{"id":"https://openalex.org/W2079345229","doi":"https://doi.org/10.1142/s0218127413501964","title":"STABILITY BOUNDARY CHARACTERIZATION OF NONLINEAR AUTONOMOUS DYNAMICAL SYSTEMS IN THE PRESENCE OF A SUPERCRITICAL HOPF EQUILIBRIUM POINT","display_name":"STABILITY BOUNDARY CHARACTERIZATION OF NONLINEAR AUTONOMOUS DYNAMICAL SYSTEMS IN THE PRESENCE OF A SUPERCRITICAL HOPF EQUILIBRIUM POINT","publication_year":2013,"publication_date":"2013-12-01","ids":{"openalex":"https://openalex.org/W2079345229","doi":"https://doi.org/10.1142/s0218127413501964","mag":"2079345229"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127413501964","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413501964","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":true,"oa_status":"green","oa_url":"http://dx.doi.org/10.1142/S0218127413501964","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007349471","display_name":"Josaphat R. R. Gouveia","orcid":null},"institutions":[{"id":"https://openalex.org/I130913789","display_name":"Instituto Federal da Bahia","ror":"https://ror.org/01tzdej37","country_code":"BR","type":"education","lineage":["https://openalex.org/I130913789"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"JOSAPHAT R. R. GOUVEIA","raw_affiliation_strings":["Mathematics of Collegiate, College Eun\u00e1polis \u2013 Federal Institute of Bahia, 458222-000, Eun\u00e1polis, BA, Brazil"],"affiliations":[{"raw_affiliation_string":"Mathematics of Collegiate, College Eun\u00e1polis \u2013 Federal Institute of Bahia, 458222-000, Eun\u00e1polis, BA, Brazil","institution_ids":["https://openalex.org/I130913789"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025187387","display_name":"Fab\u00edolo Moraes Amaral","orcid":"https://orcid.org/0000-0002-9814-9385"},"institutions":[{"id":"https://openalex.org/I130913789","display_name":"Instituto Federal da Bahia","ror":"https://ror.org/01tzdej37","country_code":"BR","type":"education","lineage":["https://openalex.org/I130913789"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"FAB\u00cdOLO MORAES AMARAL","raw_affiliation_strings":["Mathematics of Collegiate, College Eun\u00e1polis \u2013 Federal Institute of Bahia, 458222-000, Eun\u00e1polis, BA, Brazil"],"affiliations":[{"raw_affiliation_string":"Mathematics of Collegiate, College Eun\u00e1polis \u2013 Federal Institute of Bahia, 458222-000, Eun\u00e1polis, BA, Brazil","institution_ids":["https://openalex.org/I130913789"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019662484","display_name":"Lu\u00eds Alberto","orcid":"https://orcid.org/0000-0002-4195-4455"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"LU\u00cdS F. C. ALBERTO","raw_affiliation_strings":["University of S\u00e3o Paulo, School of Engineering of S\u00e3o Carlos, Department of Electrical Engineering, 13.566-590 S\u00e3o Carlos, S\u00e3o Paulo, Brazil"],"affiliations":[{"raw_affiliation_string":"University of S\u00e3o Paulo, School of Engineering of S\u00e3o Carlos, Department of Electrical Engineering, 13.566-590 S\u00e3o Carlos, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007349471"],"corresponding_institution_ids":["https://openalex.org/I130913789"],"apc_list":null,"apc_paid":null,"fwci":4.2402,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.93677575,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"23","issue":"12","first_page":"1350196","last_page":"1350196"},"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":0.9972000122070312,"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":0.9972000122070312,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9950000047683716,"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/boundary","display_name":"Boundary (topology)","score":0.6805424094200134},{"id":"https://openalex.org/keywords/transversality","display_name":"Transversality","score":0.6773155927658081},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6312900185585022},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.5995540618896484},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.5874097347259521},{"id":"https://openalex.org/keywords/supercritical-fluid","display_name":"Supercritical fluid","score":0.5396902561187744},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.47562411427497864},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4754364490509033},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4478439688682556},{"id":"https://openalex.org/keywords/hyperbolic-equilibrium-point","display_name":"Hyperbolic equilibrium