{"id":"https://openalex.org/W2015217267","doi":"https://doi.org/10.1137/s0036139999359756","title":"Global Asymptotic Behavior of a Chemostat Model with Two Perfectly Complementary Resources and Distributed Delay","display_name":"Global Asymptotic Behavior of a Chemostat Model with Two Perfectly Complementary Resources and Distributed Delay","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2015217267","doi":"https://doi.org/10.1137/s0036139999359756","mag":"2015217267"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139999359756","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139999359756","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Mathematics","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/A5017820212","display_name":"Bingtuan Li","orcid":"https://orcid.org/0000-0002-1444-6201"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]},{"id":"https://openalex.org/I2800403580","display_name":"University of Minnesota System","ror":"https://ror.org/03grvy078","country_code":"US","type":"education","lineage":["https://openalex.org/I2800403580"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bingtuan Li","raw_affiliation_strings":["University of Utah","University of Minnesota"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Utah","institution_ids":["https://openalex.org/I223532165"]},{"raw_affiliation_string":"University of Minnesota","institution_ids":["https://openalex.org/I2800403580"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003253096","display_name":"Gail S. K. Wolkowicz","orcid":"https://orcid.org/0000-0002-4501-2342"},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Gail S. K. Wolkowicz","raw_affiliation_strings":["McMaster university#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"McMaster university#TAB#","institution_ids":["https://openalex.org/I98251732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090207401","display_name":"Yang Kuang","orcid":"https://orcid.org/0000-0003-2774-4133"},"institutions":[{"id":"https://openalex.org/I4210152479","display_name":"Statistical Service","ror":"https://ror.org/05vydvf11","country_code":"CY","type":"government","lineage":["https://openalex.org/I4210152479"]}],"countries":["CY"],"is_corresponding":false,"raw_author_name":"Yang Kuang","raw_affiliation_strings":["CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)","institution_ids":["https://openalex.org/I4210152479"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5215,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.88866919,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"60","issue":"6","first_page":"2058","last_page":"2086"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.998199999332428,"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"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.998199999332428,"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"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"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9878000020980835,"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/chemostat","display_name":"Chemostat","score":0.9653302431106567},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6602200865745544},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5817746520042419},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.580985963344574},{"id":"https://openalex.org/keywords/nutrient","display_name":"Nutrient","score":0.5206465125083923},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5203075408935547},{"id":"https://openalex.org/keywords/biomass","display_name":"Biomass (ecology)","score":0.4619719088077545},{"id":"https://openalex.org/keywords/competitive-exclusion","display_name":"Competitive exclusion","score":0.45411092042922974},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.4153960049152374},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.36121028661727905},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3509560525417328},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3237813115119934},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2927321195602417},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2711940407752991},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.249840646982193},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.0938965380191803},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.09142634272575378},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0736539363861084}],"concepts":[{"id":"https://openalex.org/C125111812","wikidata":"https://www.wikidata.org/wiki/Q902311","display_name":"Chemostat","level":3,"score":0.9653302431106567},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6602200865745544},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5817746520042419},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.580985963344574},{"id":"https://openalex.org/C142796444","wikidata":"https://www.wikidata.org/wiki/Q181394","display_name":"Nutrient","level":2,"score":0.5206465125083923},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5203075408935547},{"id":"https://openalex.org/C115540264","wikidata":"https://www.wikidata.org/wiki/Q2945560","display_name":"Biomass (ecology)","level":2,"score":0.4619719088077545},{"id":"https://openalex.org/C2992687717","wikidata":"https://www.wikidata.org/wiki/Q1331830","display_name":"Competitive