{"id":"https://openalex.org/W2398128155","doi":"https://doi.org/10.1137/15m1017491","title":"Initialization of Homoclinic Solutions near Bogdanov--Takens Points: Lindstedt--Poincar\u00e9 Compared with Regular Perturbation Method","display_name":"Initialization of Homoclinic Solutions near Bogdanov--Takens Points: Lindstedt--Poincar\u00e9 Compared with Regular Perturbation Method","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2398128155","doi":"https://doi.org/10.1137/15m1017491","mag":"2398128155"},"language":"en","primary_location":{"id":"doi:10.1137/15m1017491","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1017491","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.utwente.nl/en/publications/b27dd696-f2ae-43c7-bf81-f0a33cc9855f","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052821015","display_name":"Bashir Al\u2010Hdaibat","orcid":"https://orcid.org/0000-0003-1846-7410"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"B. Al-Hdaibat","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000, Ghent, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000, Ghent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067569718","display_name":"W. Govaerts","orcid":"https://orcid.org/0000-0002-1081-6252"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"W. Govaerts","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000, Ghent, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000, Ghent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]},{"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":["Department of Mathematics, Utrecht University, Budapestlaan 6, 3508 TA Utrecht, The Netherlands,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Utrecht University, Budapestlaan 6, 3508 TA Utrecht, The Netherlands,","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 Applied Mathematics, University of Twente, 7500AE Enschede, The Netherlands (H.G"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Twente, 7500AE Enschede, The Netherlands (H.G","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":2.0719,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.89224487,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"15","issue":"2","first_page":"952","last_page":"980"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9965000152587891,"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":0.9965000152587891,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9955999851226807,"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/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.9827860593795776},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.848865270614624},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7511220574378967},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6126896739006042},{"id":"https://openalex.org/keywords/numerical-continuation","display_name":"Numerical continuation","score":0.48737508058547974},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.46032679080963135},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.45785555243492126},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.4146946668624878},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.3973454236984253},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2618519067764282},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2563106417655945},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18790841102600098},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09094598889350891}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9827860593795776},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.848865270614624},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7511220574378967},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6126896739006042},{"id":"https://openalex.org/C2775978667","wikidata":"https://www.wikidata.org/wiki/Q7069654","display_name":"Numerical continuation","level":4,"score":0.48737508058547974},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.46032679080963135},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.45785555243492126},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.4146946668624878},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.3973454236984253},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2618519067764282},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2563106417655945},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18790841102600098},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09094598889350891},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/15m1017491","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1017491","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:ris.utwente.nl:openaire/b27dd696-f2ae-43c7-bf81-f0a33cc9855f","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/b27dd696-f2ae-43c7-bf81-f0a33cc9855f","pdf_url":null,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Al Hdaibat, B, Govaerts, W, Kouznetsov, I A & Meijer, H G E 2016, 'Initialization of Homoclinic Solutions near Bogdanov-Takens Points: Lindstedt-Poincar\u00e9 Compared with Regular Perturbation Method', SIAM journal on applied dynamical systems, vol. 15, no. 2, pp. 