{"id":"https://openalex.org/W4399122097","doi":"https://doi.org/10.1137/23m1587488","title":"Nonuniqueness Phenomena in Discontinuous Dynamical Systems and Their Regularizations","display_name":"Nonuniqueness Phenomena in Discontinuous Dynamical Systems and Their Regularizations","publication_year":2024,"publication_date":"2024-05-29","ids":{"openalex":"https://openalex.org/W4399122097","doi":"https://doi.org/10.1137/23m1587488"},"language":"en","primary_location":{"id":"doi:10.1137/23m1587488","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1587488","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036438633","display_name":"Alessia And\u00f2","orcid":"https://orcid.org/0000-0002-4051-2049"},"institutions":[{"id":"https://openalex.org/I4210150763","display_name":"Gran Sasso Science Institute","ror":"https://ror.org/043qcb444","country_code":"IT","type":"education","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210150763"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Alessia And\u00f2","raw_affiliation_strings":["Gran Sasso Science Institute, 67100, L\u2019Aquila AQ, Italy","Gran Sasso Science Institute, Viale Francesco Crispi 7, 67100 L'Aquila AQ, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Gran Sasso Science Institute, 67100, L\u2019Aquila AQ, Italy","institution_ids":["https://openalex.org/I4210150763"]},{"raw_affiliation_string":"Gran Sasso Science Institute, Viale Francesco Crispi 7, 67100 L'Aquila AQ, Italy","institution_ids":["https://openalex.org/I4210150763"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056190390","display_name":"Roderick Edwards","orcid":"https://orcid.org/0000-0002-8239-5987"},"institutions":[{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Roderick Edwards","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada","Dept. of Mathematics and Statistics, University of Victoria, P.O. Box 1700 STN CSC, Victoria, B.C., Canada, V8W 2Y2"],"raw_orcid":"https://orcid.org/0000-0002-8239-5987","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada","institution_ids":["https://openalex.org/I212119943"]},{"raw_affiliation_string":"Dept. of Mathematics and Statistics, University of Victoria, P.O. Box 1700 STN CSC, Victoria, B.C., Canada, V8W 2Y2","institution_ids":["https://openalex.org/I212119943"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030219464","display_name":"Nicola Guglielmi","orcid":"https://orcid.org/0000-0003-3795-5225"},"institutions":[{"id":"https://openalex.org/I4210150763","display_name":"Gran Sasso Science Institute","ror":"https://ror.org/043qcb444","country_code":"IT","type":"education","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210150763"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Nicola Guglielmi","raw_affiliation_strings":["Gran Sasso Science Institute, 67100, L\u2019Aquila AQ, Italy","Gran Sasso Science Institute, Viale Francesco Crispi 7, 67100 L'Aquila AQ, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Gran Sasso Science Institute, 67100, L\u2019Aquila AQ, Italy","institution_ids":["https://openalex.org/I4210150763"]},{"raw_affiliation_string":"Gran Sasso Science Institute, Viale Francesco Crispi 7, 67100 L'Aquila AQ, Italy","institution_ids":["https://openalex.org/I4210150763"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5036438633"],"corresponding_institution_ids":["https://openalex.org/I4210150763"],"apc_list":null,"apc_paid":null,"fwci":0.3124,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.52532367,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"23","issue":"2","first_page":"1345","last_page":"1371"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9945999979972839,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6323907971382141},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.45658203959465027},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4372327923774719},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41507643461227417},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.37564340233802795},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09027069807052612}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6323907971382141},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.45658203959465027},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4372327923774719},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41507643461227417},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37564340233802795},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09027069807052612}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m1587488","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1587488","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6195344088","display_name":null,"funder_award_id":"RGPIN-2017-04042","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"},{"id":"https://openalex.org/F4320328429","display_name":"Gran Sasso Science Institute","ror":"https://ror.org/043qcb444"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W207692870","https://openalex.org/W1201619888","https://openalex.org/W1788065082","https://openalex.org/W1964901569","https://openalex.org/W1988383139","https://openalex.org/W2020097836","https://openalex.org/W2028118090","https://openalex.org/W2043539373","https://openalex.org/W2048250166","https://openalex.org/W2055345548","https://openalex.org/W2055975889","https://openalex.org/W2062826454","https://openalex.org/W2063397490","https://openalex.org/W2089876099","https://openalex.org/W2092488734","https://openalex.org/W2111862827","https://openalex.org/W2134619341","https://openalex.org/W2144125414","https://openalex.org/W2167751642","https://openalex.org/W2593063709","https://openalex.org/W2793737711","https://openalex.org/W2892136592","https://openalex.org/W3182721126","https://openalex.org/W4221036531","https://openalex.org/W4293078920","https://openalex.org/W4324056439"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W3148032049"],"abstract_inverted_index":{"an":[0,84],"analysis":[1],"in":[2,14,43,76,103,129,143],"the":[3,28,33,62,87,90,94,97,100,104,125,130,144],"\u03b5":[4],"\u2192":[5],"0":[6],"limit":[7,38,91,141],"was":[8,19,40,56],"proposed":[9],"of":[10,35,48,80,86,89,96,107,120,127],"regularized":[11],"discontinuous":[12,108],"ODEs":[13],"codimension-2":[15,133],"switching":[16,98],"domains;":[17],"this":[18,67,81],"obtained":[20],"by":[21],"studying":[22],"a":[23,36,46,110,114,118,140],"certain":[24],"2-dimensional":[25],"system":[26],"describing":[27],"so-called":[29],"hidden":[30,145],"dynamics.In":[31],"particular,":[32],"existence":[34],"unique":[37],"solution":[39,92],"not":[41,57,61],"proved":[42],"all":[44],"cases,":[45],"few":[47],"which":[49],"were":[50],"labeled":[51],"as":[52],"ambiguous,":[53],"and":[54],"it":[55,72],"clear":[58],"whether":[59],"or":[60],"ambiguity":[63],"could":[64],"be":[65,74],"resolved.In":[66],"paper,":[68],"we":[69,123],"show":[70],"that":[71],"cannot":[73],"resolved":[75],"general.A":[77],"first":[78],"contribution":[79,112],"paper":[82],"is":[83,113,139],"illustration":[85],"dependence":[88,102],"on":[93],"form":[95],"function.Considering":[99],"parameter":[101],"ambiguous":[105],"class":[106],"systems,":[109],"second":[111],"bifurcation":[115],"analysis,":[116],"revealing":[117],"range":[119],"possible":[121],"behaviors.Finally,":[122],"investigate":[124],"sensitivity":[126],"solutions":[128],"transition":[131],"from":[132],"domains":[134],"to":[135],"codimension-3":[136],"when":[137],"there":[138],"cycle":[142],"dynamics.":[146]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-05-04T08:30:34.212998","created_date":"2024-05-30T00:00:00"}