{"id":"https://openalex.org/W2003141915","doi":"https://doi.org/10.1109/cca.2014.6981612","title":"Bifurcation analysis using rigorous branch and bound methods","display_name":"Bifurcation analysis using rigorous branch and bound methods","publication_year":2014,"publication_date":"2014-10-01","ids":{"openalex":"https://openalex.org/W2003141915","doi":"https://doi.org/10.1109/cca.2014.6981612","mag":"2003141915"},"language":"en","primary_location":{"id":"doi:10.1109/cca.2014.6981612","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cca.2014.6981612","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 IEEE Conference on Control Applications (CCA)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5101583262","display_name":"Andrew Smith","orcid":"https://orcid.org/0000-0002-9951-6642"},"institutions":[{"id":"https://openalex.org/I1329048335","display_name":"National Institute of Aerospace","ror":"https://ror.org/00fadxs59","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1329048335"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew P. Smith","raw_affiliation_strings":["National Institute of Aerospace, Hampton, Virginia","National Institute of Aerospace, Hampton, Virginia 23666"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Institute of Aerospace, Hampton, Virginia","institution_ids":["https://openalex.org/I1329048335"]},{"raw_affiliation_string":"National Institute of Aerospace, Hampton, Virginia 23666","institution_ids":["https://openalex.org/I1329048335"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112043830","display_name":"Luis G. Crespo","orcid":null},"institutions":[{"id":"https://openalex.org/I1329048335","display_name":"National Institute of Aerospace","ror":"https://ror.org/00fadxs59","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1329048335"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Luis G. Crespo","raw_affiliation_strings":["National Institute of Aerospace, Hampton, Virginia","National Institute of Aerospace, Hampton, Virginia 23666"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Institute of Aerospace, Hampton, Virginia","institution_ids":["https://openalex.org/I1329048335"]},{"raw_affiliation_string":"National Institute of Aerospace, Hampton, Virginia 23666","institution_ids":["https://openalex.org/I1329048335"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016058241","display_name":"C\u00e9sar Mu\u00f1oz","orcid":"https://orcid.org/0000-0003-3579-8254"},"institutions":[{"id":"https://openalex.org/I1319063186","display_name":"Langley Research Center","ror":"https://ror.org/0399mhs52","country_code":"US","type":"facility","lineage":["https://openalex.org/I1319063186","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cesar A. Munoz","raw_affiliation_strings":["NASA Langley Research Center, Hampton, Virginia","NASA Langley Research Center, Hampton Virginia 23681"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NASA Langley Research Center, Hampton, Virginia","institution_ids":["https://openalex.org/I1319063186"]},{"raw_affiliation_string":"NASA Langley Research Center, Hampton Virginia 23681","institution_ids":["https://openalex.org/I1319063186"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102771078","display_name":"Mark Lowenberg","orcid":"https://orcid.org/0000-0002-1373-8237"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Mark H. Lowenberg","raw_affiliation_strings":["Department of Aerospace Engineering, University of Bristol, Bristol, UK","Department of Aerospace Engineering , University of Bristol , Bristol BS8 1TR, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, University of Bristol, Bristol, UK","institution_ids":["https://openalex.org/I36234482"]},{"raw_affiliation_string":"Department of Aerospace Engineering , University of Bristol , Bristol BS8 1TR, UK","institution_ids":["https://openalex.org/I36234482"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"51","issue":null,"first_page":"2095","last_page":"2100"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9939000010490417,"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/bifurcation","display_name":"Bifurcation","score":0.658927321434021},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6420803070068359},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5404456853866577},{"id":"https://openalex.org/keywords/rectangle","display_name":"Rectangle","score":0.5398309826850891},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.49127835035324097},{"id":"https://openalex.org/keywords/numerical-continuation","display_name":"Numerical continuation","score":0.48107266426086426},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4235169291496277},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4208257496356964},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38400059938430786},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3661772906780243},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2622118592262268},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16547676920890808}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.658927321434021},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6420803070068359},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5404456853866577},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.5398309826850891},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.49127835035324097},{"id":"https://openalex.org/C2775978667","wikidata":"https://www.wikidata.org/wiki/Q7069654","display_name":"Numerical