{"id":"https://openalex.org/W2070363926","doi":"https://doi.org/10.1142/s0218127407017434","title":"CONTROL OF CODIMENSION ONE STATIONARY BIFURCATIONS","display_name":"CONTROL OF CODIMENSION ONE STATIONARY BIFURCATIONS","publication_year":2007,"publication_date":"2007-02-01","ids":{"openalex":"https://openalex.org/W2070363926","doi":"https://doi.org/10.1142/s0218127407017434","mag":"2070363926"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127407017434","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407017434","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/A5021373250","display_name":"Fernando Verduzco","orcid":"https://orcid.org/0000-0002-3237-2090"},"institutions":[{"id":"https://openalex.org/I4061448","display_name":"Universidad de Sonora","ror":"https://ror.org/00c32gy34","country_code":"MX","type":"education","lineage":["https://openalex.org/I4061448"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"FERNANDO VERDUZCO","raw_affiliation_strings":["Department of Mathematics, University of Sonora, Rosales and Transversal, Hermosillo, Sonora, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sonora, Rosales and Transversal, Hermosillo, Sonora, Mexico","institution_ids":["https://openalex.org/I4061448"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5021373250"],"corresponding_institution_ids":["https://openalex.org/I4061448"],"apc_list":null,"apc_paid":null,"fwci":1.7682,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.82387606,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"17","issue":"02","first_page":"575","last_page":"582"},"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":0.9957000017166138,"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":0.9957000017166138,"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/T10244","display_name":"Chaos control and synchronization","score":0.9872000217437744,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9871000051498413,"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/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.7581532001495361},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.7498730421066284},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7067641019821167},{"id":"https://openalex.org/keywords/codimension","display_name":"Codimension","score":0.6775352954864502},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.6262614727020264},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6087450981140137},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.6064404249191284},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.5371509194374084},{"id":"https://openalex.org/keywords/heteroclinic-bifurcation","display_name":"Heteroclinic bifurcation","score":0.5054216384887695},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4993610382080078},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.49706438183784485},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.46972692012786865},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.438819020986557},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.43795543909072876},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.43155378103256226},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.4196022152900696},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.355915904045105},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.29509758949279785},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18569308519363403},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17575708031654358},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.13389524817466736},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12329259514808655},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.10438823699951172}],"concepts":[{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.7581532001495361},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.7498730421066284},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7067641019821167},{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.6775352954864502},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.6262614727020264},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6087450981140137},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.6064404249191284},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.5371509194374084},{"id":"https://openalex.org/C73888704","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Heteroclinic bifurcation","level":5,"score":0.5054216384887695},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4993610382080078},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.49706438183784485},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.46972692012786865},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.438819020986557},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43795543909072876},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.43155378103256226},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.4196022152900696},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.355915904045105},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.29509758949279785},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18569308519363403},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17575708031654358},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.13389524817466736},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12329259514808655},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.10438823699951172},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127407017434","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407017434","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.6800000071525574,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1581560749","https://openalex.org/W2008995486","https://openalex.org/W2026246097","https://openalex.org/W2031405129","https://openalex.org/W2036219060","https://openalex.org/W2038150727","https://openalex.org/W2039041284","https://openalex.org/W2089133395","https://openalex.org/W2094913794","https://openalex.org/W2170141373","https://openalex.org/W4293079218","https://openalex.org/W4294967943"],"related_works":["https://openalex.org/W2019027784","https://openalex.org/W2078078632","https://openalex.org/W2923981205","https://openalex.org/W2559450076","https://openalex.org/W2546487931","https://openalex.org/W3008253414","https://openalex.org/W2102865807","https://openalex.org/W2347648614","https://openalex.org/W2271873789","https://openalex.org/W3081645617"],"abstract_inverted_index":{"The":[0],"control":[1,13,38],"of":[2],"the":[3,27,42,54,59],"saddle-node,":[4],"transcritical":[5],"and":[6],"pitchfork":[7],"bifurcations":[8],"are":[9,30],"analyzed":[10],"in":[11,48],"nonlinear":[12],"systems":[14],"with":[15],"one":[16],"zero":[17],"eigenvalue.":[18],"It":[19],"is":[20,33,63],"shown":[21],"that,":[22],"provided":[23],"some":[24,49],"conditions":[25],"on":[26],"vector":[28],"fields":[29],"satisfied,":[31],"it":[32],"possible":[34],"to":[35,56],"design":[36],"a":[37],"law":[39],"such":[40],"that":[41],"bifurcation":[43],"properties":[44],"can":[45],"be":[46],"modified":[47],"desirable":[50],"way.":[51],"To":[52],"simplify":[53],"analysis":[55],"dimension":[57],"one,":[58],"center":[60],"manifold":[61],"theory":[62],"used.":[64]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
