{"id":"https://openalex.org/W2027333056","doi":"https://doi.org/10.1137/030600746","title":"Numerical Continuation of Bifurcations of Limit Cycles in MATLAB","display_name":"Numerical Continuation of Bifurcations of Limit Cycles in MATLAB","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2027333056","doi":"https://doi.org/10.1137/030600746","mag":"2027333056"},"language":"en","primary_location":{"id":"doi:10.1137/030600746","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030600746","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5067569718","display_name":"W. Govaerts","orcid":"https://orcid.org/0000-0002-1081-6252"},"institutions":[{"id":"https://openalex.org/I2801227569","display_name":"Ghent University Hospital","ror":"https://ror.org/00xmkp704","country_code":"BE","type":"healthcare","lineage":["https://openalex.org/I2801227569"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Willy Govaerts","raw_affiliation_strings":["Ghent University"],"affiliations":[{"raw_affiliation_string":"Ghent University","institution_ids":["https://openalex.org/I2801227569"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007494022","display_name":"Yuri A. Kuznetsov","orcid":"https://orcid.org/0000-0003-2289-0801"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Yuri A. Kuznetsov","raw_affiliation_strings":["Utrecht university >  >  >  >"],"affiliations":[{"raw_affiliation_string":"Utrecht university >  >  >  >","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023454427","display_name":"Annick Dhooge","orcid":null},"institutions":[{"id":"https://openalex.org/I2801227569","display_name":"Ghent University Hospital","ror":"https://ror.org/00xmkp704","country_code":"BE","type":"healthcare","lineage":["https://openalex.org/I2801227569"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Annick Dhooge","raw_affiliation_strings":["Ghent University"],"affiliations":[{"raw_affiliation_string":"Ghent University","institution_ids":["https://openalex.org/I2801227569"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067569718"],"corresponding_institution_ids":["https://openalex.org/I2801227569"],"apc_list":null,"apc_paid":null,"fwci":5.8891,"has_fulltext":false,"cited_by_count":96,"citation_normalized_percentile":{"value":0.97106005,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"27","issue":"1","first_page":"231","last_page":"252"},"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":0.9983000159263611,"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":0.9983000159263611,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9914000034332275,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/matlab","display_name":"MATLAB","score":0.6509894132614136},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6124283075332642},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6008794903755188},{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.5671787261962891},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5145113468170166},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.47414323687553406},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.45349323749542236},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.4509789049625397},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4403524398803711},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4343605637550354},{"id":"https://openalex.org/keywords/limit-point","display_name":"Limit point","score":0.4147564768791199},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4036279320716858},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3370211124420166},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2832718789577484},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1969224214553833}],"concepts":[{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.6509894132614136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6124283075332642},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6008794903755188},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.5671787261962891},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5145113468170166},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.47414323687553406},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.45349323749542236},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.4509789049625397},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4403524398803711},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4343605637550354},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.4147564768791199},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4036279320716858},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3370211124420166},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2832718789577484},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1969224214553833},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/030600746","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030600746","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.75.4423","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.75.4423","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uu.nl/publications/preprints/1280.pdf","raw_type":"text"},{"id":"pmh:oai:archive.ugent.be:323260","is_oa":false,"landing_page_url":"https://biblio.ugent.be/publication/323260","pdf_url":null,"source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1064-8275","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W160832363","https://openalex.org/W1524012213","https://openalex.org/W1530314303","https://openalex.org/W1560787783","https://openalex.org/W1596321532","https://openalex.org/W1629573449","https://openalex.org/W1969841138","https://openalex.org/W1971092129","https://openalex.org/W1981745143","https://openalex.org/W1981847400","https://openalex.org/W1987534777","https://openalex.org/W1997019928","https://openalex.org/W2003444761","https://openalex.org/W2008000547","https://openalex.org/W2018874482","https://openalex.org/W2039041284","https://openalex.org/W2045055776","https://openalex.org/W2047929780","https://openalex.org/W2081696580","https://openalex.org/W2088986191","https://openalex.org/W2155615510","https://openalex.org/W2164761951","https://openalex.org/W2165989366","https://openalex.org/W2186590998","https://openalex.org/W2798909945","https://openalex.org/W2905382927","https://openalex.org/W4230906466"],"related_works":["https://openalex.org/W3204184292","https://openalex.org/W3176564347","https://openalex.org/W1985458517","https://openalex.org/W2355833770","https://openalex.org/W3031039437","https://openalex.org/W3095877357","https://openalex.org/W2043619729","https://openalex.org/W999100079","https://openalex.org/W2119800364","https://openalex.org/W2116098329"],"abstract_inverted_index":{"${\\rm":[0,31,83],"CL\\_MATCONT}$":[1,32,84],"and":[2,30,54,71,74,82,113,116,137],"MATCONT":[3,24,81],"are":[4,123],"MATLAB":[5,109,144],"continuation":[6,67],"packages":[7,38],"for":[8],"the":[9,66,90,105,108,114,119,132,135,138,143],"interactive":[10,27],"numerical":[11],"study":[12],"of":[13,16,44,58,65,68,77,89,107,118,134],"a":[14,34],"range":[15],"parameterized":[17],"nonlinear":[18],"dynamical":[19],"systems,":[20],"in":[21,80,125,142],"particular":[22],"ODEs.":[23],"is":[25,33],"an":[26],"graphical":[28],"package":[29],"commandline":[35],"version.":[36],"Both":[37],"allow":[39],"us":[40],"to":[41],"compute":[42],"curves":[43],"equilibria,":[45],"limit":[46,50,59,69,78],"points,":[47,49],"Hopf":[48],"cycles,":[51],"flip,":[52,72],"fold,":[53,73],"torus":[55,75],"bifurcation":[56],"points":[57],"cycles.":[60],"We":[61,102],"discuss":[62],"computational":[63],"details":[64],"cycles":[70,79],"bifurcations":[76],"using":[85],"orthogonal":[86],"collocation.":[87],"Instead":[88],"more":[91],"commonly":[92],"used":[93],"fully":[94,139],"extended":[95,100,127,140],"systems":[96,141],"we":[97,130],"use":[98,106,133],"minimally":[99,126,136],"systems.":[101,128],"further":[103],"describe":[104],"sparse":[110],"matrix":[111],"routines":[112],"initialization":[115],"adaptation":[117],"bordering":[120],"vectors":[121],"that":[122],"essential":[124],"Finally,":[129],"compare":[131],"environment.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
