{"id":"https://openalex.org/W1964385385","doi":"https://doi.org/10.1137/s0036141003439173","title":"Global Attractors and Steady States for Uniformly Persistent Dynamical Systems","display_name":"Global Attractors and Steady States for Uniformly Persistent Dynamical Systems","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1964385385","doi":"https://doi.org/10.1137/s0036141003439173","mag":"1964385385"},"language":"en","primary_location":{"id":"doi:10.1137/s0036141003439173","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141003439173","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical 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/A5035929676","display_name":"Pierre Magal","orcid":"https://orcid.org/0000-0002-4776-0061"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pierre Magal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5040724309","display_name":"Xiaoqiang Zhao","orcid":"https://orcid.org/0000-0001-5687-942X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiao-Qiang Zhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.705,"has_fulltext":false,"cited_by_count":621,"citation_normalized_percentile":{"value":0.97525657,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"37","issue":"1","first_page":"251","last_page":"275"},"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":0.998199999332428,"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":0.998199999332428,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.968999981880188,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9463000297546387,"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/attractor","display_name":"Attractor","score":0.906828761100769},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8274146318435669},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6592605710029602},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5287991166114807},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.5182394981384277},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5164023041725159},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.5078876614570618},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4540969729423523},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4252851605415344},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.386624813079834},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38009247183799744},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10503572225570679}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.906828761100769},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8274146318435669},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6592605710029602},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5287991166114807},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.5182394981384277},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5164023041725159},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5078876614570618},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4540969729423523},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4252851605415344},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.386624813079834},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38009247183799744},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10503572225570679},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036141003439173","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141003439173","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W338396539","https://openalex.org/W348312448","https://openalex.org/W429124266","https://openalex.org/W1502315489","https://openalex.org/W1519411840","https://openalex.org/W1519611344","https://openalex.org/W1540294802","https://openalex.org/W1541939020","https://openalex.org/W1555674425","https://openalex.org/W1557040331","https://openalex.org/W1559403043","https://openalex.org/W1594759473","https://openalex.org/W1939101225","https://openalex.org/W1963489043","https://openalex.org/W1974446246","https://openalex.org/W1995608339","https://openalex.org/W2002094851","https://openalex.org/W2011401245","https://openalex.org/W2016662457","https://openalex.org/W2034853934","https://openalex.org/W2072867280","https://openalex.org/W2083321256","https://openalex.org/W2094508707","https://openalex.org/W2123261528","https://openalex.org/W2161876659","https://openalex.org/W2482947249","https://openalex.org/W3038830718","https://openalex.org/W4230015191","https://openalex.org/W4245066456","https://openalex.org/W4292366025"],"related_works":["https://openalex.org/W4250831671","https://openalex.org/W2230606337","https://openalex.org/W4301329516","https://openalex.org/W2089869689","https://openalex.org/W4388681848","https://openalex.org/W2078952919","https://openalex.org/W2945666329","https://openalex.org/W2617651062","https://openalex.org/W2330535098","https://openalex.org/W2460935991"],"abstract_inverted_index":{"By":[0],"appealing":[1],"to":[2,43,60,84],"the":[3,18,32,53,62,102],"theory":[4],"of":[5,20,46,55,64,94,104],"global":[6,22,72,77],"attractors":[7,23],"on":[8,35],"complete":[9],"metric":[10],"spaces,":[11],"we":[12],"obtain":[13],"weaker":[14],"sufficient":[15],"conditions":[16],"for":[17,24],"existence":[19,63],"interior":[21,48],"uniformly":[25],"persistent":[26],"dynamical":[27,68],"systems,":[28],"and":[29,59,66,91],"hence":[30],"generalize":[31],"earlier":[33],"results":[34],"coexistence":[36],"steady":[37],"states.":[38],"We":[39],"also":[40],"provide":[41],"examples":[42],"show":[44],"applicability":[45],"our":[47],"fixed":[49],"point":[50],"theorem":[51],"in":[52,101],"case":[54,103],"convex":[56],"$\\kappa$-contracting":[57],"maps,":[58],"prove":[61],"discrete-":[65],"continuous-time":[67,105],"systems":[69],"that":[70],"admit":[71],"attractors,":[73,78],"but":[74],"no":[75],"strong":[76],"which":[79],"gives":[80],"an":[81,85],"affirmative":[82],"answer":[83],"open":[86],"question":[87],"presented":[88],"by":[89],"Sell":[90],"You":[92],"[Dynamics":[93],"Evolutionary":[95],"Equations,":[96],"Springer-Verlag,":[97],"New":[98],"York,":[99],"2002]":[100],"semiflows.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":39},{"year":2025,"cited_by_count":80},{"year":2024,"cited_by_count":69},{"year":2023,"cited_by_count":71},{"year":2022,"cited_by_count":61},{"year":2021,"cited_by_count":47},{"year":2020,"cited_by_count":51},{"year":2019,"cited_by_count":48},{"year":2018,"cited_by_count":32},{"year":2017,"cited_by_count":34},{"year":2016,"cited_by_count":19},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":7}],"updated_date":"2026-06-17T08:01:34.144755","created_date":"2025-10-10T00:00:00"}