exclusion","level":3,"score":0.45411092042922974},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.4153960049152374},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.36121028661727905},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3509560525417328},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3237813115119934},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2927321195602417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2711940407752991},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.249840646982193},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0938965380191803},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.09142634272575378},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0736539363861084},{"id":"https://openalex.org/C523546767","wikidata":"https://www.wikidata.org/wiki/Q10876","display_name":"Bacteria","level":2,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C91306197","wikidata":"https://www.wikidata.org/wiki/Q45767","display_name":"Competition (biology)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139999359756","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139999359756","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":63,"referenced_works":["https://openalex.org/W10129326","https://openalex.org/W139022562","https://openalex.org/W625396986","https://openalex.org/W1587425752","https://openalex.org/W1965267854","https://openalex.org/W1966552169","https://openalex.org/W1967444104","https://openalex.org/W1968201943","https://openalex.org/W1974186209","https://openalex.org/W1975326031","https://openalex.org/W1979140770","https://openalex.org/W1986978791","https://openalex.org/W1988025776","https://openalex.org/W1988681504","https://openalex.org/W1989998020","https://openalex.org/W1994831429","https://openalex.org/W1995986570","https://openalex.org/W1996800916","https://openalex.org/W2000949264","https://openalex.org/W2004572088","https://openalex.org/W2009710695","https://openalex.org/W2013232283","https://openalex.org/W2015067077","https://openalex.org/W2016377588","https://openalex.org/W2016451527","https://openalex.org/W2019311512","https://openalex.org/W2023782823","https://openalex.org/W2023893235","https://openalex.org/W2029188246","https://openalex.org/W2032828164","https://openalex.org/W2034171352","https://openalex.org/W2034305650","https://openalex.org/W2042789668","https://openalex.org/W2047403678","https://openalex.org/W2048854153","https://openalex.org/W2054817264","https://openalex.org/W2062247832","https://openalex.org/W2064924936","https://openalex.org/W2067167672","https://openalex.org/W2067831904","https://openalex.org/W2069653542","https://openalex.org/W2072938666","https://openalex.org/W2072985897","https://openalex.org/W2074412622","https://openalex.org/W2080351913","https://openalex.org/W2080943457","https://openalex.org/W2081827062","https://openalex.org/W2085722279","https://openalex.org/W2090413088","https://openalex.org/W2090938538","https://openalex.org/W2105224249","https://openalex.org/W2118504105","https://openalex.org/W2124462761","https://openalex.org/W2129992593","https://openalex.org/W2153465537","https://openalex.org/W2158227234","https://openalex.org/W2170299557","https://openalex.org/W2222476656","https://openalex.org/W3025136633","https://openalex.org/W4237564398","https://openalex.org/W4239085533","https://openalex.org/W4250992172","https://openalex.org/W4299993032"],"related_works":["https://openalex.org/W2050425148","https://openalex.org/W2091370530","https://openalex.org/W1466912161","https://openalex.org/W1611997902","https://openalex.org/W4307563307","https://openalex.org/W2034305650","https://openalex.org/W2916484535","https://openalex.org/W4248174108","https://openalex.org/W3114074494","https://openalex.org/W3139211375"],"abstract_inverted_index":{"A":[0,55],"model":[1,20,77,104,112],"of":[2,8,28,58,99,102,109],"the":[3,26,36,49,76,95,103,110,122],"chemostat":[4],"involving":[5],"two":[6,12],"species":[7,52],"microorganisms":[9],"competing":[10],"for":[11,84,90],"perfectly":[13],"complementary,":[14],"growth-limiting":[15],"nutrients":[16],"is":[17,62,105],"considered.":[18],"The":[19,44],"incorporates":[21],"distributed":[22],"time":[23,37,114],"delay":[24],"in":[25,32,39,48,75,126,133],"form":[27],"integral":[29],"differential":[30],"equations":[31],"order":[33],"to":[34,42,64,107],"describe":[35,65],"involved":[38],"converting":[40],"nutrient":[41,50,66],"biomass.":[43],"delays":[45,124],"are":[46,78,125],"included":[47],"and":[51,88],"concentrations":[53],"simultaneously.":[54],"general":[56],"class":[57],"monotone":[59],"increasing":[60],"functions":[61],"used":[63],"uptake.":[67],"Sufficient":[68],"conditions":[69],"based":[70],"on":[71],"biologically":[72],"meaningful":[73],"parameters":[74],"given":[79],"that":[80,94,108,120],"predict":[81],"competitive":[82],"exclusion":[83],"certain":[85],"parameter":[86],"ranges":[87],"coexistence":[89],"others.":[91],"We":[92],"prove":[93],"global":[96],"asymptotic":[97],"attractivity":[98],"steady":[100],"states":[101],"similar":[106],"corresponding":[111],"without":[113],"delays.":[115],"However,":[116],"our":[117],"results":[118],"indicate":[119],"when":[121],"inherent":[123],"fact":[127],"large,":[128],"ignoring":[129],"them":[130],"may":[131],"result":[132],"incorrect":[134],"predictions.":[135]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}