{"id":"https://openalex.org/W2081245642","doi":"https://doi.org/10.1137/090766826","title":"An Analytical Approach to Codimension-2 Sliding Bifurcations in the Dry-Friction Oscillator","display_name":"An Analytical Approach to Codimension-2 Sliding Bifurcations in the Dry-Friction Oscillator","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2081245642","doi":"https://doi.org/10.1137/090766826","mag":"2081245642"},"language":"en","primary_location":{"id":"doi:10.1137/090766826","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090766826","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":"http://hdl.handle.net/2117/9131","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086464434","display_name":"Marcel Gu\u00e0rdia","orcid":"https://orcid.org/0000-0002-4802-3151"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Marcel Guardia","raw_affiliation_strings":["Polytechnic University of Catalonia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Polytechnic University of Catalonia","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013257413","display_name":"S. J. Hogan","orcid":"https://orcid.org/0000-0001-6012-6527"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"S. John Hogan","raw_affiliation_strings":["Polytechnic University of Catalonia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Polytechnic University of Catalonia","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003594826","display_name":"Tere M. Seara","orcid":"https://orcid.org/0000-0001-8421-8717"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Tere M. Seara","raw_affiliation_strings":["University of Bristol"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Bristol","institution_ids":["https://openalex.org/I36234482"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9421,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.91067041,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"9","issue":"3","first_page":"769","last_page":"798"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T10244","display_name":"Chaos control and synchronization","score":0.9968000054359436,"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":0.9950000047683716,"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/codimension","display_name":"Codimension","score":0.9590641260147095},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.7594667673110962},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6796751022338867},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6059584617614746},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.5859838724136353},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.5057170391082764},{"id":"https://openalex.org/keywords/dry-friction","display_name":"Dry friction","score":0.485838383436203},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4633965790271759},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44629934430122375},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3394695520401001},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3365916609764099},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2673853933811188},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18819424510002136},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.14271554350852966},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05481451749801636}],"concepts":[{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.9590641260147095},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.7594667673110962},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6796751022338867},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6059584617614746},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.5859838724136353},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.5057170391082764},{"id":"https://openalex.org/C2987647002","wikidata":"https://www.wikidata.org/wiki/Q82580","display_name":"Dry friction","level":2,"score":0.485838383436203},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4633965790271759},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44629934430122375},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3394695520401001},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3365916609764099},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2673853933811188},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18819424510002136},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.14271554350852966},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05481451749801636},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/090766826","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090766826","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:research-information.bris.ac.uk:openaire_cris_publications/a2e96f7e-b974-42c8-b325-17f533674446","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/a2e96f7e-b974-42c8-b325-17f533674446","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Guardia, M, Hogan, SJ & Martinez-Seara, T 2010, 'An analytical approach to codimension-2 sliding bifurcations in the dry friction oscillator', SIAM Journal on Applied Dynamical Systems, vol. 9, no. 3, pp. 769 - 798. https://doi.org/10.1137/090766826","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/a2e96f7e-b974-42c8-b325-17f533674446","is_oa":false,"landing_page_url":"http://epubs.siam.org/siads/resource/1/sjaday/v9/i3/p769_s1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Guardia, M, Hogan, SJ & Martinez-Seara, T 2010, 'An analytical approach to codimension-2 sliding bifurcations in the dry friction oscillator', SIAM Journal on Applied Dynamical Systems, vol. 9, no. 3, pp. 769 - 798. https://doi.org/10.1137/090766826","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:upcommons.upc.edu:2117/9131","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/9131","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:upcommons.upc.edu:2117/9131","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/9131","pdf_url":null,"source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W49800840","https://openalex.org/W607491616","https://openalex.org/W1516289514","https://openalex.org/W1517510293","https://openalex.org/W1592648094","https://openalex.org/W1593811304","https://openalex.org/W1969485390","https://openalex.org/W1972735070","https://openalex.org/W1979807014","https://openalex.org/W1982248493","https://openalex.org/W1982656837","https://openalex.org/W1998649787","https://openalex.org/W2011227277","https://openalex.org/W2012996283","https://openalex.org/W2033706714","https://openalex.org/W2034847893","https://openalex.org/W2047449028","https://openalex.org/W2050416508","https://openalex.org/W2056494071","https://openalex.org/W2057162775","https://openalex.org/W2061862587","https://openalex.org/W2071780273","https://openalex.org/W2080761408","https://openalex.org/W2085685508","https://openalex.org/W2090022960","https://openalex.org/W2091083214","https://openalex.org/W2098085850","https://openalex.org/W2118395206","https://openalex.org/W2121253368","https://openalex.org/W2125605829","https://openalex.org/W2140505231","https://openalex.org/W2160775133","https://openalex.org/W2169337538","https://openalex.org/W3102140334","https://openalex.org/W4366166980"],"related_works":["https://openalex.org/W2215301093","https://openalex.org/W1970311793","https://openalex.org/W2150264438","https://openalex.org/W2091442046","https://openalex.org/W3026479466","https://openalex.org/W4290072500","https://openalex.org/W2939676003","https://openalex.org/W2023944991","https://openalex.org/W2138040070","https://openalex.org/W2081245642"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"analytically":[4],"consider":[5],"sliding":[6],"bifurcations":[7],"of":[8,27,34,41,53,90],"periodic":[9],"orbits":[10],"in":[11,65],"the":[12,25,28,32,35,39,71,87],"dry-friction":[13],"oscillator.":[14],"The":[15],"system":[16],"depends":[17],"on":[18,51],"two":[19,52],"parameters:":[20],"F,":[21],"which":[22],"corresponds":[23],"to":[24],"intensity":[26],"friction,":[29],"and":[30,47,58,79,92],"$\\omega$,":[31],"frequency":[33],"forcing.":[36],"We":[37,61],"prove":[38],"existence":[40],"infinitely":[42],"many":[43],"codimension-2":[44],"bifurcation":[45,73],"points":[46],"focus":[48],"our":[49],"attention":[50],"them:":[54],"$A_1:=(\\omega\\ii,":[55],"F)=(2,":[56],"1/3)$":[57],"$B_1:=(\\omega\\ii,":[59],"F)=(3,0)$.":[60],"derive":[62],"analytic":[63],"expressions":[64],"($\\omega\\ii$,":[66],"F)":[67],"parameter":[68],"space":[69],"for":[70],"codimension-1":[72],"curves":[74],"that":[75],"emanate":[76],"from":[77],"$A_1$":[78],"$B_1$.":[80],"Our":[81],"results":[82],"show":[83],"excellent":[84],"agreement":[85],"with":[86],"numerical":[88],"calculations":[89],"Kowalczyk":[91],"Piiroinen":[93],"[Phys.":[94],"D,":[95],"237":[96],"(2008),":[97],"pp.":[98],"1053\u20131073].":[99]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2016-06-24T00:00:00"}
