{"id":"https://openalex.org/W2138415657","doi":"https://doi.org/10.1137/s0036141001399222","title":"A Global Stability Criterion for Scalar Functional Differential Equations","display_name":"A Global Stability Criterion for Scalar Functional Differential Equations","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2138415657","doi":"https://doi.org/10.1137/s0036141001399222","mag":"2138415657"},"language":"en","primary_location":{"id":"doi:10.1137/s0036141001399222","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141001399222","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":true,"oa_status":"green","oa_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3231441","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018186636","display_name":"Eduardo Liz","orcid":"https://orcid.org/0000-0003-1975-5182"},"institutions":[{"id":"https://openalex.org/I6289922","display_name":"Universidade de Vigo","ror":"https://ror.org/05rdf8595","country_code":"ES","type":"education","lineage":["https://openalex.org/I6289922"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Eduardo Liz","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada II, E.T.S.I. Telecomunicaci\u00f3n, Universidad de Vigo, Campus Marcosende, 36280 Vigo, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada II, E.T.S.I. Telecomunicaci\u00f3n, Universidad de Vigo, Campus Marcosende, 36280 Vigo, Spain","institution_ids":["https://openalex.org/I6289922"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048906728","display_name":"V. \u0406. \u0422kachenko","orcid":"https://orcid.org/0000-0003-0587-2943"},"institutions":[{"id":"https://openalex.org/I190444043","display_name":"Institute of Mathematics","ror":"https://ror.org/04q3mp532","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I190444043"]},{"id":"https://openalex.org/I149851306","display_name":"National Academy of Sciences of Ukraine","ror":"https://ror.org/00je4t102","country_code":"UA","type":"funder","lineage":["https://openalex.org/I149851306"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Victor Tkachenko","raw_affiliation_strings":["Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs'ka str. 3, Kiev, Ukraine"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs'ka str. 3, Kiev, Ukraine","institution_ids":["https://openalex.org/I190444043","https://openalex.org/I149851306"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063285153","display_name":"Sergei Trof\u0131mchuk","orcid":"https://orcid.org/0000-0003-1605-222X"},"institutions":[{"id":"https://openalex.org/I69737025","display_name":"University of Chile","ror":"https://ror.org/047gc3g35","country_code":"CL","type":"education","lineage":["https://openalex.org/I69737025"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Sergei Trofimchuk","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santia-go, Chile"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santia-go, Chile","institution_ids":["https://openalex.org/I69737025"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018186636"],"corresponding_institution_ids":["https://openalex.org/I6289922"],"apc_list":null,"apc_paid":null,"fwci":6.4297,"has_fulltext":false,"cited_by_count":79,"citation_normalized_percentile":{"value":0.96487603,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"35","issue":"3","first_page":"596","last_page":"622"},"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":0.9987000226974487,"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":0.9987000226974487,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9872000217437744,"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/mathematics","display_name":"Mathematics","score":0.9157031774520874},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5719412565231323},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5639134645462036},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5495815873146057},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5291588306427002},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5284642577171326},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5075563192367554},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4553970396518707},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.43559035658836365},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4162874221801758},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4155523180961609},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24352771043777466},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0731835663318634}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9157031774520874},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5719412565231323},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5639134645462036},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5495815873146057},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5291588306427002},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5284642577171326},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5075563192367554},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4553970396518707},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.43559035658836365},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4162874221801758},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4155523180961609},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24352771043777466},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0731835663318634},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/s0036141001399222","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141001399222","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:10.1.1.237.9016","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.237.9016","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0112047v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.531.6001","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.531.6001","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dma.uvigo.es/~eliz/pdf/siam.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.763.8203","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.763.8203","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0112047.pdf","raw_type":"text"},{"id":"pmh:oai:americanae.aecid.es:3231441","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3231441","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM JOURNAL ON MATHEMATICAL ANALYSIS","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:localhost:10533/174607","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/174607","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM JOURNAL ON MATHEMATICAL ANALYSIS","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:americanae.aecid.es:3231441","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3231441","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM JOURNAL ON MATHEMATICAL ANALYSIS","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1557040331","https://openalex.org/W1586658033","https://openalex.org/W1607633954","https://openalex.org/W1851248039","https://openalex.org/W2002944058","https://openalex.org/W2027184719","https://openalex.org/W2033518907","https://openalex.org/W2039876893","https://openalex.org/W2046557303","https://openalex.org/W2070324104","https://openalex.org/W2114090429","https://openalex.org/W2127691837","https://openalex.org/W2141159836","https://openalex.org/W2964280372","https://openalex.org/W4211202937"],"related_works":["https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W2784911598","https://openalex.org/W4297950433","https://openalex.org/W4287023968","https://openalex.org/W4288279572","https://openalex.org/W1973978937","https://openalex.org/W4286909116","https://openalex.org/W4292635168"],"abstract_inverted_index":{"We":[0],"consider":[1],"scalar":[2],"delay":[3],"differential":[4],"equations":[5,33,39],"$x'(t)":[6],"=":[7],"-\\delta":[8],"x(t)":[9],"+":[10],"f(t,x_t)":[11],"\\":[12],"(*)$":[13],"with":[14,25,40],"nonlinear":[15],"f":[16],"satisfying":[17,34],"a":[18,26,50,58],"sort":[19],"of":[20,57],"negative":[21],"feedback":[22],"condition":[23],"combined":[24],"boundedness":[27],"condition.":[28],"The":[29],"well-known":[30],"Mackey--Glass-type":[31],"equations,":[32],"the":[35,53,76,80],"Yorke":[36],"condition,":[37],"and":[38,84],"maxima":[41],"all":[42],"fall":[43],"within":[44],"our":[45,73],"considerations.":[46],"Here,":[47],"we":[48,67],"establish":[49],"criterion":[51],"for":[52],"global":[54,83],"asymptotical":[55,86],"stability":[56],"unique":[59],"steady":[60],"state":[61],"to":[62],"(*).":[63],"As":[64],"an":[65],"example,":[66],"study":[68],"Nicholson's":[69],"blowflies":[70],"equation,":[71],"where":[72],"computations":[74],"support":[75],"Smith":[77],"conjecture":[78],"about":[79],"equivalence":[81],"between":[82],"local":[85],"stabilities":[87],"in":[88],"this":[89],"population":[90],"model.":[91]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}