{"id":"https://openalex.org/W2020906290","doi":"https://doi.org/10.1142/s0218127405014131","title":"BIFURCATIONS OF RELAXATION OSCILLATIONS NEAR FOLDED SADDLES","display_name":"BIFURCATIONS OF RELAXATION OSCILLATIONS NEAR FOLDED SADDLES","publication_year":2005,"publication_date":"2005-11-01","ids":{"openalex":"https://openalex.org/W2020906290","doi":"https://doi.org/10.1142/s0218127405014131","mag":"2020906290"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127405014131","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405014131","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/A5018563718","display_name":"John Guckenheimer","orcid":"https://orcid.org/0000-0001-6655-7862"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"JOHN GUCKENHEIMER","raw_affiliation_strings":["Mathematics Department, Cornell University, Ithaca, NY 14853, USA","Mathematics Department, Cornell University, Ithaca, NY, 14853, USA"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Cornell University, Ithaca, NY 14853, USA","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Mathematics Department, Cornell University, Ithaca, NY, 14853, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057312329","display_name":"Kathleen Hoffman","orcid":"https://orcid.org/0000-0002-1776-319X"},"institutions":[{"id":"https://openalex.org/I79272384","display_name":"University of Maryland, Baltimore County","ror":"https://ror.org/02qskvh78","country_code":"US","type":"education","lineage":["https://openalex.org/I79272384"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"KATHLEEN HOFFMAN","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD 21250, USA","Department of Mathematics and Statistics , University of Maryland Baltimore County , Baltimore, MD, 21250, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD 21250, USA","institution_ids":["https://openalex.org/I79272384"]},{"raw_affiliation_string":"Department of Mathematics and Statistics , University of Maryland Baltimore County , Baltimore, MD, 21250, USA","institution_ids":["https://openalex.org/I79272384"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050562889","display_name":"Warren Weckesser","orcid":null},"institutions":[{"id":"https://openalex.org/I39660569","display_name":"Colgate University","ror":"https://ror.org/05d23ve83","country_code":"US","type":"education","lineage":["https://openalex.org/I39660569"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"WARREN WECKESSER","raw_affiliation_strings":["Mathematics Department, Colgate University, Hamilton, NY 13346, USA","Mathematics Department, Colgate University, Hamilton, NY, 13346, USA"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Colgate University, Hamilton, NY 13346, USA","institution_ids":["https://openalex.org/I39660569"]},{"raw_affiliation_string":"Mathematics Department, Colgate University, Hamilton, NY, 13346, USA","institution_ids":["https://openalex.org/I39660569"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018563718"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":null,"apc_paid":null,"fwci":1.4928,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.81648455,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"15","issue":"11","first_page":"3411","last_page":"3421"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9973999857902527,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9973999857902527,"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/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/T10244","display_name":"Chaos control and synchronization","score":0.9958999752998352,"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":0.8471678495407104},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.7126401662826538},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.6645360589027405},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.5968868732452393},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5870121121406555},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.567710280418396},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5654723644256592},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.48892512917518616},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.4816542863845825},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.47762221097946167},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4655305743217468},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4641379714012146},{"id":"https://openalex.org/keywords/heteroclinic-bifurcation","display_name":"Heteroclinic bifurcation","score":0.4580354690551758},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4477696716785431},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.4374791979789734},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4032239615917206},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.2348988950252533},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20169034600257874},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11450421810150146},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08418411016464233}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.8471678495407104},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.7126401662826538},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.6645360589027405},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.5968868732452393},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5870121121406555},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.567710280418396},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5654723644256592},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.48892512917518616},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.4816542863845825},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.47762221097946167},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4655305743217468},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4641379714012146},{"id":"https://openalex.org/C73888704","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Heteroclinic bifurcation","level":5,"score":0.4580354690551758},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4477696716785431},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4374791979789734},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4032239615917206},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.2348988950252533},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20169034600257874},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11450421810150146},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08418411016464233},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127405014131","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405014131","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:CiteSeerX.psu:10.1.1.120.95","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.120.95","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cornell.edu/~gucken/PDF/folded_saddle.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W575067585","https://openalex.org/W650925811","https://openalex.org/W1484182740","https://openalex.org/W1603139886","https://openalex.org/W1965780186","https://openalex.org/W1983924943","https://openalex.org/W2024858188","https://openalex.org/W2092680287","https://openalex.org/W2101714536","https://openalex.org/W2114385471","https://openalex.org/W2494463665","https://openalex.org/W2909373143","https://openalex.org/W2973869319","https://openalex.org/W3138705879","https://openalex.org/W4247295024","https://openalex.org/W4291439952"],"related_works":["https://openalex.org/W1109308563","https://openalex.org/W2049546479","https://openalex.org/W2055410928","https://openalex.org/W2921474356","https://openalex.org/W2015099410","https://openalex.org/W2037345720","https://openalex.org/W1977877422","https://openalex.org/W1976114002","https://openalex.org/W3145975296","https://openalex.org/W2052180011"],"abstract_inverted_index":{"Relaxation":[0],"oscillations":[1,74],"are":[2,56],"periodic":[3],"orbits":[4,23],"of":[5,21,38,47,61],"multiple":[6],"time":[7],"scale":[8],"dynamical":[9],"systems":[10,66],"that":[11,41,55,63],"contain":[12],"both":[13],"slow":[14,69],"and":[15],"fast":[16],"segments.":[17],"The":[18],"slow\u2013fast":[19],"decomposition":[20],"these":[22,39],"is":[24],"defined":[25],"in":[26,32,43,65,71],"the":[27,53],"singular":[28,33],"limit.":[29],"Geometric":[30],"methods":[31],"perturbation":[34],"theory":[35],"classify":[36],"degeneracies":[37],"decompositions":[40],"occur":[42],"generic":[44],"one-parameter":[45],"families":[46],"relaxation":[48,73],"oscillations.":[49],"This":[50],"paper":[51],"investigates":[52],"bifurcations":[54],"associated":[57],"with":[58,67],"one":[59],"type":[60],"degeneracy":[62],"occurs":[64],"two":[68],"variables,":[70],"which":[72],"become":[75],"homoclinic":[76],"to":[77],"a":[78],"folded":[79],"saddle.":[80]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
