{"id":"https://openalex.org/W2803094674","doi":"https://doi.org/10.1137/16m1066154","title":"Symmetry-Breaking Bifurcations and Patterns of Oscillations in Rings of Crystal Oscillators","display_name":"Symmetry-Breaking Bifurcations and Patterns of Oscillations in Rings of Crystal Oscillators","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2803094674","doi":"https://doi.org/10.1137/16m1066154","mag":"2803094674"},"language":"en","primary_location":{"id":"doi:10.1137/16m1066154","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1066154","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085865750","display_name":"Pietro-Luciano Buono","orcid":"https://orcid.org/0000-0003-1460-4465"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Pietro-Luciano Buono","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064805896","display_name":"Bernard S. Chan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bernard Chan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023978015","display_name":"Jocirei D. Ferreira","orcid":"https://orcid.org/0000-0001-7479-3056"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jocirei Ferreira","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012308437","display_name":"Antonio Palacios","orcid":"https://orcid.org/0000-0003-0580-3657"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Antonio Palacios","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062023198","display_name":"Steven I. Reeves","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steven Reeves","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016503531","display_name":"Patrick Longhini","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Patrick Longhini","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5063982891","display_name":"Visarath In","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Visarath In","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5085865750"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2917,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.82060985,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"17","issue":"2","first_page":"1310","last_page":"1352"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9973999857902527,"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":0.9973999857902527,"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/T11449","display_name":"Mechanical and Optical Resonators","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11230","display_name":"Innovative Energy Harvesting Technologies","score":0.9635999798774719,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/symmetry-breaking","display_name":"Symmetry breaking","score":0.6058732867240906},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5783958435058594},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.480551540851593},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.47061946988105774},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46157535910606384},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3618581295013428},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3571866750717163},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35438549518585205},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21396508812904358},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.19905105233192444},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1443394422531128}],"concepts":[{"id":"https://openalex.org/C204795200","wikidata":"https://www.wikidata.org/wiki/Q903282","display_name":"Symmetry breaking","level":2,"score":0.6058732867240906},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5783958435058594},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.480551540851593},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.47061946988105774},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46157535910606384},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3618581295013428},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3571866750717163},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35438549518585205},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21396508812904358},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.19905105233192444},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1443394422531128}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1066154","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1066154","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1402723485","display_name":null,"funder_award_id":"200628/2014-3/PDE","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G5316558530","display_name":null,"funder_award_id":"N00014-16-1-2134","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1546721432","https://openalex.org/W1990028683","https://openalex.org/W1996272580","https://openalex.org/W1997277490","https://openalex.org/W2007203792","https://openalex.org/W2025865630","https://openalex.org/W2029537795","https://openalex.org/W2046861067","https://openalex.org/W2057864643","https://openalex.org/W2070850306","https://openalex.org/W2075774995","https://openalex.org/W2080159910","https://openalex.org/W2082412309","https://openalex.org/W2086328213","https://openalex.org/W2093066866","https://openalex.org/W2108610728","https://openalex.org/W2119325655","https://openalex.org/W2132070310","https://openalex.org/W2135630993","https://openalex.org/W2151603769","https://openalex.org/W2158334808","https://openalex.org/W2173542753","https://openalex.org/W2326492740","https://openalex.org/W4212880698","https://openalex.org/W4252911570"],"related_works":["https://openalex.org/W1663354388","https://openalex.org/W2318061648","https://openalex.org/W1982022398","https://openalex.org/W2353522932","https://openalex.org/W2174670249","https://openalex.org/W2047973473","https://openalex.org/W1963690981","https://openalex.org/W3135194337","https://openalex.org/W2159473547","https://openalex.org/W2595473884"],"abstract_inverted_index":{"Symmetry":[0],"is":[1,29,131,248],"used":[2],"to":[3,42,55,90,94,123,146,193,207,223,235,249],"investigate":[4],"the":[5,40,83,87,102,108,116,124,148,156,169,179,186,198,208,224],"existence":[6,149],"and":[7,45,51,60,106,143,150,160,190,218,253],"stability":[8,151],"of":[9,12,16,73,80,82,104,152,155,168,178,185,197,204,211,239,255],"collective":[10],"patterns":[11],"oscillations":[13],"in":[14,115,128],"rings":[15],"coupled":[17],"crystal":[18,24],"oscillators.":[19,77],"We":[20,37],"assume":[21,39],"$N$":[22,74],"identical":[23,44],"oscillators,":[25],"where":[26],"each":[27],"oscillator":[28],"described":[30],"by":[31],"a":[32,194],"two-mode":[33,76],"nonlinear":[34],"oscillatory":[35],"circuit.":[36],"also":[38],"coupling":[41],"be":[43,68],"consider":[46],"two":[47],"different":[48],"topologies,":[49],"unidirectional":[50],"bidirectional,":[52],"which":[53],"lead":[54],"networks":[56],"with":[57,228],"$\\Gamma=":[58],"\\mathbb{Z}_N$":[59],"$\\Gamma=\\mathbb{D}_N$":[61],"symmetry,":[62],"respectively.":[63],"The":[64,78,121,243],"whole":[65],"system":[66,85,172],"can":[67],"seen":[69],"as":[70,165],"an":[71],"$\\varepsilon$-perturbation":[72],"uncoupled,":[75],"spectrum":[79],"eigenvalues":[81,205],"linearized":[84,199],"near":[86,112],"origin":[88],"leads":[89,192,206],"expressions":[91],"not":[92],"amenable":[93],"analysis.":[95],"To":[96],"circumvent":[97],"this":[98,246],"problem,":[99],"we":[100,136],"apply":[101],"method":[103],"averaging":[105,144],"rewrite":[107],"model":[109],"equations,":[110],"via":[111,216],"identity":[113],"transformations,":[114],"so-called":[117],"full":[118,170],"averaged":[119,158,171,200],"equations.":[120,201],"truncation":[122],"average":[125],"part,":[126],"expressed":[127],"complex":[129],"coordinates,":[130],"${O(2)}":[132],"\\times":[133],"{O(2)}\\times\\Gamma$-equivariant.":[134],"Then,":[135],"present":[137],"new":[138],"theoretical":[139],"results":[140],"linking":[141],"symmetry":[142,187],"theory":[145],"study":[147],"steady":[153],"states":[154],"truncated":[157],"systems,":[159],"show":[161,236],"that":[162,214],"they":[163],"persist":[164],"periodic":[166,212,226],"solutions":[167,213,227],"for":[173,245],"small":[174],"$\\varepsilon$.":[175],"A":[176],"decomposition":[177],"phase-space":[180],"dynamics":[181],"along":[182],"irreducible":[183],"representations":[184],"groups":[188],"$\\mathbb{Z}_N$":[189],"$\\mathbb{D}_N$":[191],"block":[195],"diagonalization":[196],"Direct":[202],"computation":[203],"desired":[209],"identification":[210],"emerge":[215],"symmetry-preserving":[217],"symmetry-breaking":[219],"steady-state":[220],"bifurcations":[221],"leading":[222],"corresponding":[225],"spatio-temporal":[229],"symmetries.":[230],"Numerical":[231],"simulations":[232],"are":[233],"conducted":[234],"representative":[237],"examples":[238],"emergent":[240],"rotating":[241],"waves.":[242],"motivation":[244],"work":[247],"aid":[250],"future":[251],"design":[252],"fabrication":[254],"novel":[256],"precision":[257],"timing":[258],"devices.":[259]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
