{"id":"https://openalex.org/W2110197045","doi":"https://doi.org/10.1109/cdc.2008.4739082","title":"Control of the Hopf bifurcation in the Takens-Bogdanov bifurcation","display_name":"Control of the Hopf bifurcation in the Takens-Bogdanov bifurcation","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2110197045","doi":"https://doi.org/10.1109/cdc.2008.4739082","mag":"2110197045"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2008.4739082","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4739082","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th IEEE Conference on Decision and Control","raw_type":"proceedings-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/A5070267007","display_name":"Francisco Armando Carrillo Navarro","orcid":null},"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":false,"raw_author_name":"Francisco Armando Carrillo Navarro","raw_affiliation_strings":["Mathematics Department, Sonora University, Hermosillo, Sonora, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Sonora University, Hermosillo, Sonora, Mexico","institution_ids":["https://openalex.org/I4061448"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080440363","display_name":"Fernando Verduzco Gonz\u00e1lez","orcid":null},"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":false,"raw_author_name":"Fernando Verduzco Gonzalez","raw_affiliation_strings":["Mathematics Department, Sonora University, Hermosillo, Sonora, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Sonora University, Hermosillo, Sonora, Mexico","institution_ids":["https://openalex.org/I4061448"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15756046,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"4438","last_page":"4443"},"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":0.9994000196456909,"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":0.9994000196456909,"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":0.9947999715805054,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9904999732971191,"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/bogdanov\u2013takens-bifurcation","display_name":"Bogdanov\u2013Takens bifurcation","score":0.8827233910560608},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.8260883092880249},{"id":"https://openalex.org/keywords/pitchfork-bifurcation","display_name":"Pitchfork bifurcation","score":0.8000614643096924},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.7922574281692505},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.6935299038887024},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.6738723516464233},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.6732957363128662},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.6013166904449463},{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.5983612537384033},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5779709219932556},{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.5532702803611755},{"id":"https://openalex.org/keywords/heteroclinic-bifurcation","display_name":"Heteroclinic bifurcation","score":0.486575722694397},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.43341535329818726},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4302389919757843},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4026969373226166},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.31054264307022095},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21803945302963257},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1788545846939087},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1233510971069336},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0588318407535553}],"concepts":[{"id":"https://openalex.org/C22257346","wikidata":"https://www.wikidata.org/wiki/Q4937510","display_name":"Bogdanov\u2013Takens bifurcation","level":5,"score":0.8827233910560608},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.8260883092880249},{"id":"https://openalex.org/C155092403","wikidata":"https://www.wikidata.org/wiki/Q1785924","display_name":"Pitchfork bifurcation","level":5,"score":0.8000614643096924},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.7922574281692505},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.6935299038887024},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.6738723516464233},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.6732957363128662},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.6013166904449463},{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.5983612537384033},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5779709219932556},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.5532702803611755},{"id":"https://openalex.org/C73888704","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Heteroclinic bifurcation","level":5,"score":0.486575722694397},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.43341535329818726},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4302389919757843},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4026969373226166},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.31054264307022095},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21803945302963257},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1788545846939087},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1233510971069336},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0588318407535553},{"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:10.1109/cdc.2008.4739082","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4739082","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.5899999737739563,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1509966585","https://openalex.org/W1567812234","https://openalex.org/W2008995486","https://openalex.org/W2036219060","https://openalex.org/W2038150727","https://openalex.org/W2038472812","https://openalex.org/W2070363926","https://openalex.org/W2074843101","https://openalex.org/W2089876099","https://openalex.org/W2480701976","https://openalex.org/W2739685101"],"related_works":["https://openalex.org/W2356715721","https://openalex.org/W2049615654","https://openalex.org/W2025138898","https://openalex.org/W2110197045","https://openalex.org/W2923981205","https://openalex.org/W1982778171","https://openalex.org/W2775656422","https://openalex.org/W2054075447","https://openalex.org/W2028337061","https://openalex.org/W2312845532"],"abstract_inverted_index":{"It":[0],"is":[1,14,37,51],"a":[2,7,30,54],"well-known":[3],"result":[4],"that":[5,20,59],"in":[6,34],"versal":[8],"deformation":[9],"of":[10],"the":[11,35,44,49,60,64],"Takens-Bogdanov":[12,45],"bifurcation":[13],"possible":[15],"to":[16,52],"find":[17],"dynamical":[18],"systems":[19],"undergo":[21],"saddle-node,":[22],"homoclinic":[23],"and":[24,47],"Hopf":[25,67],"bifurcations.":[26],"In":[27],"this":[28],"document":[29],"nonlinear":[31],"control":[32,56],"system":[33,62],"plane":[36],"considered,":[38],"whose":[39],"nominal":[40],"vector":[41],"field":[42],"undergoes":[43,63],"bifurcation,":[46],"then":[48],"idea":[50],"design":[53],"scalar":[55],"law":[57],"such":[58],"closed-loop":[61],"called":[65],"controllable":[66],"bifurcation.":[68]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
