{"id":"https://openalex.org/W2586628801","doi":"https://doi.org/10.1142/s0218127417500055","title":"Bifurcation Diagram of Saddle/Spiral Bimodal Linear Systems","display_name":"Bifurcation Diagram of Saddle/Spiral Bimodal Linear Systems","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2586628801","doi":"https://doi.org/10.1142/s0218127417500055","mag":"2586628801"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127417500055","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417500055","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":"http://hdl.handle.net/2117/103748","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037103898","display_name":"Josep Ferrer","orcid":"https://orcid.org/0000-0003-3380-231X"},"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":true,"raw_author_name":"Josep Ferrer","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Polit\u00e8cnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Polit\u00e8cnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063612342","display_name":"Marta Pe\u00f1a","orcid":"https://orcid.org/0000-0003-3889-8584"},"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":"Marta Pe\u00f1a","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Polit\u00e8cnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Polit\u00e8cnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022025761","display_name":"Antoni Sus\u00edn","orcid":null},"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":"Antoni Susin","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Polit\u00e8cnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Polit\u00e8cnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5037103898"],"corresponding_institution_ids":["https://openalex.org/I9617848"],"apc_list":null,"apc_paid":null,"fwci":0.4274,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56026619,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"27","issue":"01","first_page":"1750005","last_page":"1750005"},"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":1.0,"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":1.0,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9929999709129333,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9898999929428101,"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/bifurcation","display_name":"Bifurcation","score":0.7944632768630981},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.767510175704956},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.66073077917099},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.657818615436554},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.6209621429443359},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.5945229530334473},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.5315477848052979},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5105872750282288},{"id":"https://openalex.org/keywords/spiral","display_name":"Spiral (railway)","score":0.4999270439147949},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4707420766353607},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.4487888514995575},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4160216450691223},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3887399435043335},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.25579309463500977},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22868072986602783},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.19285431504249573},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.05052590370178223}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7944632768630981},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.767510175704956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.66073077917099},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.657818615436554},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.6209621429443359},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.5945229530334473},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.5315477848052979},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5105872750282288},{"id":"https://openalex.org/C174128100","wikidata":"https://www.wikidata.org/wiki/Q846907","display_name":"Spiral (railway)","level":2,"score":0.4999270439147949},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4707420766353607},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.4487888514995575},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4160216450691223},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3887399435043335},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25579309463500977},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22868072986602783},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.19285431504249573},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.05052590370178223},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218127417500055","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127417500055","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:recercat.cat:2072/283885","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/103748","pdf_url":null,"source":{"id":"https://openalex.org/S4306402147","display_name":"RECERCAT (Consorci de Serveis Universitaris de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210090028","host_organization_name":"Consorci de Serveis Universitaris de Catalunya","host_organization_lineage":["https://openalex.org/I4210090028"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/submittedVersion"},{"id":"pmh:oai:upcommons.upc.edu:2117/103748","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/103748","pdf_url":null,"source":{"id":"https://openalex.org/S4210207057","display_name":"QRU Quaderns de Recerca en Urbanisme","issn_l":"2014-9689","issn":["2014-9689","2385-6777"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310322448","host_organization_name":"Q71272178","host_organization_lineage":["https://openalex.org/P4310322448"],"host_organization_lineage_names":["Q71272178"],"type":"journal"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:recercat.cat:2072/283885","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/103748","pdf_url":null,"source":{"id":"https://openalex.org/S4306402147","display_name":"RECERCAT (Consorci de Serveis Universitaris de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210090028","host_organization_name":"Consorci de Serveis Universitaris de Catalunya","host_organization_lineage":["https://openalex.org/I4210090028"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/submittedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G419500086","display_name":null,"funder_award_id":"DGICYTMTM2011-23892","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G4589820310","display_name":null,"funder_award_id":"TIN2014-52211-C2-1-R","funder_id":"https://openalex.org/F4320321764","funder_display_name":"Ministerio de Educaci\u00f3n, Cultura y Deporte"}],"funders":[{"id":"https://openalex.org/F4320321764","display_name":"Ministerio de Educaci\u00f3n, Cultura y Deporte","ror":"https://ror.org/03nc27g21"},{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1968323027","https://openalex.org/W1980709212","https://openalex.org/W1996518355","https://openalex.org/W2002282594","https://openalex.org/W2023599497","https://openalex.org/W2024150315","https://openalex.org/W2037024940","https://openalex.org/W2075372712","https://openalex.org/W2136632272","https://openalex.org/W2146447376","https://openalex.org/W2157651338"],"related_works":["https://openalex.org/W2803928976","https://openalex.org/W2546487931","https://openalex.org/W3097933399","https://openalex.org/W2404180431","https://openalex.org/W2348340245","https://openalex.org/W37064175","https://openalex.org/W3138146974","https://openalex.org/W4214875847","https://openalex.org/W2560127293","https://openalex.org/W2361529576"],"abstract_inverted_index":{"We":[0,32],"complete":[1],"the":[2,5,14,34,38,45,49],"study":[3],"of":[4,7,29,48],"bifurcations":[6],"saddle/spiral":[8],"bimodal":[9],"linear":[10],"systems,":[11],"depending":[12],"on":[13],"respective":[15],"traces":[16],"[Formula:":[17,21,39],"see":[18,22,40],"text]":[19],"and":[20,42],"text]:":[23],"one":[24],"2-codimensional":[25],"bifurcation;":[26],"four":[27],"kinds":[28],"1-codimensional":[30],"bifurcations.":[31],"stratify":[33],"bifurcation":[35,54],"set":[36],"in":[37],"text]-plane":[41],"we":[43],"describe":[44],"qualitative":[46],"changes":[47],"dynamical":[50],"behavior":[51],"at":[52],"each":[53],"point.":[55]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}