{"id":"https://openalex.org/W2561461495","doi":"https://doi.org/10.1137/16m1064611","title":"Smooth Dynamics Becomes Hybrid in the Limit","display_name":"Smooth Dynamics Becomes Hybrid in the Limit","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2561461495","doi":"https://doi.org/10.1137/16m1064611","mag":"2561461495"},"language":"en","primary_location":{"id":"doi:10.1137/16m1064611","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1064611","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11250/2577735","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034369477","display_name":"Arcady Ponosov","orcid":"https://orcid.org/0000-0001-5018-6577"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Arcady Ponosov","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066206471","display_name":"Eugene Stepanov","orcid":"https://orcid.org/0000-0002-0517-155X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eugene Stepanov","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034369477"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00896315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"55","issue":"1","first_page":"29","last_page":"50"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9973000288009644,"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"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9973000288009644,"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":0.9932000041007996,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.8713263273239136},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7836878895759583},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.7559937834739685},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5993788838386536},{"id":"https://openalex.org/keywords/limit-point","display_name":"Limit point","score":0.5153195858001709},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.47698265314102173},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4713175892829895},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.457358717918396},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.45552003383636475},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.42379891872406006},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3775765299797058},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10184073448181152},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08868834376335144},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.06530997157096863}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.8713263273239136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7836878895759583},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.7559937834739685},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5993788838386536},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.5153195858001709},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.47698265314102173},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4713175892829895},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.457358717918396},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.45552003383636475},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.42379891872406006},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3775765299797058},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10184073448181152},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08868834376335144},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.06530997157096863},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/16m1064611","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1064611","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arpi.unipi.it:11568/1302230","is_oa":false,"landing_page_url":"https://hdl.handle.net/11568/1302230","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:brage.bibsys.no:11250/2577735","is_oa":true,"landing_page_url":"http://hdl.handle.net/11250/2577735","pdf_url":null,"source":{"id":"https://openalex.org/S4306401716","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"29-50","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:brage.bibsys.no:11250/2577804","is_oa":true,"landing_page_url":"http://hdl.handle.net/11250/2577804","pdf_url":null,"source":{"id":"https://openalex.org/S4306401716","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"29-50","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:brage.bibsys.no:11250/2577735","is_oa":true,"landing_page_url":"http://hdl.handle.net/11250/2577735","pdf_url":null,"source":{"id":"https://openalex.org/S4306401716","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"29-50","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7240477248","display_name":null,"funder_award_id":"239070","funder_id":"https://openalex.org/F4320323299","funder_display_name":"Norges Forskningsr\u00e5d"}],"funders":[{"id":"https://openalex.org/F4320323299","display_name":"Norges Forskningsr\u00e5d","ror":"https://ror.org/00epmv149"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1504756454","https://openalex.org/W1522579744","https://openalex.org/W1535498797","https://openalex.org/W1984319180","https://openalex.org/W1988383139","https://openalex.org/W2005276415","https://openalex.org/W2028118090","https://openalex.org/W2031369606","https://openalex.org/W2043539373","https://openalex.org/W2055345548","https://openalex.org/W2083309269","https://openalex.org/W2093939816","https://openalex.org/W2102955267","https://openalex.org/W2111862827","https://openalex.org/W2121922603","https://openalex.org/W2325450327","https://openalex.org/W2962996317"],"related_works":["https://openalex.org/W3042698916","https://openalex.org/W1271291390","https://openalex.org/W4230102134","https://openalex.org/W4250831671","https://openalex.org/W1991117052","https://openalex.org/W2230606337","https://openalex.org/W275305536","https://openalex.org/W2137183140","https://openalex.org/W2363533283","https://openalex.org/W2617651062"],"abstract_inverted_index":{"We":[0,80],"show":[1],"the":[2,10,38,85,90,114],"appearance":[3],"of":[4,13,15,18,58,88,93,96],"an":[5,50,94,103],"essentially":[6],"nonlocal":[7],"dynamics":[8,43,75],"describing":[9],"limit":[11,42,91],"behavior":[12,92],"trajectories":[14,97],"a":[16,31,59,65],"class":[17],"dynamical":[19,55],"systems":[20],"defined":[21],"by":[22,49,102],"classical":[23],"autonomous":[24],"ODEs":[25],"with":[26,76,105],"smooth":[27],"right-hand":[28,110],"sides":[29],"containing":[30],"small":[32],"parameter":[33],"and":[34,64,72,108],"becoming":[35],"discontinuous":[36,109],"in":[37],"formal":[39],"limit.":[40],"The":[41],"is":[44],"shown":[45],"to":[46],"be":[47,100],"described":[48,101],"explicitly":[51],"constructed":[52],"Nerode--Kohn":[53],"hybrid":[54,74],"system":[56],"consisting":[57],"continuous":[60],"plant":[61],"(an":[62],"ODE)":[63],"finite":[66],"state":[67],"machine":[68],"which":[69],"are":[70],"interacting":[71],"producing":[73],"possible":[77],"memory":[78],"effects.":[79],"remark,":[81],"however,":[82],"that,":[83],"from":[84],"\u201cstatistical\u201d":[86],"point":[87],"view,":[89],"ensemble":[95],"can":[98],"still":[99],"ODE,":[104],"possibly":[106],"time-dependent":[107],"side":[111],"depending":[112],"on":[113],"chosen":[115],"ensemble.":[116]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2017-01-06T00:00:00"}