{"id":"https://openalex.org/W2050425148","doi":"https://doi.org/10.1137/130921386","title":"Competitive Exclusion in Delayed Chemostat Models with Differential Removal Rates","display_name":"Competitive Exclusion in Delayed Chemostat Models with Differential Removal Rates","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2050425148","doi":"https://doi.org/10.1137/130921386","mag":"2050425148"},"language":"en","primary_location":{"id":"doi:10.1137/130921386","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130921386","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/A5060432914","display_name":"Shengqiang Liu","orcid":"https://orcid.org/0000-0001-7919-0801"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shengqiang Liu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100406826","display_name":"Xinxin Wang","orcid":"https://orcid.org/0000-0001-8238-7832"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xinxin Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100403191","display_name":"Lin Wang","orcid":"https://orcid.org/0000-0002-7215-8750"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5055687136","display_name":"Haitao Song","orcid":"https://orcid.org/0000-0003-1977-4308"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Haitao Song","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1671,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.91280495,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"74","issue":"3","first_page":"634","last_page":"648"},"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":0.9980000257492065,"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":0.9980000257492065,"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":0.9894999861717224,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9775999784469604,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9948569536209106},{"id":"https://openalex.org/keywords/competitive-exclusion","display_name":"Competitive exclusion","score":0.8920814394950867},{"id":"https://openalex.org/keywords/extinction","display_name":"Extinction (optical mineralogy)","score":0.636425256729126},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.6183855533599854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5794656872749329},{"id":"https://openalex.org/keywords/competition","display_name":"Competition (biology)","score":0.5434953570365906},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4553442895412445},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39370959997177124},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3388150930404663},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.2147234082221985},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17401322722434998},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.14783993363380432},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.07055667042732239},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06666192412376404}],"concepts":[{"id":"https://openalex.org/C125111812","wikidata":"https://www.wikidata.org/wiki/Q902311","display_name":"Chemostat","level":3,"score":0.9948569536209106},{"id":"https://openalex.org/C2992687717","wikidata":"https://www.wikidata.org/wiki/Q1331830","display_name":"Competitive exclusion","level":3,"score":0.8920814394950867},{"id":"https://openalex.org/C101991246","wikidata":"https://www.wikidata.org/wiki/Q5422078","display_name":"Extinction (optical mineralogy)","level":2,"score":0.636425256729126},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.6183855533599854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5794656872749329},{"id":"https://openalex.org/C91306197","wikidata":"https://www.wikidata.org/wiki/Q45767","display_name":"Competition (biology)","level":2,"score":0.5434953570365906},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4553442895412445},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39370959997177124},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3388150930404663},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.2147234082221985},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17401322722434998},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.14783993363380432},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.07055667042732239},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06666192412376404},{"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/C523546767","wikidata":"https://www.wikidata.org/wiki/Q10876","display_name":"Bacteria","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130921386","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130921386","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":[{"score":0.7599999904632568,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W626516838","https://openalex.org/W1494118823","https://openalex.org/W1586658033","https://openalex.org/W1587425752","https://openalex.org/W1607633954","https://openalex.org/W1967444104","https://openalex.org/W1968201943","https://openalex.org/W1970718404","https://openalex.org/W1974186209","https://openalex.org/W1986978791","https://openalex.org/W1988681504","https://openalex.org/W1989998020","https://openalex.org/W1993444065","https://openalex.org/W1994831429","https://openalex.org/W2015217267","https://openalex.org/W2022792025","https://openalex.org/W2023893235","https://openalex.org/W2027356146","https://openalex.org/W2032828164","https://openalex.org/W2034305650","https://openalex.org/W2054817264","https://openalex.org/W2057260959","https://openalex.org/W2062247832","https://openalex.org/W2064924936","https://openalex.org/W2067831904","https://openalex.org/W2072938666","https://openalex.org/W2076326718","https://openalex.org/W2105224249","https://openalex.org/W2129026789","https://openalex.org/W2171731938","https://openalex.org/W2240752256","https://openalex.org/W3083379616","https://openalex.org/W4239085533"],"related_works":["https://openalex.org/W2050425148","https://openalex.org/W2091370530","https://openalex.org/W2315440589","https://openalex.org/W1466912161","https://openalex.org/W1611997902","https://openalex.org/W4307563307","https://openalex.org/W2916484535","https://openalex.org/W4248174108","https://openalex.org/W3114074494","https://openalex.org/W2034305650"],"abstract_inverted_index":{"Competitive":[0],"exclusion":[1,24,59],"is":[2,25,111,120],"frequently":[3],"observed":[4],"in":[5,130],"the":[6,42,52,108,115,121,124,131],"chemostat":[7,31,66,80,132],"when":[8],"multiple":[9],"species":[10,122,136],"compete":[11],"exploitatively":[12],"for":[13,22,29,65],"a":[14,62,83],"single":[15],"growth-limiting":[16],"nutrient.":[17],"However,":[18],"rigorous":[19],"mathematical":[20],"proof":[21],"competitive":[23,58],"very":[26],"limited,":[27],"especially":[28],"delayed":[30,79],"models":[32,67,81],"with":[33,68,82,123],"differential":[34,69],"removal":[35,70],"rates.":[36],"In":[37],"this":[38],"paper,":[39],"by":[40,114],"employing":[41],"method":[43],"of":[44,86],"Liapunov":[45],"functionals":[46],"and":[47,72,96,98,133],"placing":[48],"two":[49],"assumptions":[50],"on":[51],"response":[53,89,102],"functions,":[54,90,103],"we":[55],"prove":[56],"that":[57,107,128],"holds":[60],"under":[61],"generic":[63],"condition":[64],"rates":[71],"discrete":[73],"(also":[74],"finitely":[75],"distributed)":[76],"delays.":[77],"For":[78],"large":[84],"variety":[85],"widely":[87],"used":[88],"including":[91],"Holling":[92],"types":[93],"I,":[94],"II,":[95],"III":[97],"even":[99],"some":[100],"nonmonotone":[101],"our":[104],"results":[105],"show":[106],"competition":[109],"outcome":[110],"completely":[112],"determined":[113],"species'":[116],"break-even":[117,126],"concentrations:":[118],"it":[119],"lowest":[125],"concentration":[127],"survives":[129],"drives":[134],"other":[135],"to":[137],"extinction.":[138]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3}],"updated_date":"2026-07-19T07:52:34.831488","created_date":"2025-10-10T00:00:00"}