{"id":"https://openalex.org/W2157037569","doi":"https://doi.org/10.1142/s0218127414500576","title":"Improved Homoclinic Predictor for Bogdanov\u2013Takens Bifurcation","display_name":"Improved Homoclinic Predictor for Bogdanov\u2013Takens Bifurcation","publication_year":2014,"publication_date":"2014-04-01","ids":{"openalex":"https://openalex.org/W2157037569","doi":"https://doi.org/10.1142/s0218127414500576","mag":"2157037569"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127414500576","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414500576","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/6421254/BT.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007494022","display_name":"Yuri A. Kuznetsov","orcid":"https://orcid.org/0000-0003-2289-0801"},"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"]},{"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":["BE","NL"],"is_corresponding":false,"raw_author_name":"Yu. A. Kuznetsov","raw_affiliation_strings":["Department of Applied Mathematics, University of Twente, Zilverling Building, P. O. Box 217, 7500AE Enschede, The Netherlands","Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, 9000 Gent, Belgium","Department of Applied Mathematics, University of Twente, Zilverling Building, P.O. Box 217, 7500AE Enschede, The Netherlands [I.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Twente, Zilverling Building, P. O. Box 217, 7500AE Enschede, The Netherlands","institution_ids":["https://openalex.org/I94624287"]},{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, 9000 Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Department of Applied Mathematics, University of Twente, Zilverling Building, P.O. Box 217, 7500AE Enschede, The Netherlands [I.A","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"middle","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/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]},{"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":["BE","NL"],"is_corresponding":false,"raw_author_name":"H. G. E. Meijer","raw_affiliation_strings":["Department of Applied Mathematics, University of Twente, Zilverling Building, P. O. Box 217, 7500AE Enschede, The Netherlands","Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, 9000 Gent, Belgium","Department of Applied Mathematics, University of Twente, Zilverling Building, P.O. Box 217, 7500AE Enschede, The Netherlands [I.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Twente, Zilverling Building, P. O. Box 217, 7500AE Enschede, The Netherlands","institution_ids":["https://openalex.org/I94624287"]},{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, 9000 Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Department of Applied Mathematics, University of Twente, Zilverling Building, P.O. Box 217, 7500AE Enschede, The Netherlands [I.A","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"middle","author":{"id":null,"display_name":"B. Al Hdaibat","orcid":null},"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"]},{"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":["BE","NL"],"is_corresponding":false,"raw_author_name":"B. Al Hdaibat","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, 9000 Gent, Belgium","Department of Applied Mathematics, University of Twente, Zilverling Building, P.O. Box 217, 7500AE Enschede, The Netherlands [I.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, 9000 Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Department of Applied Mathematics, University of Twente, Zilverling Building, P.O. Box 217, 7500AE Enschede, The Netherlands [I.A","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"last","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"]},{"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":["BE","NL"],"is_corresponding":true,"raw_author_name":"W. Govaerts","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, 9000 Gent, Belgium","Department of Applied Mathematics, University of Twente, Zilverling Building, P.O. Box 217, 7500AE Enschede, The Netherlands [I.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, 9000 Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Department of Applied Mathematics, University of Twente, Zilverling Building, P.O. Box 217, 7500AE Enschede, The Netherlands [I.A","institution_ids":["https://openalex.org/I94624287"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5067569718"],"corresponding_institution_ids":["https://openalex.org/I32597200","https://openalex.org/I94624287"],"apc_list":null,"apc_paid":null,"fwci":0.6591,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.70768607,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","issue":"04","first_page":"1450057","last_page":"1450057"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9984999895095825,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9968000054359436,"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":0.9954000115394592,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.9304397106170654},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.802703857421875},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.7185907363891602},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.6767613291740417},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.531532347202301},{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.5077303647994995},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5013046264648438},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.48817068338394165},{"id":"https://openalex.org/keywords/invariant-manifold","display_name":"Invariant