{"id":"https://openalex.org/W2143936181","doi":"https://doi.org/10.1142/s0218127412502719","title":"ANDRONOV\u2013HOPF BIFURCATION OF HIGHER CODIMENSIONS IN A LI\u00c9NARD SYSTEM","display_name":"ANDRONOV\u2013HOPF BIFURCATION OF HIGHER CODIMENSIONS IN A LI\u00c9NARD SYSTEM","publication_year":2012,"publication_date":"2012-11-01","ids":{"openalex":"https://openalex.org/W2143936181","doi":"https://doi.org/10.1142/s0218127412502719","mag":"2143936181"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127412502719","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127412502719","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":["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/A5001786215","display_name":"Alexander Grin","orcid":"https://orcid.org/0000-0002-0955-9789"},"institutions":[{"id":"https://openalex.org/I4210132691","display_name":"Grodno State Medical University","ror":"https://ror.org/039ryp971","country_code":"BY","type":"education","lineage":["https://openalex.org/I4210132691"]}],"countries":["BY"],"is_corresponding":true,"raw_author_name":"ALEXANDER GRIN","raw_affiliation_strings":["Grodno State University, Ozheshko Street 22, 230023 Grodno, Belarus"],"affiliations":[{"raw_affiliation_string":"Grodno State University, Ozheshko Street 22, 230023 Grodno, Belarus","institution_ids":["https://openalex.org/I4210132691"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110090871","display_name":"\u041a. R. Schneider","orcid":null},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"KLAUS R. SCHNEIDER","raw_affiliation_strings":["Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001786215"],"corresponding_institution_ids":["https://openalex.org/I4210132691"],"apc_list":null,"apc_paid":null,"fwci":0.4191,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.64277027,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","issue":"11","first_page":"1250271","last_page":"1250271"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9988999962806702,"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":0.9864000082015991,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7679868340492249},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.7077760100364685},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.5474461317062378},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5450050234794617},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.5316826701164246},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5234817266464233},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.47583627700805664},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4571644067764282},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.45338308811187744},{"id":"https://openalex.org/keywords/bogdanov\u2013takens-bifurcation","display_name":"Bogdanov\u2013Takens bifurcation","score":0.44732141494750977},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1932103931903839},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18174421787261963},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.17949798703193665}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7679868340492249},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.7077760100364685},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.5474461317062378},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5450050234794617},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.5316826701164246},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5234817266464233},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.47583627700805664},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4571644067764282},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.45338308811187744},{"id":"https://openalex.org/C22257346","wikidata":"https://www.wikidata.org/wiki/Q4937510","display_name":"Bogdanov\u2013Takens bifurcation","level":5,"score":0.44732141494750977},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1932103931903839},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18174421787261963},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.17949798703193665},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127412502719","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127412502719","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":"mag:2776850007","is_oa":false,"landing_page_url":"https://www.elib.grsu.by/doc/1424","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W615448849","https://openalex.org/W1539776296","https://openalex.org/W1992346078","https://openalex.org/W1992514772","https://openalex.org/W2004027758","https://openalex.org/W2026785981","https://openalex.org/W2074786370","https://openalex.org/W2074879692","https://openalex.org/W2182274314","https://openalex.org/W2324297661","https://openalex.org/W4214513274"],"related_works":["https://openalex.org/W2546487931","https://openalex.org/W3207962526","https://openalex.org/W2385240050","https://openalex.org/W3113797113","https://openalex.org/W4311619526","https://openalex.org/W1197805819","https://openalex.org/W2356715721","https://openalex.org/W2803928976","https://openalex.org/W4379507489","https://openalex.org/W2342467592"],"abstract_inverted_index":{"We":[0,43,63],"study":[1],"a":[2,30,45],"polynomial":[3],"Li\u00e9nard":[4],"system":[5],"depending":[6],"on":[7,56],"three":[8,94],"parameters":[9,59],"a,":[10],"b,":[11],"c":[12],"and":[13,39,49,61,65,72,93],"exhibiting":[14],"the":[15,22,34,51,57,68,76,79,84],"following":[16],"properties:":[17],"(i)":[18],"The":[19],"origin":[20,35,77],"is":[21],"unique":[23],"equilibrium":[24],"for":[25],"all":[26],"parameters.":[27],"(ii)":[28],"If":[29],"crosses":[31],"zero,":[32],"then":[33],"changes":[36],"its":[37],"stability,":[38],"Andronov\u2013Hopf":[40,54,98],"bifurcation":[41,55],"arises.":[42],"consider":[44],"as":[46],"control":[47],"parameter":[48,80],"investigate":[50],"dependence":[52],"of":[53,70,86,90,96],"\"unfolding\"":[58],"b":[60],"c.":[62],"establish":[64],"describe":[66],"analytically":[67],"existence":[69,85],"surfaces":[71],"curves":[73],"located":[74],"near":[75],"in":[78],"space":[81],"connected":[82],"with":[83],"small-amplitude":[87],"limit":[88],"cycles":[89],"multiplicity":[91],"two":[92],"(existence":[95],"degenerate":[97],"bifurcation).":[99]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