952-980. https://doi.org/10.1137/15M1017491","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:archive.ugent.be:8023782","is_oa":true,"landing_page_url":"https://biblio.ugent.be/publication/8023782","pdf_url":"https://biblio.ugent.be/publication/8023782/file/8023783.pdf","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1536-0040","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:dspace.library.uu.nl:1874/341561","is_oa":true,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/341561","pdf_url":null,"source":{"id":"https://openalex.org/S4306401649","display_name":"Utrecht University Repository (Utrecht University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193662353","host_organization_name":"Utrecht University","host_organization_lineage":["https://openalex.org/I193662353"],"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":"","raw_type":"Article"},{"id":"pmh:oai:ris.utwente.nl:publications/b27dd696-f2ae-43c7-bf81-f0a33cc9855f","is_oa":false,"landing_page_url":null,"pdf_url":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:ris.utwente.nl:openaire/b27dd696-f2ae-43c7-bf81-f0a33cc9855f","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/b27dd696-f2ae-43c7-bf81-f0a33cc9855f","pdf_url":null,"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Al Hdaibat, B, Govaerts, W, Kouznetsov, I A & Meijer, H G E 2016, 'Initialization of Homoclinic Solutions near Bogdanov-Takens Points: Lindstedt-Poincar\u00e9 Compared with Regular Perturbation Method', SIAM journal on applied dynamical systems, vol. 15, no. 2, pp. 952-980. https://doi.org/10.1137/15M1017491","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W84041004","https://openalex.org/W1823752871","https://openalex.org/W1971092129","https://openalex.org/W1973516628","https://openalex.org/W2017473796","https://openalex.org/W2023605401","https://openalex.org/W2029788019","https://openalex.org/W2032604276","https://openalex.org/W2033980468","https://openalex.org/W2035270688","https://openalex.org/W2042532395","https://openalex.org/W2053439704","https://openalex.org/W2057456335","https://openalex.org/W2063646186","https://openalex.org/W2076831813","https://openalex.org/W2079371292","https://openalex.org/W2081696580","https://openalex.org/W2088827616","https://openalex.org/W2091534537","https://openalex.org/W2097835225","https://openalex.org/W2136308364","https://openalex.org/W2136698794","https://openalex.org/W2149406938","https://openalex.org/W2159263765"],"related_works":["https://openalex.org/W3026479466","https://openalex.org/W2095521025","https://openalex.org/W2052199806","https://openalex.org/W2000874527","https://openalex.org/W2576530575","https://openalex.org/W2090154871","https://openalex.org/W2364857955","https://openalex.org/W1969170083","https://openalex.org/W2132550995","https://openalex.org/W1987899225"],"abstract_inverted_index":{"To":[0],"continue":[1,187],"a":[2,9,20,50,66,70,101,147,214],"branch":[3,98],"of":[4,57,69,105,210],"homoclinic":[5,34,47,67,93,97,188,196,211],"solutions":[6],"starting":[7],"from":[8,77,213],"Bogdanov--Takens":[10],"(BT)":[11],"point":[12,104],"in":[13,36,190,200],"parameter":[14,28],"and":[15,30,131],"state":[16,221],"space,":[17],"one":[18],"needs":[19],"predictor":[21,94],"based":[22,157],"on":[23,158],"asymptotics":[24,44,156,180],"for":[25,45,171],"the":[26,31,37,46,58,80,96,115,119,124,128,132,142,151,159,183,201,208],"bifurcation":[27],"values":[29],"corresponding":[32],"small":[33],"orbits":[35,48,189,212],"phase":[38],"space.":[39],"We":[40,112,174],"derive":[41,89],"two":[42,191],"explicit":[43],"near":[49,150],"generic":[51,102],"BT":[52,81,103,215],"point.":[53,153,216],"A":[54],"recent":[55],"generalization":[56],"Lindstedt--Poincar\u00e9":[59],"(L-P)":[60],"method":[61,116,144,161],"is":[62,139],"applied":[63],"to":[64,88,95,118,146,177,181,186,206],"approximate":[65],"solution":[68,85],"strongly":[71],"nonlinear":[72],"autonomous":[73],"system":[74],"that":[75,114,141],"results":[76],"blowing":[78],"up":[79],"normal":[82],"form.":[83],"This":[84],"allows":[86],"us":[87],"an":[90,106],"accurate":[91],"second-order":[92],"rooted":[99],"at":[100],"$n$-dimensional":[107],"ordinary":[108],"differential":[109],"equation":[110],"(ODE).":[111],"prove":[113],"leads":[117,145],"same":[120],"homoclinicity":[121],"conditions":[122],"as":[123],"classical":[125],"Melnikov":[126],"technique,":[127],"branching":[129],"method,":[130],"regular":[133],"perturbation":[134],"(R-P)":[135],"method.":[136],"However,":[137],"it":[138],"known":[140],"R-P":[143],"\u201cparasitic":[148],"turn\u201d":[149],"saddle":[152],"The":[154,194],"new":[155,195],"L-P":[160],"do":[162],"not":[163],"have":[164],"this":[165],"turn,":[166],"making":[167],"them":[168],"more":[169],"suitable":[170],"numerical":[172],"implementation.":[173],"show":[175],"how":[176],"use":[178],"these":[179],"calculate":[182],"initial":[184],"data":[185],"free":[192],"parameters.":[193],"predictors":[197],"are":[198,223],"implemented":[199],"MATLAB":[202],"continuation":[203,209],"package":[204],"MatCont":[205],"initialize":[207],"Two":[217],"examples":[218],"with":[219],"multidimensional":[220],"spaces":[222],"included.":[224]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
