{"id":"https://openalex.org/W1542762295","doi":"https://doi.org/10.1109/ecctd.2005.1522950","title":"On the bifurcation properties of a class of differentiable mappings","display_name":"On the bifurcation properties of a class of differentiable mappings","publication_year":2006,"publication_date":"2006-10-11","ids":{"openalex":"https://openalex.org/W1542762295","doi":"https://doi.org/10.1109/ecctd.2005.1522950","mag":"1542762295"},"language":"en","primary_location":{"id":"doi:10.1109/ecctd.2005.1522950","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecctd.2005.1522950","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2005 European Conference on Circuit Theory and Design, 2005.","raw_type":"proceedings-article"},"type":"conference-paper","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/A5044279601","display_name":"Colm P. O\u2019Donnell","orcid":"https://orcid.org/0000-0002-8004-450X"},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"B. O'Donnell","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University College Dublin, Ireland","Dept. of Electr. & Electron. Eng., Univ. Coll., Dublin, Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University College Dublin, Ireland","institution_ids":["https://openalex.org/I100930933"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., Univ. Coll., Dublin, Ireland","institution_ids":["https://openalex.org/I100930933"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091106135","display_name":"Paul Curran","orcid":null},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"P.F. Curran","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University College Dublin, Ireland","Dept. of Electr. & Electron. Eng., Univ. Coll., Dublin, Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University College Dublin, Ireland","institution_ids":["https://openalex.org/I100930933"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., Univ. Coll., Dublin, Ireland","institution_ids":["https://openalex.org/I100930933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074660128","display_name":"Orla Feely","orcid":"https://orcid.org/0000-0003-3426-6854"},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"O. Feely","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University College Dublin, Ireland","Dept. of Electr. & Electron. Eng., Univ. Coll., Dublin, Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University College Dublin, Ireland","institution_ids":["https://openalex.org/I100930933"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., Univ. Coll., Dublin, Ireland","institution_ids":["https://openalex.org/I100930933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I100930933"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"1","issue":null,"first_page":"221","last_page":"224"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9927999973297119,"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":0.76004958152771},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6873980760574341},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.6451735496520996},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6281508207321167},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5919957756996155},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.5797712802886963},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5522013306617737},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5246204137802124},{"id":"https://openalex.org/keywords/bogdanov\u2013takens-bifurcation","display_name":"Bogdanov\u2013Takens bifurcation","score":0.5031699538230896},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.4967806935310364},{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.4803263247013092},{"id":"https://openalex.org/keywords/period","display_name":"Period (music)","score":0.46340441703796387},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4495396614074707},{"id":"https://openalex.org/keywords/infinite-period-bifurcation","display_name":"Infinite-period bifurcation","score":0.43524831533432007},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3841395676136017},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.25405165553092957},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14296764135360718},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12808078527450562},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.09669375419616699}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.76004958152771},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6873980760574341},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.6451735496520996},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6281508207321167},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5919957756996155},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.5797712802886963},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5522013306617737},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5246204137802124},{"id":"https://openalex.org/C22257346","wikidata":"https://www.wikidata.org/wiki/Q4937510","display_name":"Bogdanov\u2013Takens bifurcation","level":5,"score":0.5031699538230896},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.4967806935310364},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.4803263247013092},{"id":"https://openalex.org/C2781291010","wikidata":"https://www.wikidata.org/wiki/Q178580","display_name":"Period (music)","level":2,"score":0.46340441703796387},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4495396614074707},{"id":"https://openalex.org/C165150564","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Infinite-period bifurcation","level":5,"score":0.43524831533432007},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3841395676136017},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.25405165553092957},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14296764135360718},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12808078527450562},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.09669375419616699},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ecctd.2005.1522950","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecctd.2005.1522950","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2005 European Conference on Circuit Theory and Design, 2005.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1969817005","https://openalex.org/W1995163729","https://openalex.org/W1998464603","https://openalex.org/W2010183034","https://openalex.org/W2018672845","https://openalex.org/W2109629461"],"related_works":["https://openalex.org/W2978098199","https://openalex.org/W2075769438","https://openalex.org/W2054978396","https://openalex.org/W2546487931","https://openalex.org/W1973618006","https://openalex.org/W2003334682","https://openalex.org/W4245057904","https://openalex.org/W2143208590","https://openalex.org/W4311809865","https://openalex.org/W4214875847"],"abstract_inverted_index":{"The":[0],"bifurcation":[1,36,67,72],"properties":[2],"of":[3,6,26,38,74,78],"a":[4,46],"class":[5,12],"differential":[7],"mappings":[8],"are":[9,17],"examined.":[10],"This":[11],"describes":[13],"perturbed":[14,40],"systems":[15],"that":[16,35,59],"characterized":[18],"in":[19,28,60],"the":[20,29,39,50,71,75,79,83],"steady-state":[21],"by":[22],"an":[23],"invariant":[24],"set":[25],"points":[27,37,73,77],"period-1":[30,51],"region.":[31],"It":[32],"was":[33],"found":[34],"and":[41],"associated":[42],"unperturbed":[43,80],"system":[44],"satisfy":[45],"strict":[47],"ordering":[48,85],"for":[49],"case.":[52],"In":[53],"this":[54],"paper":[55],"it":[56],"is":[57],"proven":[58],"general":[61],"there":[62],"exists":[63],"period-n":[64,76],"intervals":[65],"whose":[66],"points,":[68],"together":[69],"with":[70],"system,":[81],"obey":[82],"same":[84],"result.":[86]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
