{"id":"https://openalex.org/W2255727392","doi":"https://doi.org/10.1137/16m1059217","title":"Reduction to a Single Closed Equation for 2-by-2 Reaction-Diffusion Systems of Lotka--Volterra Type","display_name":"Reduction to a Single Closed Equation for 2-by-2 Reaction-Diffusion Systems of Lotka--Volterra Type","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2255727392","doi":"https://doi.org/10.1137/16m1059217","mag":"2255727392"},"language":"en","primary_location":{"id":"doi:10.1137/16m1059217","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1059217","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1602.01058","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013901413","display_name":"Martin Strugarek","orcid":"https://orcid.org/0000-0002-1605-8712"},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Martin Strugarek","raw_affiliation_strings":["LJLL - Laboratoire Jacques-Louis Lions (Universit\u00e9 Pierre et Marie Curie, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)"],"affiliations":[{"raw_affiliation_string":"LJLL - Laboratoire Jacques-Louis Lions (Universit\u00e9 Pierre et Marie Curie, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)","institution_ids":["https://openalex.org/I4210158291"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055143921","display_name":"Nicolas Vauchelet","orcid":"https://orcid.org/0000-0002-5683-8633"},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Vauchelet","raw_affiliation_strings":["MAMBA - Modelling and Analysis for Medical and Biological Applications (France)","LJLL - Laboratoire Jacques-Louis Lions (Universit\u00e9 Pierre et Marie Curie, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)"],"affiliations":[{"raw_affiliation_string":"MAMBA - Modelling and Analysis for Medical and Biological Applications (France)","institution_ids":[]},{"raw_affiliation_string":"LJLL - Laboratoire Jacques-Louis Lions (Universit\u00e9 Pierre et Marie Curie, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)","institution_ids":["https://openalex.org/I4210158291"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013901413"],"corresponding_institution_ids":["https://openalex.org/I4210158291"],"apc_list":null,"apc_paid":null,"fwci":3.8517,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.91912332,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"76","issue":"5","first_page":"2060","last_page":"2080"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12134","display_name":"Insect symbiosis and bacterial influences","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1109","display_name":"Insect Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12134","display_name":"Insect symbiosis and bacterial influences","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1109","display_name":"Insect Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11641","display_name":"Insect and Pesticide Research","score":0.932200014591217,"subfield":{"id":"https://openalex.org/subfields/1109","display_name":"Insect Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.7486910223960876},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.624711275100708},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.6127417683601379},{"id":"https://openalex.org/keywords/bistability","display_name":"Bistability","score":0.6034412384033203},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5416633486747742},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5323268175125122},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5040854215621948},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45717743039131165},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4539886713027954},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.42490968108177185},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37381845712661743},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.32949894666671753},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20100852847099304},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.1541188657283783},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.08069926500320435},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.07605701684951782}],"concepts":[{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.7486910223960876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.624711275100708},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6127417683601379},{"id":"https://openalex.org/C97292510","wikidata":"https://www.wikidata.org/wiki/Q2304620","display_name":"Bistability","level":2,"score":0.6034412384033203},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5416633486747742},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5323268175125122},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5040854215621948},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45717743039131165},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4539886713027954},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.42490968108177185},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37381845712661743},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32949894666671753},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20100852847099304},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.1541188657283783},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.08069926500320435},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.07605701684951782},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1059217","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1059217","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"},{"id":"pmh:oai:arXiv.org:1602.01058","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.01058","pdf_url":"https://arxiv.org/pdf/1602.01058","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1602.01058","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1602.01058","pdf_url":"https://arxiv.org/pdf/1602.01058","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"score":0.7799999713897705,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[{"id":"https://openalex.org/G1143563004","display_name":null,"funder_award_id":"Programme Convergence","funder_id":"https://openalex.org/F4320322749","funder_display_name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro"},{"id":"https://openalex.org/G549620510","display_name":null,"funder_award_id":"Capes/Cofecub project Ma 855-1","funder_id":"https://openalex.org/F4320323942","funder_display_name":"Campus France"}],"funders":[{"id":"https://openalex.org/F4320322749","display_name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro","ror":"https://ror.org/03kk0s825"},{"id":"https://openalex.org/F4320323942","display_name":"Campus France","ror":"https://ror.org/04wtce741"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1550382162","https://openalex.org/W1975822178","https://openalex.org/W1978933919","https://openalex.org/W1993959062","https://openalex.org/W2007352956","https://openalex.org/W2011148871","https://openalex.org/W2034017401","https://openalex.org/W2047526274","https://openalex.org/W2052186195","https://openalex.org/W2053330217","https://openalex.org/W2058824011","https://openalex.org/W2059597623","https://openalex.org/W2071226931","https://openalex.org/W2073078790","https://openalex.org/W2079949023","https://openalex.org/W2084143341","https://openalex.org/W2092133388","https://openalex.org/W2120118602","https://openalex.org/W2133250947","https://openalex.org/W2136062469","https://openalex.org/W2164430172","https://openalex.org/W2332657612"],"related_works":["https://openalex.org/W2089759803","https://openalex.org/W2044153511","https://openalex.org/W2962972930","https://openalex.org/W2068647081","https://openalex.org/W2893162179","https://openalex.org/W2143560132","https://openalex.org/W2952935899","https://openalex.org/W2980279618","https://openalex.org/W3204476032","https://openalex.org/W2000402520"],"abstract_inverted_index":{"We":[0],"consider":[1],"general":[2],"models":[3],"of":[4,11,30,39],"coupled":[5],"reaction-diffusion":[6,42],"systems":[7],"for":[8,63],"interacting":[9],"variants":[10],"a":[12,31,40,45,50,71],"species.":[13],"When":[14],"the":[15,26,37,59],"total":[16],"population":[17,69],"becomes":[18],"large":[19],"with":[20],"intensive":[21],"competition,":[22],"we":[23,57],"prove":[24],"that":[25],"frequency":[27],"(i.e.,":[28],"proportion)":[29],"variant":[32],"can":[33],"be":[34],"approached":[35],"by":[36],"solution":[38],"single":[41],"equation,":[43],"through":[44],"singular":[46],"limit":[47],"method":[48],"and":[49,77],"relative":[51],"compactness":[52],"argument.":[53],"Applying":[54],"this":[55],"result,":[56],"retrieve":[58],"classical":[60],"bistable":[61],"equation":[62],"Wolbachia's":[64],"spread":[65],"into":[66],"an":[67],"arthropod":[68],"from":[70],"system":[72],"modeling":[73],"interaction":[74],"between":[75],"infected":[76],"uninfected":[78],"individuals.":[79]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
