{"id":"https://openalex.org/W2930130240","doi":"https://doi.org/10.3233/asy-181501","title":"Tail convergences of pullback attractors for asymptotically converging multi-valued dynamical systems","display_name":"Tail convergences of pullback attractors for asymptotically converging multi-valued dynamical systems","publication_year":2019,"publication_date":"2019-04-01","ids":{"openalex":"https://openalex.org/W2930130240","doi":"https://doi.org/10.3233/asy-181501","mag":"2930130240"},"language":"en","primary_location":{"id":"doi:10.3233/asy-181501","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-181501","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","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/A5023933569","display_name":"Hongyong Cui","orcid":"https://orcid.org/0000-0002-4037-749X"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongyong Cui","raw_affiliation_strings":["School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P.R.\u00a0China. E-mails:\u00a0,\u00a0"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P.R.\u00a0China. E-mails:\u00a0,\u00a0","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021471659","display_name":"Peter E. Kloeden","orcid":"https://orcid.org/0000-0001-9505-2257"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peter E. Kloeden","raw_affiliation_strings":["School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P.R.\u00a0China. E-mails:\u00a0,\u00a0"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P.R.\u00a0China. E-mails:\u00a0,\u00a0","institution_ids":["https://openalex.org/I47720641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023933569"],"corresponding_institution_ids":["https://openalex.org/I47720641"],"apc_list":null,"apc_paid":null,"fwci":1.5172,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.82542907,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"112","issue":"3-4","first_page":"165","last_page":"184"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9919000267982483,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9833999872207642,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pullback-attractor","display_name":"Pullback attractor","score":0.9932673573493958},{"id":"https://openalex.org/keywords/pullback","display_name":"Pullback","score":0.8968487977981567},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.834883451461792},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6655869483947754},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.5811635851860046},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5514947175979614},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.5510669946670532},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4765370786190033},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46383747458457947},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4388478994369507},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3496205806732178},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1325061321258545},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10701742768287659}],"concepts":[{"id":"https://openalex.org/C2778100799","wikidata":"https://www.wikidata.org/wiki/Q7259416","display_name":"Pullback attractor","level":3,"score":0.9932673573493958},{"id":"https://openalex.org/C2777680557","wikidata":"https://www.wikidata.org/wiki/Q7259417","display_name":"Pullback","level":2,"score":0.8968487977981567},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.834883451461792},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6655869483947754},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.5811635851860046},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5514947175979614},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.5510669946670532},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4765370786190033},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46383747458457947},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4388478994369507},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3496205806732178},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1325061321258545},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10701742768287659},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/asy-181501","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-181501","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W91588129","https://openalex.org/W148742480","https://openalex.org/W1973343816","https://openalex.org/W1976221710","https://openalex.org/W1991014733","https://openalex.org/W2002865886","https://openalex.org/W2036198930","https://openalex.org/W2075005555","https://openalex.org/W2507170421","https://openalex.org/W2509441329","https://openalex.org/W2557613019","https://openalex.org/W2601104850","https://openalex.org/W2607887446","https://openalex.org/W2625894742","https://openalex.org/W2769021578","https://openalex.org/W2963078916","https://openalex.org/W2964088223"],"related_works":["https://openalex.org/W4248741366","https://openalex.org/W1997786140","https://openalex.org/W2037296061","https://openalex.org/W2132944121","https://openalex.org/W2013443755","https://openalex.org/W1979224606","https://openalex.org/W3087962578","https://openalex.org/W2366849099","https://openalex.org/W2075005555","https://openalex.org/W2944338505"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"study":[4],"pullback":[5,26,40,55],"attractors":[6],"of":[7,24,28,38,42],"multi-valued":[8],"dynamical":[9,30,45],"systems":[10],"that":[11],"are":[12,49,63,70],"asymptotically":[13,50,53],"convergent.":[14],"It":[15],"is":[16],"shown":[17],"that,":[18],"under":[19],"certain":[20],"conditions,":[21],"the":[22,25,39,43],"components":[23],"attractor":[27,41],"a":[29],"system":[31],"can":[32],"converge":[33],"in":[34],"time":[35],"to":[36],"those":[37],"limiting":[44],"system.":[46],"Particular":[47],"examples":[48],"autonomous":[51],"and":[52,65,68],"periodic":[54],"attractors.":[56],"Different":[57],"criteria":[58],"theorems":[59],"requiring":[60],"different":[61],"conditions":[62],"established":[64],"their":[66],"applicability":[67],"advantages":[69],"highlighted.":[71]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
