{"id":"https://openalex.org/W2139696771","doi":"https://doi.org/10.1109/tcsi.2008.916457","title":"Synchronization and Small-Signal Analysis of Nonlinear Periodic Circuits","display_name":"Synchronization and Small-Signal Analysis of Nonlinear Periodic Circuits","publication_year":2008,"publication_date":"2008-05-01","ids":{"openalex":"https://openalex.org/W2139696771","doi":"https://doi.org/10.1109/tcsi.2008.916457","mag":"2139696771"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2008.916457","doi":"https://doi.org/10.1109/tcsi.2008.916457","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2008.916457","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","ccf-c","cwts-core","dongbi-b","jufo-2","norway-2","poland-140","russia-white-list-1","vabb-shw"],"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 Circuits and Systems I: Regular Papers","raw_type":"journal-article"},"volume":null,"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/A5080022239","display_name":"Angelo Brambilla","orcid":"https://orcid.org/0000-0001-9422-6446","observed_orcids":["https://orcid.org/0000-0001-9422-6446"]},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"A. Brambilla","raw_affiliation_strings":["Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milan, Italy","Dipt. di Elettron. e Inf., Politec. di Milano, Milan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"Dipt. di Elettron. e Inf., Politec. di Milano, Milan","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064664899","display_name":"Giancarlo Storti Gajani","orcid":"https://orcid.org/0000-0001-8182-7891","observed_orcids":["https://orcid.org/0000-0001-8182-7891"]},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G.S. Gajani","raw_affiliation_strings":["Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milan, Italy","Dipt. di Elettron. e Inf., Politec. di Milano, Milan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"Dipt. di Elettron. e Inf., Politec. di Milano, Milan","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":1.0977,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.87755412,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":94},"biblio":{"volume":"55","issue":"4","first_page":"1064","last_page":"1073"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.5365999937057495,"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":0.5365999937057495,"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/T10244","display_name":"Chaos control and synchronization","score":0.20409999787807465,"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"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.1509000062942505,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/synchronization","display_name":"synchronization","score":0.8299999833106995},{"id":"https://openalex.org/keywords/small-signal-analysis","display_name":"small-signal analysis","score":0.9380000233650208},{"id":"https://openalex.org/keywords/variational-model","display_name":"variational model","score":0.902999997138977},{"id":"https://openalex.org/keywords/perturbation-theory","display_name":"perturbation theory","score":0.49399998784065247},{"id":"https://openalex.org/keywords/phase-shift","display_name":"phase shift","score":0.5899999737739563},{"id":"https://openalex.org/keywords/autonomous-circuits","display_name":"autonomous circuits","score":0.5410000085830688},{"id":"https://openalex.org/keywords/van-der-pol-oscillator","display_name":"Van der Pol oscillator","score":0.9509999752044678},{"id":"https://openalex.org/keywords/steady-state-behavior","display_name":"steady-state behavior","score":0.6060000061988831}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7607544660568237},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.7210533618927002},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.6478747725486755},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5933533906936646},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5604739785194397},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.4881516098976135},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.48617619276046753},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.45249080657958984},{"id":"https://openalex.org/C98010927","wikidata":"https://www.wikidata.org/wiki/Q2081515","display_name":"Van der Pol