{"id":"https://openalex.org/W1992844963","doi":"https://doi.org/10.1137/s0036141002402189","title":"Competing Species near a Degenerate Limit","display_name":"Competing Species near a Degenerate Limit","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1992844963","doi":"https://doi.org/10.1137/s0036141002402189","mag":"1992844963"},"language":"en","primary_location":{"id":"doi:10.1137/s0036141002402189","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141002402189","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/A5075859177","display_name":"V. Hutson","orcid":null},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"V. Hutson","raw_affiliation_strings":["University of  Sheffield"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of  Sheffield","institution_ids":["https://openalex.org/I91136226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108749023","display_name":"Y. Lou","orcid":null},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Y. Lou","raw_affiliation_strings":["the Ohio State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"the Ohio State University","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049298090","display_name":"Konstantin Mischaikow","orcid":"https://orcid.org/0000-0003-2876-4558"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"K. Mischaikow","raw_affiliation_strings":["[Georgia Institute of Technology.]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[Georgia Institute of Technology.]","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024182662","display_name":"P. Pol\u00e1cik","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. Pol\u00e1cik","raw_affiliation_strings":["University of\u00a0Minnesota"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of\u00a0Minnesota","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.2117,"has_fulltext":false,"cited_by_count":62,"citation_normalized_percentile":{"value":0.93220269,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"35","issue":"2","first_page":"453","last_page":"491"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9973999857902527,"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":0.994700014591217,"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/pointwise","display_name":"Pointwise","score":0.7543011903762817},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7263876795768738},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6243000030517578},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5558840036392212},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5471231341362},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5089211463928223},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5067127346992493},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.49845314025878906},{"id":"https://openalex.org/keywords/extinction","display_name":"Extinction (optical mineralogy)","score":0.4472459852695465},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3636113405227661},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3339097499847412},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13903969526290894},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09251841902732849},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08932408690452576}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.7543011903762817},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7263876795768738},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6243000030517578},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5558840036392212},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5471231341362},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5089211463928223},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5067127346992493},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.49845314025878906},{"id":"https://openalex.org/C101991246","wikidata":"https://www.wikidata.org/wiki/Q5422078","display_name":"Extinction (optical mineralogy)","level":2,"score":0.4472459852695465},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3636113405227661},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3339097499847412},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13903969526290894},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09251841902732849},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08932408690452576},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036141002402189","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141002402189","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.23.7674","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.23.7674","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.gatech.edu/~mischaik/papers/smalldiff.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1514801494","https://openalex.org/W1540580484","https://openalex.org/W1555674425","https://openalex.org/W1560060148","https://openalex.org/W1575147392","https://openalex.org/W1585999563","https://openalex.org/W1866311589","https://openalex.org/W1982357817","https://openalex.org/W1985016450","https://openalex.org/W1990636052","https://openalex.org/W2005862991","https://openalex.org/W2007924835","https://openalex.org/W2009217095","https://openalex.org/W2031792309","https://openalex.org/W2046904024","https://openalex.org/W2066496593","https://openalex.org/W2066653126","https://openalex.org/W2110668450","https://openalex.org/W2577694891","https://openalex.org/W4299150230","https://openalex.org/W4302061159"],"related_works":["https://openalex.org/W3121176436","https://openalex.org/W4287373462","https://openalex.org/W1966487117","https://openalex.org/W1978188451","https://openalex.org/W2011570454","https://openalex.org/W1455884086","https://openalex.org/W4302364990","https://openalex.org/W4317035819","https://openalex.org/W1992107226","https://openalex.org/W4206911432"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,11,29,44,53,80,93,124],"competitive":[3],"reaction":[4],"diffusion":[5,57,140],"model":[6],"of":[7,46,49,55,74,84,89,92,120,129],"two":[8],"species":[9],"in":[10,17,70,87,122],"bounded":[12],"domain":[13],"which":[14,25,71],"are":[15,99],"identical":[16],"all":[18],"aspects":[19],"except":[20],"for":[21,104],"their":[22],"birth":[23,64],"rates":[24,65],"differ":[26],"according":[27],"to":[28,101],"function":[30,54,114],"g.":[31,66],"Under":[32],"fairly":[33,81],"weak":[34],"hypothesis,":[35],"the":[36,47,56,60,63,68,72,85,90,112,127,130,139],"semitrivial":[37,131],"solutions":[38,51,132],"always":[39],"exist.":[40],"Our":[41],"analysis":[42],"provides":[43],"description":[45],"stability":[48,86,128],"these":[50],"as":[52,138],"rate":[58],"and":[59],"difference":[61,113],"between":[62],"In":[67,96],"case":[69],"magnitude":[73],"g":[75,115],"is":[76,142],"small":[77],"we":[78,98],"provide":[79],"complete":[82],"characterization":[83],"terms":[88],"zeros":[91],"single":[94],"function.":[95],"particular,":[97],"able":[100],"show":[102],"that":[103,126],"any":[105],"fixed":[106],"number":[107],"n,":[108],"one":[109],"can":[110],"choose":[111],"from":[116],"an":[117],"open":[118],"set":[119],"possibilities":[121],"such":[123],"way":[125],"changes":[133],"at":[134],"least":[135],"n":[136],"times":[137],"\u00b5":[141],"varied":[143],"over":[144],"(0,":[145],"\u221e).":[146],"This":[147],"result":[148]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
