fundamental":[34,44,75],"networks.":[35],"The":[36],"class":[37,50],"admissible":[39],"vector":[40,53],"fields":[41,54],"these":[43],"is":[46],"equal":[47],"to":[48,85],"the":[49,56,87],"equivariant":[52],"regular":[57],"representation":[58],"monoid.":[61],"Using":[62],"insight,":[64],"we":[65],"set":[66],"up":[67],"framework":[69],"center":[71],"manifold":[72],"reduction":[73],"in":[74,89],"and":[77,100],"their":[78],"quotients.":[79],"We":[80],"then":[81],"use":[82],"machinery":[84],"explain":[86],"difference":[88],"between":[92],"three":[93],"example":[94],"identical":[97,101],"spectral":[98],"properties":[99],"robust":[102],"synchrony":[103],"spaces.<br/>":[104]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2019-07-30T00:00:00"}