{"id":"https://openalex.org/W2736490243","doi":"https://doi.org/10.1134/s0005117917070050","title":"Stability and synchronization of oscillators: New Lyapunov functions","display_name":"Stability and synchronization of oscillators: New Lyapunov functions","publication_year":2017,"publication_date":"2017-07-01","ids":{"openalex":"https://openalex.org/W2736490243","doi":"https://doi.org/10.1134/s0005117917070050","mag":"2736490243"},"language":"en","primary_location":{"id":"doi:10.1134/s0005117917070050","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0005117917070050","pdf_url":null,"source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote Control","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/A5032697658","display_name":"B. T. Polyak","orcid":"https://orcid.org/0000-0002-1898-2984"},"institutions":[{"id":"https://openalex.org/I125989756","display_name":"Skolkovo Institute of Science and Technology","ror":"https://ror.org/03f9nc143","country_code":"RU","type":"education","lineage":["https://openalex.org/I125989756"]},{"id":"https://openalex.org/I4210157430","display_name":"V. A. Trapeznikov Institute of Control Sciences","ror":"https://ror.org/05f3yt521","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210157430","https://openalex.org/I4210164537"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"B. T. Polyak","raw_affiliation_strings":["Center for Energy Systems, Skolkovo Institute of Science and Technology, Moscow, Russia","Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Energy Systems, Skolkovo Institute of Science and Technology, Moscow, Russia","institution_ids":["https://openalex.org/I125989756"]},{"raw_affiliation_string":"Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia","institution_ids":["https://openalex.org/I4210157430"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004694966","display_name":"Ya. I. Kvinto","orcid":null},"institutions":[{"id":"https://openalex.org/I4210157430","display_name":"V. A. Trapeznikov Institute of Control Sciences","ror":"https://ror.org/05f3yt521","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210157430","https://openalex.org/I4210164537"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Ya. I. Kvinto","raw_affiliation_strings":["Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia","institution_ids":["https://openalex.org/I4210157430"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032697658"],"corresponding_institution_ids":["https://openalex.org/I125989756","https://openalex.org/I4210157430"],"apc_list":null,"apc_paid":null,"fwci":0.4207,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.65876082,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"78","issue":"7","first_page":"1234","last_page":"1242"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998000264167786,"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":0.9998000264167786,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/synchronization","display_name":"Synchronization (alternating current)","score":0.7031656503677368},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.681717038154602},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6639419794082642},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5566585063934326},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5423948764801025},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.48254579305648804},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4692784547805786},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.46606022119522095},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4527835547924042},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4183323085308075},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.41376951336860657},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29871007800102234},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.21949514746665955},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1978602111339569},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.06936982274055481},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0673518180847168}],"concepts":[{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.7031656503677368},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.681717038154602},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6639419794082642},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5566585063934326},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5423948764801025},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.48254579305648804},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4692784547805786},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.46606022119522095},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4527835547924042},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4183323085308075},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.41376951336860657},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29871007800102234},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.21949514746665955},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1978602111339569},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.06936982274055481},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0673518180847168},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0005117917070050","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0005117917070050","pdf_url":null,"source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.7699999809265137,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320324099","display_name":"Russian Science Foundation","ror":"https://ror.org/03y2gwe85"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W592936356","https://openalex.org/W607713943","https://openalex.org/W628746759","https://openalex.org/W649457022","https://openalex.org/W1509227760","https://openalex.org/W1521492382","https://openalex.org/W2015084265","https://openalex.org/W2017295476","https://openalex.org/W2049343272","https://openalex.org/W2110472103","https://openalex.org/W2289970804","https://openalex.org/W2300974746","https://openalex.org/W2470020017","https://openalex.org/W2516953637","https://openalex.org/W2588793982","https://openalex.org/W3207989330"],"related_works":["https://openalex.org/W2380573388","https://openalex.org/W2369636957","https://openalex.org/W1517908938","https://openalex.org/W2544687545","https://openalex.org/W2375357969","https://openalex.org/W2151535469","https://openalex.org/W2371841467","https://openalex.org/W4248830168","https://openalex.org/W2902867629","https://openalex.org/W2889330909"],"abstract_inverted_index":{"The":[0],"analysis":[1,104,148],"of":[2,5,10,17,30,34,57,59,85,90,92,105,109,111,124,132,135,141,149],"asymptotic":[3],"stability":[4],"nonlinear":[6],"oscillator":[7],"is":[8,21,144],"one":[9],"the":[11,15,28,31,35,38,55,60,83,88,130,147],"classical":[12],"problems":[13],"in":[14,146],"theory":[16],"oscillations.":[18],"Usually,":[19],"it":[20],"solved":[22],"by":[23],"exploiting":[24],"Lyapunov":[25,72],"functions":[26],"having":[27],"meaning":[29],"full":[32],"energy":[33],"system.":[36],"However,":[37],"Barbashin\u2013Krasovskii":[39],"theorem":[40],"has":[41],"to":[42,62,129],"be":[43,52,96],"used":[44],"along":[45],"this":[46,66,80,142],"way,":[47],"and":[48,87],"no":[49],"estimates":[50],"can":[51,95],"found":[53],"for":[54],"rate":[56,84],"convergence":[58,86],"trajectories":[61],"equilibria":[63,93],"points.":[64],"In":[65],"paper":[67],"we":[68],"propose":[69],"a":[70],"different":[71],"function":[73],"which":[74],"lacks":[75],"transparent":[76],"physical":[77],"meaning.":[78],"With":[79],"function,":[81],"both":[82],"domain":[89],"attraction":[91],"points":[94],"estimated.":[97],"This":[98],"result":[99],"also":[100,138],"enables":[101],"an":[102],"efficient":[103],"another":[106],"problem,":[107],"synchronization":[108,120],"oscillations":[110],"two":[112],"oscillators.":[113],"We":[114],"formulate":[115],"conditions":[116],"that":[117],"guarantee":[118],"frequency":[119],"and,":[121],"on":[122],"top":[123],"that,":[125],"phase":[126],"synchronization.":[127],"Generalizations":[128],"case":[131],"arbitrary":[133],"number":[134],"oscillators":[136],"are":[137],"discussed;":[139],"solution":[140],"problem":[143],"crucial":[145],"power":[150],"systems.":[151]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}