{"id":"https://openalex.org/W2099631180","doi":"https://doi.org/10.1137/060653858","title":"Numerical Methods for Two-Parameter Local Bifurcation Analysis of Maps","display_name":"Numerical Methods for Two-Parameter Local Bifurcation Analysis of Maps","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2099631180","doi":"https://doi.org/10.1137/060653858","mag":"2099631180"},"language":"en","primary_location":{"id":"doi:10.1137/060653858","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060653858","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":true,"oa_status":"green","oa_url":"https://ris.utwente.nl/ws/files/6873507/GKKM_CLMATCONTM_2007.pdf","any_repository_has_fulltext":true},"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":false,"raw_author_name":"W. Govaerts","raw_affiliation_strings":["Ghent University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ghent University","institution_ids":["https://openalex.org/I2801227569"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009585221","display_name":"Reza Khoshsiar Ghaziani","orcid":"https://orcid.org/0000-0002-1839-6619"},"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":"R. Khoshsiar Ghaziani","raw_affiliation_strings":["Ghent University"],"raw_orcid":null,"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":"Yu. A. Kuznetsov","raw_affiliation_strings":["Utrecht university >  >  >  >"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Utrecht university >  >  >  >","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062882766","display_name":"Hil G. E. Meijer","orcid":"https://orcid.org/0000-0003-1526-3762"},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"H. G. E. Meijer","raw_affiliation_strings":["Department of Electrical Engineering, Mathematics and Computer Science, Universiteit Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Mathematics and Computer Science, Universiteit Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands","institution_ids":["https://openalex.org/I94624287"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3643,"has_fulltext":true,"cited_by_count":113,"citation_normalized_percentile":{"value":0.9283702,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"29","issue":"6","first_page":"2644","last_page":"2667"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9969000220298767,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9945999979972839,"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/mathematics","display_name":"Mathematics","score":0.7989672422409058},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6430738568305969},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5372853875160217},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4496479630470276},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39080432057380676},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.21710193157196045}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7989672422409058},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6430738568305969},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5372853875160217},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4496479630470276},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39080432057380676},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.21710193157196045},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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":3,"locations":[{"id":"doi:10.1137/060653858","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060653858","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:ris.utwente.nl:openaire/72856ed6-ec0f-4eec-9d03-e6ffe90f7b5f","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/72856ed6-ec0f-4eec-9d03-e6ffe90f7b5f","pdf_url":"https://ris.utwente.nl/ws/files/6873507/GKKM_CLMATCONTM_2007.pdf","source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Govaerts, W, Khoshsiar Ghaziani, R, Kuznetsov, Y A & Meijer, H G E 2007, 'Numerical methods for two-parameter local bifurcation analysis of maps', SIAM journal on scientific computing, vol. 29, no. 6, pp. 2644-2667. https://doi.org/10.1137/060653858","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:archive.ugent.be:394448","is_oa":false,"landing_page_url":"http://hdl.handle.net/1854/LU-394448","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/article"}],"best_oa_location":{"id":"pmh:oai:ris.utwente.nl:openaire/72856ed6-ec0f-4eec-9d03-e6ffe90f7b5f","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/72856ed6-ec0f-4eec-9d03-e6ffe90f7b5f","pdf_url":"https://ris.utwente.nl/ws/files/6873507/GKKM_CLMATCONTM_2007.pdf","source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Govaerts, W, Khoshsiar Ghaziani, R, Kuznetsov, Y A & Meijer, H G E 2007, 'Numerical methods for two-parameter local bifurcation analysis of maps', SIAM journal on scientific computing, vol. 29, no. 6, pp. 2644-2667. https://doi.org/10.1137/060653858","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2099631180.pdf","grobid_xml":"https://content.openalex.org/works/W2099631180.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W130666822","https://openalex.org/W1530314303","https://openalex.org/W1531715726","https://openalex.org/W1984163485","https://openalex.org/W2013474806","https://openalex.org/W2018263586","https://openalex.org/W2027529973","https://openalex.org/W2040093184","https://openalex.org/W2068460942","https://openalex.org/W2069149364","https://openalex.org/W2081696580","https://openalex.org/W2083922917","https://openalex.org/W2088986191","https://openalex.org/W2110599588","https://openalex.org/W2110670499","https://openalex.org/W2116410587","https://openalex.org/W2128949314","https://openalex.org/W2618795383","https://openalex.org/W2905382927","https://openalex.org/W3144818527"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W4285308861"],"abstract_inverted_index":{"We":[0,171],"discuss":[1],"new":[2],"and":[3,13,19,29,53,62,64,75,93,108,131,152,167,183],"improved":[4],"algorithms":[5],"for":[6,27,126],"the":[7,37,46,84,95,113,150,162,165,176],"bifurcation":[8,30,56,81,127],"analysis":[9,31],"of":[10,17,32,40,43,45,77,90,112,129,140,164],"fixed":[11,41],"points":[12,42,57,82,139,160],"periodic":[14],"orbits":[15],"(cycles)":[16],"maps":[18],"their":[20,55,65],"implementation":[21],"in":[22,67],"matcont,":[23],"a":[24,117,179,184],"MATLAB":[25],"toolbox":[26],"continuation":[28,39,66,163],"dynamical":[33],"systems.":[34],"This":[35],"includes":[36],"numerical":[38],"iterates":[44],"map":[47,182],"with":[48,104,142],"one":[49,154],"control":[50,69],"parameter,":[51],"detecting":[52],"locating":[54],"(i.e.,":[58],"limit":[59],"point,":[60],"period-doubling,":[61],"Neimark\u2013Sacker)":[63],"two":[68,173],"parameters,":[70],"as":[71,73],"well":[72],"detection":[74],"location":[76],"all":[78,88],"codimension":[79],"2":[80,138,159],"on":[83],"corresponding":[85],"curves.":[86],"For":[87],"bifurcations":[89],"codim":[91,137,158],"1":[92],"2,":[94],"critical":[96],"normal":[97],"form":[98],"coefficients":[99],"are":[100,124,147],"computed,":[101],"both":[102],"numerically":[103],"finite":[105],"directional":[106],"differences":[107],"using":[109],"symbolic":[110],"derivatives":[111],"original":[114],"map.":[115],"Using":[116],"parameter-dependent":[118],"center":[119],"manifold":[120],"reduction,":[121],"explicit":[122],"asymptotics":[123,146],"derived":[125],"curves":[128],"double":[130,166],"quadruple":[132,168],"period":[133,169],"cycles":[134,141],"rooted":[135],"at":[136,157],"arbitrary":[143],"period.":[144],"These":[145],"implemented":[148],"into":[149],"software":[151],"allow":[153],"to":[155,161],"switch":[156],"bifurcations.":[170],"provide":[172],"examples":[174],"illustrating":[175],"developed":[177],"techniques:":[178],"generalized":[180],"H\u00e9non":[181],"juvenile/adult":[185],"competition":[186],"model":[187],"from":[188],"mathematical":[189],"biology.":[190]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":17},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":20},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}