point","score":0.431610643863678},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.3291545808315277},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17070960998535156},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.104977548122406},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.08286029100418091},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.06342190504074097}],"concepts":[{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6805424094200134},{"id":"https://openalex.org/C24167531","wikidata":"https://www.wikidata.org/wiki/Q2300767","display_name":"Transversality","level":2,"score":0.6773155927658081},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6312900185585022},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.5995540618896484},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.5874097347259521},{"id":"https://openalex.org/C118419359","wikidata":"https://www.wikidata.org/wiki/Q682585","display_name":"Supercritical fluid","level":2,"score":0.5396902561187744},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.47562411427497864},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4754364490509033},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4478439688682556},{"id":"https://openalex.org/C51691630","wikidata":"https://www.wikidata.org/wiki/Q3925833","display_name":"Hyperbolic equilibrium point","level":4,"score":0.431610643863678},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.3291545808315277},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17070960998535156},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.104977548122406},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.08286029100418091},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.06342190504074097},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"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/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127413501964","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127413501964","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:002444232","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1142/S0218127413501964","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:002444232","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1142/S0218127413501964","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320323339","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W20229","https://openalex.org/W1531897854","https://openalex.org/W1932984273","https://openalex.org/W1965385865","https://openalex.org/W1975219960","https://openalex.org/W1979693273","https://openalex.org/W1985821177","https://openalex.org/W1999023593","https://openalex.org/W2042261048","https://openalex.org/W2052657810","https://openalex.org/W2062427814","https://openalex.org/W2077161564","https://openalex.org/W2078899217","https://openalex.org/W2081257826","https://openalex.org/W2089876099","https://openalex.org/W2110538135","https://openalex.org/W2145258958","https://openalex.org/W2154295268","https://openalex.org/W2158006846","https://openalex.org/W2495772062","https://openalex.org/W4212928962","https://openalex.org/W4214513274","https://openalex.org/W4231941367","https://openalex.org/W4240376470","https://openalex.org/W4242448156","https://openalex.org/W4297440205","https://openalex.org/W4299993032","https://openalex.org/W4310301864"],"related_works":["https://openalex.org/W1987790493","https://openalex.org/W1975783007","https://openalex.org/W2038701038","https://openalex.org/W1996991127","https://openalex.org/W2382752082","https://openalex.org/W1986426368","https://openalex.org/W2363522146","https://openalex.org/W2061491569","https://openalex.org/W2243704867","https://openalex.org/W2385265028"],"abstract_inverted_index":{"A":[0],"complete":[1],"characterization":[2],"of":[3,6,12,14,24,28,44,55,59,76],"the":[4,7,22,33,36,50,60,66,71,77,87],"boundary":[5,52,68],"stability":[8,34,51,67,88],"region":[9],"(or":[10],"area":[11],"attraction)":[13],"nonlinear":[15],"autonomous":[16],"dynamical":[17],"systems":[18],"is":[19,47,53],"developed":[20],"admitting":[21],"existence":[23],"a":[25,42],"particular":[26],"type":[27],"nonhyperbolic":[29],"equilibrium":[30,39,62,84],"point":[31],"on":[32,65,86],"boundary,":[35],"supercritical":[37,82],"Hopf":[38,83],"point.":[40],"Under":[41],"condition":[43],"transversality,":[45],"it":[46],"shown":[48],"that":[49],"comprised":[54],"all":[56],"stable":[57],"manifolds":[58,75],"hyperbolic":[61],"points":[63,85],"lying":[64],"union":[69],"with":[70],"center-stable":[72],"and\\or":[73],"center":[74],"type-k,":[78],"k":[79],"\u2265":[80],"1,":[81],"boundary.":[89]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}