continuation","level":4,"score":0.48107266426086426},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4235169291496277},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4208257496356964},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38400059938430786},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3661772906780243},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2622118592262268},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16547676920890808},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/cca.2014.6981612","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cca.2014.6981612","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 IEEE Conference on Control Applications (CCA)","raw_type":"proceedings-article"},{"id":"pmh:oai:casi.ntrs.nasa.gov:20150000570","is_oa":false,"landing_page_url":"http://hdl.handle.net/2060/20150000570","pdf_url":null,"source":{"id":"https://openalex.org/S4377196257","display_name":"NASA STI Repository (National Aeronautics and Space Administration)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210124779","host_organization_name":"National Aeronautics and Space Administration","host_organization_lineage":["https://openalex.org/I4210124779"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CASI","raw_type":"NF1676L-18550"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/931cfb0e-e8c1-4c8f-9282-ae3e4f3d6c33","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/931cfb0e-e8c1-4c8f-9282-ae3e4f3d6c33","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Smith , A P , Crespo , L G , Munoz , C A &amp; Lowenberg , M H 2014 , Bifurcation analysis using rigorous branch and bound methods . in 2014 IEEE Conference on Control Applications, CCA 2014 . , 6981612 , Institute of Electrical and Electronics Engineers (IEEE) , pp. 2095-2100 , 2014 IEEE Conference on Control Applications, CCA 2014 , Juan Les Antibes , France , 8/10/14 . https://doi.org/10.1109/CCA.2014.6981612","raw_type":"contributionToPeriodical"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/931cfb0e-e8c1-4c8f-9282-ae3e4f3d6c33","is_oa":false,"landing_page_url":"https://hdl.handle.net/1983/931cfb0e-e8c1-4c8f-9282-ae3e4f3d6c33","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Smith, A P, Crespo, L G, Munoz, C A & Lowenberg, M H 2014, Bifurcation analysis using rigorous branch and bound methods. in 2014 IEEE Conference on Control Applications, CCA 2014., 6981612, Institute of Electrical and Electronics Engineers (IEEE), pp. 2095-2100. https://doi.org/10.1109/CCA.2014.6981612","raw_type":"contributionToPeriodical"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.5,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1421638684","https://openalex.org/W1507872748","https://openalex.org/W1979084035","https://openalex.org/W1993722858","https://openalex.org/W2018250057","https://openalex.org/W2041313350","https://openalex.org/W2047950861","https://openalex.org/W2096156227","https://openalex.org/W2119763521","https://openalex.org/W2131845859","https://openalex.org/W2186590998","https://openalex.org/W2778765202","https://openalex.org/W3106534923","https://openalex.org/W4254045686","https://openalex.org/W6747209573"],"related_works":["https://openalex.org/W3097020820","https://openalex.org/W2137413016","https://openalex.org/W2094046875","https://openalex.org/W2069713792","https://openalex.org/W110415256","https://openalex.org/W370258010","https://openalex.org/W2334634358","https://openalex.org/W2084334224","https://openalex.org/W2005079237","https://openalex.org/W1877398956"],"abstract_inverted_index":{"For":[0],"the":[1,12,36,61,71,87,95,102,115,123,134,144,178,182,194,210,213],"study":[2],"of":[3,59,73,89,97,122,140,152,177,196,203,212],"nonlinear":[4],"dynamic":[5],"systems,":[6],"it":[7,34,217],"is":[8,43,143,206],"important":[9],"to":[10,35,54,78,107,129,146,165,200,208,222],"locate":[11],"equilibria":[13],"and":[14,32,47,49,63,91,126,221],"bifurcations":[15],"occurring":[16],"within":[17,133,181],"a":[18,25,148,157,174,197],"specified":[19],"computational":[20,135,183,225],"domain.":[21,136],"This":[22,170],"paper":[23],"proposes":[24],"new":[26,41],"approach":[27,42],"for":[28,86,114],"solving":[29],"these":[30],"problems":[31],"compares":[33],"numerical":[37,219],"continuation":[38,220],"method.":[39],"The":[40,112],"based":[44,192],"upon":[45],"branch":[46],"bound":[48],"utilizes":[50],"rigorous":[51],"enclosure":[52],"techniques":[53],"yield":[55],"outer":[56],"bounding":[57],"sets":[58,117],"both":[60],"equilibrium":[62,90,124],"local":[64],"bifurcation":[65,92,116,168,179],"manifolds.":[66],"These":[67],"sets,":[68],"which":[69,172],"comprise":[70],"union":[72],"hyper-rectangles,":[74],"can":[75,118],"be":[76,79,119,186],"made":[77],"as":[80,82],"tight":[81],"desired.":[83],"Sufficient":[84],"conditions":[85],"existence":[88],"points":[93],"taking":[94],"form":[96],"algebraic":[98],"inequality":[99],"constraints":[100],"in":[101],"state-parameter":[103],"space":[104],"are":[105,127,163],"used":[106,207],"calculate":[108],"their":[109],"enclosures":[110,113],"directly.":[111],"computed":[120],"independently":[121],"manifold,":[125],"guaranteed":[128,164],"contain":[130],"all":[131,167],"solutions":[132],"A":[137,189],"further":[138],"advantage":[139],"this":[141],"method":[142,214],"ability":[145],"compute":[147],"near-maximally":[149],"sized":[150],"hyper-rectangle":[151],"high":[153],"dimension":[154],"centered":[155],"at":[156],"fixed":[158],"parameter-state":[159],"point":[160],"whose":[161],"elements":[162],"exclude":[166],"points.":[169],"hyper-rectangle,":[171],"requires":[173],"global":[175],"description":[176],"manifold":[180],"domain,":[184],"cannot":[185],"obtained":[187],"otherwise.":[188],"test":[190],"case,":[191],"on":[193],"dynamics":[195],"UAV":[198],"subject":[199],"uncertain":[201],"center":[202],"gravity":[204],"location,":[205],"illustrate":[209],"efficacy":[211],"by":[215],"comparing":[216],"with":[218],"evaluate":[223],"its":[224],"complexity.":[226]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
