{"id":"https://openalex.org/W2065303481","doi":"https://doi.org/10.1109/cdc.2011.6160337","title":"Topological equivalence of a structure-preserving power network model and a non-uniform Kuramoto model of coupled oscillators","display_name":"Topological equivalence of a structure-preserving power network model and a non-uniform Kuramoto model of coupled oscillators","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2065303481","doi":"https://doi.org/10.1109/cdc.2011.6160337","mag":"2065303481"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6160337","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160337","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-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/A5091434894","display_name":"Florian D\u00f6rfler","orcid":"https://orcid.org/0000-0002-9649-5305"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Florian Dorfler","raw_affiliation_strings":["Center for Control, Dynamical Systems and Computation, University of California, Santa Barbara, Santa Barbara, CA, USA","Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, 93106, USA"],"affiliations":[{"raw_affiliation_string":"Center for Control, Dynamical Systems and Computation, University of California, Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, 93106, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068353454","display_name":"Francesco Bullo","orcid":"https://orcid.org/0000-0002-4785-2118"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Francesco Bullo","raw_affiliation_strings":["Center for Control, Dynamical Systems and Computation, University of California, Santa Barbara, Santa Barbara, CA, USA","Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, 93106, USA"],"affiliations":[{"raw_affiliation_string":"Center for Control, Dynamical Systems and Computation, University of California, Santa Barbara, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, 93106, USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091434894"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":3.6436,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.93027375,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"97","issue":null,"first_page":"7099","last_page":"7104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9810000061988831,"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/T13362","display_name":"Slime Mold and Myxomycetes Research","score":0.9710000157356262,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/kuramoto-model","display_name":"Kuramoto model","score":0.9658287167549133},{"id":"https://openalex.org/keywords/synchronization-networks","display_name":"Synchronization networks","score":0.7992973327636719},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.7431938648223877},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.7171499729156494},{"id":"https://openalex.org/keywords/topological-conjugacy","display_name":"Topological conjugacy","score":0.5076271295547485},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4883379638195038},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.44360867142677307},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.4334893524646759},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4246065318584442},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41836249828338623},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40803301334381104},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18727779388427734},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11676692962646484}],"concepts":[{"id":"https://openalex.org/C2780042749","wikidata":"https://www.wikidata.org/wiki/Q604374","display_name":"Kuramoto model","level":4,"score":0.9658287167549133},{"id":"https://openalex.org/C111097370","wikidata":"https://www.wikidata.org/wiki/Q10969923","display_name":"Synchronization networks","level":4,"score":0.7992973327636719},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.7431938648223877},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.7171499729156494},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.5076271295547485},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4883379638195038},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.44360867142677307},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.4334893524646759},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4246065318584442},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41836249828338623},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40803301334381104},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18727779388427734},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11676692962646484},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2011.6160337","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160337","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.352.1473","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.352.1473","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://motion.me.ucsb.edu/pdf/2011j-db.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1515493836","https://openalex.org/W1542938076","https://openalex.org/W1589876408","https://openalex.org/W1592980365","https://openalex.org/W1603360505","https://openalex.org/W1844872857","https://openalex.org/W1908390342","https://openalex.org/W1974485522","https://openalex.org/W2009030410","https://openalex.org/W2019120678","https://openalex.org/W2030851210","https://openalex.org/W2049343272","https://openalex.org/W2051238374","https://openalex.org/W2063357812","https://openalex.org/W2072643460","https://openalex.org/W2072694395","https://openalex.org/W2075032588","https://openalex.org/W2112565515","https://openalex.org/W2119589757","https://openalex.org/W2130518506","https://openalex.org/W2147246923","https://openalex.org/W2152556309","https://openalex.org/W2160324078","https://openalex.org/W2164808178","https://openalex.org/W2167430353","https://openalex.org/W2168448159","https://openalex.org/W2285880935","https://openalex.org/W2577900305","https://openalex.org/W2962910558","https://openalex.org/W2963784516","https://openalex.org/W2964098315","https://openalex.org/W3010676235","https://openalex.org/W3146418138","https://openalex.org/W6655193972"],"related_works":["https://openalex.org/W3118528670","https://openalex.org/W2969606317","https://openalex.org/W2169358986","https://openalex.org/W2085782938","https://openalex.org/W1488962991","https://openalex.org/W2282239531","https://openalex.org/W1805674502","https://openalex.org/W4292952218","https://openalex.org/W2065303481","https://openalex.org/W2072084517"],"abstract_inverted_index":{"We":[0,15,85],"study":[1],"synchronization":[2,21,60,81,106],"in":[3,61,65,82],"the":[4,20,23,29,37,56,73,115,119,136],"classic":[5,120],"structure-preserving":[6],"power":[7,30,62,83,140],"network":[8,31],"model":[9,32,44,123],"proposed":[10],"by":[11,145],"Bergen":[12],"and":[13,25,48,64,88,99,101,124],"Hill.":[14],"find":[16],"that,":[17],"locally":[18],"near":[19],"manifold,":[22],"phase":[24,38,92],"frequency":[26,50,97,105],"dynamics":[27,39],"of":[28,40,58],"are":[33],"topologically":[34],"conjugate":[35],"to":[36,79],"a":[41,108,132],"non-uniform":[42,66],"Kuramoto":[43,67,77,122],"together":[45],"with":[46,107],"decoupled":[47],"stable":[49],"dynamics.":[51],"This":[52],"topological":[53],"conjugacy":[54],"implies":[55],"equivalence":[57],"local":[59],"networks":[63],"oscillators.":[68],"Hence,":[69],"we":[70],"can":[71],"harness":[72],"results":[74,116],"available":[75],"for":[76,91,96,104,118],"oscillators":[78],"analyze":[80],"networks.":[84],"establish":[86],"necessary":[87,100],"sufficient":[89,94,102],"conditions":[90,95,103,112,129],"synchronization,":[93,98],"uniform":[109],"topology.":[110],"These":[111],"also":[113],"extend":[114],"known":[117],"first-order":[121],"second-order":[125],"consensus":[126],"protocols.":[127],"Our":[128],"all":[130],"share":[131],"common":[133],"physical":[134],"interpretation:":[135],"non-uniformity":[137],"between":[138],"real":[139],"injections":[141],"has":[142],"be":[143],"compensated":[144],"sufficiently":[146],"strong":[147],"coupling.":[148]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
