{"id":"https://openalex.org/W2160502717","doi":"https://doi.org/10.1142/s0218127416500103","title":"Oscillations and Synchronization in a System of Three Reactively Coupled Oscillators","display_name":"Oscillations and Synchronization in a System of Three Reactively Coupled Oscillators","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2160502717","doi":"https://doi.org/10.1142/s0218127416500103","mag":"2160502717"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416500103","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500103","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1503.05313","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Alexander P. Kuznetsov","orcid":null},"institutions":[{"id":"https://openalex.org/I4210152187","display_name":"Kotelnikov Institute of Radioengineering and Electronics of the Russian Academy of Sciences","ror":"https://ror.org/05gbyky62","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210096333","https://openalex.org/I4210152187"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Alexander P. Kuznetsov","raw_affiliation_strings":["Kotel\u2019nikov\u2019s Institute of Radio-Engineering, and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov 410019, Russian Federation"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kotel\u2019nikov\u2019s Institute of Radio-Engineering, and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov 410019, Russian Federation","institution_ids":["https://openalex.org/I4210152187"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Ludmila V. Turukina","orcid":null},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]},{"id":"https://openalex.org/I4210152187","display_name":"Kotelnikov Institute of Radioengineering and Electronics of the Russian Academy of Sciences","ror":"https://ror.org/05gbyky62","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210096333","https://openalex.org/I4210152187"]}],"countries":["DE","RU"],"is_corresponding":false,"raw_author_name":"Ludmila V. Turukina","raw_affiliation_strings":["Department of Physics and Astronomy, Potsdam University, 14476 Potsdam-Golm, Germany","Kotel\u2019nikov\u2019s Institute of Radio-Engineering, and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov 410019, Russian Federation"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy, Potsdam University, 14476 Potsdam-Golm, Germany","institution_ids":["https://openalex.org/I176453806"]},{"raw_affiliation_string":"Kotel\u2019nikov\u2019s Institute of Radio-Engineering, and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov 410019, Russian Federation","institution_ids":["https://openalex.org/I4210152187"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Nikolai Yu. Chernyshov","orcid":null},"institutions":[{"id":"https://openalex.org/I125219893","display_name":"Saratov State University","ror":"https://ror.org/05jcsqx24","country_code":"RU","type":"education","lineage":["https://openalex.org/I125219893"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Nikolai Yu. Chernyshov","raw_affiliation_strings":["Saratov State University, Astrachanskaya 83, Saratov 410012, Russian Federation"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saratov State University, Astrachanskaya 83, Saratov 410012, Russian Federation","institution_ids":["https://openalex.org/I125219893"]}]},{"author_position":"last","author":{"id":null,"display_name":"Yuliya V. Sedova","orcid":null},"institutions":[{"id":"https://openalex.org/I4210152187","display_name":"Kotelnikov Institute of Radioengineering and Electronics of the Russian Academy of Sciences","ror":"https://ror.org/05gbyky62","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210096333","https://openalex.org/I4210152187"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Yuliya V. Sedova","raw_affiliation_strings":["Kotel\u2019nikov\u2019s Institute of Radio-Engineering, and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov 410019, Russian Federation"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kotel\u2019nikov\u2019s Institute of Radio-Engineering, and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov 410019, Russian Federation","institution_ids":["https://openalex.org/I4210152187"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3967,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.61547158,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"26","issue":"01","first_page":"1650010","last_page":"1650010"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.3750999867916107,"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"}},"topics":[{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.3750999867916107,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.22419999539852142,"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":0.19619999825954437,"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/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.7232999801635742},{"id":"https://openalex.org/keywords/van-der-pol-oscillator","display_name":"Van der Pol oscillator","score":0.7146000266075134},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.6786999702453613},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.6154000163078308},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6000999808311462},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5461999773979187},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.397599995136261},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.38019999861717224},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.3716999888420105}],"concepts":[{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.7232999801635742},{"id":"https://openalex.org/C98010927","wikidata":"https://www.wikidata.org/wiki/Q2081515","display_name":"Van der Pol oscillator","level":3,"score":0.7146000266075134},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.6786999702453613},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.6154000163078308},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6000999808311462},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5773000121116638},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5461999773979187},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4065000116825104},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.397599995136261},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.38019999861717224},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.3716999888420105},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3637000024318695},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.3610999882221222},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.33869999647140503},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.33399999141693115},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.3303999900817871},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3253999948501587},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C111097370","wikidata":"https://www.wikidata.org/wiki/Q10969923","display_name":"Synchronization networks","level":4,"score":0.27399998903274536},{"id":"https://openalex.org/C194027367","wikidata":"https://www.wikidata.org/wiki/Q4420475","display_name":"Phase synchronization","level":3,"score":0.27239999175071716},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.26820001006126404},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C2989183493","wikidata":"https://www.wikidata.org/wiki/Q2040587","display_name":"Phase locking","level":3,"score":0.260699987411499},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.25839999318122864},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.25529998540878296}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127416500103","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416500103","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1503.05313","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.05313","pdf_url":"https://arxiv.org/pdf/1503.05313","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1503.05313","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.05313","pdf_url":"https://arxiv.org/pdf/1503.05313","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W111157985","https://openalex.org/W950991549","https://openalex.org/W1606811344","https://openalex.org/W1655770772","https://openalex.org/W1855719876","https://openalex.org/W1983879740","https://openalex.org/W1987699357","https://openalex.org/W1989208500","https://openalex.org/W2003666303","https://openalex.org/W2008985884","https://openalex.org/W2010363060","https://openalex.org/W2011941326","https://openalex.org/W2019474388","https://openalex.org/W2033632707","https://openalex.org/W2068916507","https://openalex.org/W2069032592","https://openalex.org/W2073693520","https://openalex.org/W2082760835","https://openalex.org/W2086383234","https://openalex.org/W2089468210","https://openalex.org/W2093120175","https://openalex.org/W2105763846","https://openalex.org/W2139803627","https://openalex.org/W2159653980","https://openalex.org/W2229470139","https://openalex.org/W2334687011","https://openalex.org/W2964183488","https://openalex.org/W4214617048","https://openalex.org/W4248666415","https://openalex.org/W4254677853"],"related_works":[],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2],"system":[3,31],"of":[4,21,29,36,44,53],"three":[5],"interacting":[6],"van":[7],"der":[8],"Pol":[9],"oscillators":[10],"with":[11,41],"reactive":[12,55],"coupling.":[13],"Phase":[14],"equations":[15],"are":[16,57],"derived,":[17],"using":[18],"proper":[19],"order":[20],"expansion":[22],"over":[23],"the":[24,30,37,42,54],"coupling":[25,56],"parameter.":[26],"The":[27],"dynamics":[28],"is":[32],"studied":[33],"by":[34],"means":[35],"bifurcation":[38],"analysis":[39],"and":[40,49],"method":[43],"Lyapunov":[45],"exponent":[46],"charts.":[47],"Essential":[48],"physically":[50],"meaningful":[51],"features":[52],"discussed.":[58]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2016-06-24T00:00:00"}