{"id":"https://openalex.org/W2039299540","doi":"https://doi.org/10.1142/s0218127401002675","title":"HOMOCLINIC BIFURCATIONS IN A PLANAR DYNAMICAL SYSTEM","display_name":"HOMOCLINIC BIFURCATIONS IN A PLANAR DYNAMICAL SYSTEM","publication_year":2001,"publication_date":"2001-04-01","ids":{"openalex":"https://openalex.org/W2039299540","doi":"https://doi.org/10.1142/s0218127401002675","mag":"2039299540"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127401002675","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127401002675","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008213029","display_name":"Fotios Giannakopoulos","orcid":null},"institutions":[{"id":"https://openalex.org/I143379178","display_name":"FZI Research Center for Information Technology","ror":"https://ror.org/04kdh6x72","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I143379178"]},{"id":"https://openalex.org/I4210110507","display_name":"Fraunhofer Institute for Applied Information Technology","ror":"https://ror.org/01ak24c12","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210110507","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"FOTIOS GIANNAKOPOULOS","raw_affiliation_strings":["GMD-German National Research Center for Information Technology, Schloss Birlinghoven, 53754 Sankt Augustin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"GMD-German National Research Center for Information Technology, Schloss Birlinghoven, 53754 Sankt Augustin, Germany","institution_ids":["https://openalex.org/I4210110507","https://openalex.org/I143379178"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011966936","display_name":"Tassilo K\u00fcpper","orcid":null},"institutions":[{"id":"https://openalex.org/I180923762","display_name":"University of Cologne","ror":"https://ror.org/00rcxh774","country_code":"DE","type":"education","lineage":["https://openalex.org/I180923762"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"TASSILO K\u00dcPPER","raw_affiliation_strings":["Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany","Mathematical Institute, University of Cologne, Weyertal 86-90, 50931, Cologne, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany","institution_ids":["https://openalex.org/I180923762"]},{"raw_affiliation_string":"Mathematical Institute, University of Cologne, Weyertal 86-90, 50931, Cologne, Germany","institution_ids":["https://openalex.org/I180923762"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016150299","display_name":"Yongkui Zou","orcid":"https://orcid.org/0000-0001-9519-1804"},"institutions":[{"id":"https://openalex.org/I180923762","display_name":"University of Cologne","ror":"https://ror.org/00rcxh774","country_code":"DE","type":"education","lineage":["https://openalex.org/I180923762"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"YONGKUI ZOU","raw_affiliation_strings":["Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany","Mathematical Institute, University of Cologne, Weyertal 86-90, 50931, Cologne, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany","institution_ids":["https://openalex.org/I180923762"]},{"raw_affiliation_string":"Mathematical Institute, University of Cologne, Weyertal 86-90, 50931, Cologne, Germany","institution_ids":["https://openalex.org/I180923762"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.16289291,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"11","issue":"04","first_page":"1183","last_page":"1191"},"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":0.9987999796867371,"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":0.9987999796867371,"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":0.9914000034332275,"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/T10244","display_name":"Chaos control and synchronization","score":0.9902999997138977,"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":0.9902958869934082},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.900783896446228},{"id":"https://openalex.org/keywords/heteroclinic-orbit","display_name":"Heteroclinic orbit","score":0.7569513916969299},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6365768313407898},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.6280456781387329},{"id":"https://openalex.org/keywords/bogdanov\u2013takens-bifurcation","display_name":"Bogdanov\u2013Takens bifurcation","score":0.5491995811462402},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5333976745605469},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5306714177131653},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5182042717933655},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.5154638886451721},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.456245094537735},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2443174123764038},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.05542099475860596},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.05266711115837097}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9902958869934082},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.900783896446228},{"id":"https://openalex.org/C184481792","wikidata":"https://www.wikidata.org/wiki/Q1992087","display_name":"Heteroclinic orbit","level":5,"score":0.7569513916969299},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6365768313407898},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.6280456781387329},{"id":"https://openalex.org/C22257346","wikidata":"https://www.wikidata.org/wiki/Q4937510","display_name":"Bogdanov\u2013Takens bifurcation","level":5,"score":0.5491995811462402},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5333976745605469},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5306714177131653},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5182042717933655},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.5154638886451721},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.456245094537735},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2443174123764038},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.05542099475860596},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.05266711115837097},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace 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":3,"locations":[{"id":"doi:10.1142/s0218127401002675","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127401002675","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:fraunhofer.de:2004922320","is_oa":false,"landing_page_url":"http://publica.fraunhofer.de/documents/2004922320.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400801","display_name":"Publikationsdatenbank der Fraunhofer-Gesellschaft (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Fraunhofer AIS","raw_type":"Journal Article"},{"id":"pmh:oai:publica.fraunhofer.de:publica/200719","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/200719","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W205802462","https://openalex.org/W597049470","https://openalex.org/W1562727027","https://openalex.org/W1584414181","https://openalex.org/W1596321532","https://openalex.org/W1971808848","https://openalex.org/W1987200360","https://openalex.org/W2007242618","https://openalex.org/W2061154922","https://openalex.org/W2083922917","https://openalex.org/W2088986191","https://openalex.org/W2089876099","https://openalex.org/W4230054495"],"related_works":["https://openalex.org/W1999123830","https://openalex.org/W3151500797","https://openalex.org/W2350473807","https://openalex.org/W3142626835","https://openalex.org/W2356323067","https://openalex.org/W944345475","https://openalex.org/W2362555640","https://openalex.org/W2890492950","https://openalex.org/W2067447470","https://openalex.org/W2943888718"],"abstract_inverted_index":{"The":[0,18,98],"homoclinic":[1,31,43,60,72,83,96,100,107,114],"bifurcation":[2,14,23,101],"properties":[3],"of":[4,20,30,59,82,103,113],"a":[5,34,63,86,94,117],"planar":[6],"dynamical":[7],"system":[8],"are":[9,50,74,119],"analyzed":[10],"and":[11,110,125],"the":[12,37,42,53,66,71,105,111],"corresponding":[13],"diagram":[15,102],"is":[16],"presented.":[17],"occurrence":[19],"two":[21,26],"Bogdanov\u2013Takens":[22],"points":[24,112],"provides":[25],"local":[27,99],"existing":[28],"curves":[29,49,58,81],"orbits":[32,61,73,84,115],"to":[33,41,62,70,116],"saddle":[35,64],"excluding":[36],"separatrices":[38,67],"not":[39,68],"belonging":[40,69],"orbits.":[44],"Using":[45],"numerical":[46,77,123],"techniques,":[47],"these":[48,80],"continued":[51],"in":[52],"parameter":[54],"space.":[55],"Two":[56],"further":[57],"including":[65],"calculated":[75],"by":[76,122],"methods.":[78],"All":[79],"have":[85],"unique":[87],"intersection":[88],"point,":[89],"at":[90],"which":[91],"there":[92],"exists":[93],"double":[95,106],"orbit.":[97],"both":[104],"orbit":[108],"point":[109],"saddle-node":[118],"also":[120],"gained":[121],"computation":[124],"simulation.":[126]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}