manifold","score":0.46636804938316345},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.42171019315719604},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3818584382534027},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.22024598717689514},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06398573517799377}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9304397106170654},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.802703857421875},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.7185907363891602},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.6767613291740417},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.531532347202301},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.5077303647994995},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5013046264648438},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.48817068338394165},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.46636804938316345},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.42171019315719604},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3818584382534027},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.22024598717689514},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06398573517799377},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1142/s0218127414500576","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414500576","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:ris.utwente.nl:publications/a616b48a-9403-4fa8-a8bc-bf5d4d4eb454","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/a616b48a-9403-4fa8-a8bc-bf5d4d4eb454","pdf_url":"https://ris.utwente.nl/ws/files/6421254/BT.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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Kouznetsov, I A, Meijer, H G E, Al Hdaibat, B & Govaerts, W 2014, 'Improved homoclinic predictor for Bogdanov-Takens bifurcation', International journal of bifurcation and chaos in applied sciences and engineering, vol. 24, no. 4, pp. 1450057. https://doi.org/10.1142/S0218127414500576","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:archive.ugent.be:4387839","is_oa":false,"landing_page_url":"http://hdl.handle.net/1854/LU-4387839","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: 0218-1274","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:ris.utwente.nl:publications/a616b48a-9403-4fa8-a8bc-bf5d4d4eb454","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":""},{"id":"pmh:uu:oai:dspace.library.uu.nl:1874/306709","is_oa":false,"landing_page_url":"https://dspace.library.uu.nl/handle/1874/306709","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 24(4). World Scientific Publishing Co. Pte Ltd","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:ris.utwente.nl:publications/a616b48a-9403-4fa8-a8bc-bf5d4d4eb454","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/a616b48a-9403-4fa8-a8bc-bf5d4d4eb454","pdf_url":"https://ris.utwente.nl/ws/files/6421254/BT.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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Kouznetsov, I A, Meijer, H G E, Al Hdaibat, B & Govaerts, W 2014, 'Improved homoclinic predictor for Bogdanov-Takens bifurcation', International journal of bifurcation and chaos in applied sciences and engineering, vol. 24, no. 4, pp. 1450057. https://doi.org/10.1142/S0218127414500576","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/W2157037569.pdf","grobid_xml":"https://content.openalex.org/works/W2157037569.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W355012799","https://openalex.org/W563922805","https://openalex.org/W1530314303","https://openalex.org/W1567812234","https://openalex.org/W1596321532","https://openalex.org/W2017473796","https://openalex.org/W2029788019","https://openalex.org/W2033980468","https://openalex.org/W2057456335","https://openalex.org/W2079371292","https://openalex.org/W2081696580","https://openalex.org/W2089876099","https://openalex.org/W2091534537","https://openalex.org/W2096470846","https://openalex.org/W2149406938","https://openalex.org/W2297521577","https://openalex.org/W2480701976","https://openalex.org/W2905382927","https://openalex.org/W4285719527","https://openalex.org/W4293079168"],"related_works":["https://openalex.org/W2010606039","https://openalex.org/W1547807244","https://openalex.org/W2096327469","https://openalex.org/W1536954903","https://openalex.org/W2767051478","https://openalex.org/W2129195111","https://openalex.org/W2032911812","https://openalex.org/W2481001085","https://openalex.org/W1984417388","https://openalex.org/W1972846926"],"abstract_inverted_index":{"An":[0],"improved":[1,117],"homoclinic":[2,52],"predictor":[3,118],"at":[4],"a":[5,28,33,38],"generic":[6,29],"codim":[7],"2":[8],"Bogdanov\u2013Takens":[9],"(BT)":[10],"bifucation":[11],"is":[12,79],"derived.":[13],"We":[14],"use":[15],"the":[16,22,50,59,63,68,76,82,86,97,105,110,116],"classical":[17],"\"blow-up\"":[18],"technique":[19],"to":[20,32],"reduce":[21],"canonical":[23],"smooth":[24],"normal":[25,60],"form":[26,61],"near":[27],"BT":[30],"bifurcation":[31],"perturbed":[34],"Hamiltonian":[35],"system.":[36],"With":[37],"simple":[39],"perturbation":[40],"method,":[41],"we":[42,66,100],"derive":[43],"explicit":[44],"first-":[45],"and":[46,54,121],"second-order":[47],"corrections":[48],"of":[49,85,115],"unperturbed":[51],"orbit":[53],"parameter":[55,106],"value.":[56],"To":[57],"obtain":[58],"on":[62,81],"center":[64,71],"manifold,":[65],"apply":[67],"standard":[69],"parameter-dependent":[70],"manifold":[72],"reduction":[73],"combined":[74],"with":[75],"normalization,":[77],"that":[78],"based":[80],"Fredholm":[83],"solvability":[84],"homological":[87,98],"equation.":[88],"By":[89],"systematically":[90],"solving":[91],"all":[92],"linear":[93],"systems":[94],"appearing":[95],"from":[96],"equation,":[99],"remove":[101],"an":[102],"ambiguity":[103],"in":[104,109,119],"transformation":[107],"existing":[108],"literature.":[111],"The":[112],"actual":[113],"implementation":[114],"MatCont":[120],"numerical":[122],"examples":[123],"illustrating":[124],"its":[125],"efficiency":[126],"are":[127],"discussed.":[128]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2016-06-24T00:00:00"}