oscillator","level":3,"score":0.4250304102897644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3810175657272339},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.337017297744751},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3057750463485718},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3050164580345154},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2841242551803589},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06526094675064087},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcsi.2008.916457","doi":"https://doi.org/10.1109/tcsi.2008.916457","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2008.916457","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","ccf-c","cwts-core","dongbi-b","jufo-2","norway-2","poland-140","russia-white-list-1","vabb-shw"],"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 Circuits and Systems I: Regular Papers","raw_type":"journal-article"},{"id":"pmh:oai:re.public.polimi.it:11311/521741","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/521741","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W82367613","https://openalex.org/W950991549","https://openalex.org/W1495851026","https://openalex.org/W1596321532","https://openalex.org/W1876456565","https://openalex.org/W2065787689","https://openalex.org/W2071861249","https://openalex.org/W2072558413","https://openalex.org/W2088678566","https://openalex.org/W2097007944","https://openalex.org/W2111079473","https://openalex.org/W2115477597","https://openalex.org/W2336839322","https://openalex.org/W4214513274","https://openalex.org/W4214617048","https://openalex.org/W4233863580","https://openalex.org/W4246840763"],"related_works":["https://openalex.org/W2321701423","https://openalex.org/W2325589451","https://openalex.org/W2541598132","https://openalex.org/W2367068036","https://openalex.org/W2551989526","https://openalex.org/W2058244203","https://openalex.org/W2578522691","https://openalex.org/W3146825778","https://openalex.org/W2531773183","https://openalex.org/W2071518436"],"abstract_inverted_index":{"Common":[0],"approaches":[1,183],"to":[2,27,38,83,114,162,202],"simulate":[3],"the":[4,21,28,32,39,42,46,75,78,84,88,131,182,186,196,199,203,212,218,221],"steady-state":[5,29],"behavior":[6],"of":[7,16,31,41,45,77,87,153,158,181,206,220],"nonlinear":[8,47,90,133],"periodic":[9,14],"circuits":[10,71],"forced":[11],"by":[12],"a":[13,120,141],"signal":[15,23,80],"small":[17],"amplitude":[18],"assume":[19],"that":[20,194],"forcing":[22,79],"effects":[24,99],"are":[25,72,108,128,192,224],"additive":[26],"solution":[30],"unperturbed":[33,48,89,132],"circuit.":[34,49,91],"This":[35],"assumption":[36],"leads":[37],"adoption":[40],"variational":[43,51,121,126,187],"model":[44,52],"The":[50],"does":[53],"not":[54],"pose":[55],"any":[56,151,159],"particular":[57],"problem":[58],"when":[59,69,217],"dealing":[60],"with":[61,140],"nonautonomous":[62],"circuits,":[63],"but":[64],"must":[65,100],"be":[66,101],"suitably":[67],"formulated":[68],"autonomous":[70],"considered":[73],"and":[74,139,147],"frequency":[76,86],"is":[81,112],"close":[82],"working":[85,135],"We":[92],"show":[93,195],"that,":[94],"in":[95],"this":[96,167,175,179],"case,":[97],"synchronization":[98,106,204],"accounted":[102],"for,":[103],"and,":[104],"as":[105,211],"phenomena":[107],"intrinsically":[109],"nonlinear,":[110],"it":[111],"impossible":[113],"take":[115],"them":[116],"into":[117],"account":[118],"using":[119],"model.":[122,188],"In":[123,165,174],"fact,":[124],"conventional":[125],"models":[127],"derived":[129],"from":[130],"circuit":[134],"at":[136],"steady":[137],"state":[138],"fixed":[142],"relative":[143],"phase":[144,154],"between":[145,198],"perturbation":[146,223],"system,":[148],"i.e.,":[149],"without":[150],"possibility":[152],"shifts":[155],"(that":[156],"is,":[157],"dynamics":[160],"leading":[161],"possible":[163],"synchronization).":[164],"general,":[166],"yields":[168],"inaccurate":[169],"or":[170],"even":[171],"wrong":[172],"results.":[173],"paper,":[176],"we":[177],"investigate":[178],"limitation":[180],"based":[184],"on":[185],"Some":[189],"simulation":[190],"results":[191],"reported":[193],"transition":[197],"nonsynchronization":[200],"region":[201],"one":[205,216],"well-known":[207],"simple":[208],"oscillators,":[209],"such":[210],"Van":[213],"der":[214],"Pol":[215],"parameters":[219],"small-signal":[222],"varied.":[225]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-10T09:11:00.788812","created_date":"2025-10-10T00:00:00"}