{"id":"https://openalex.org/W2057084277","doi":"https://doi.org/10.3103/s0146411614070104","title":"Asymptotics of solutions of finite-difference approximations of a logistic equation with delay and small diffusion","display_name":"Asymptotics of solutions of finite-difference approximations of a logistic equation with delay and small diffusion","publication_year":2014,"publication_date":"2014-12-01","ids":{"openalex":"https://openalex.org/W2057084277","doi":"https://doi.org/10.3103/s0146411614070104","mag":"2057084277"},"language":"en","primary_location":{"id":"doi:10.3103/s0146411614070104","is_oa":false,"landing_page_url":"https://doi.org/10.3103/s0146411614070104","pdf_url":null,"source":{"id":"https://openalex.org/S17203304","display_name":"Automatic Control and Computer Sciences","issn_l":"0146-4116","issn":["0146-4116","1558-108X"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatic Control and Computer Sciences","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/A5110530785","display_name":"\u0421. \u0410. \u041a\u0430\u0449\u0435\u043d\u043a\u043e","orcid":null},"institutions":[{"id":"https://openalex.org/I198371094","display_name":"Yaroslavl State University","ror":"https://ror.org/044s2fj67","country_code":"RU","type":"education","lineage":["https://openalex.org/I198371094"]},{"id":"https://openalex.org/I887846188","display_name":"Moscow Engineering Physics Institute","ror":"https://ror.org/04w8z7f34","country_code":"RU","type":"education","lineage":["https://openalex.org/I887846188"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"S. A. Kashchenko","raw_affiliation_strings":["Demidov Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia","National Research Nuclear University MEPhI, sh. Kashirskoye 31, Moscow, 115409, Russia","National Research Nuclear University MEPhI","Demidov Yaroslavl State University"],"affiliations":[{"raw_affiliation_string":"Demidov Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia","institution_ids":["https://openalex.org/I198371094"]},{"raw_affiliation_string":"National Research Nuclear University MEPhI, sh. Kashirskoye 31, Moscow, 115409, Russia","institution_ids":["https://openalex.org/I887846188"]},{"raw_affiliation_string":"National Research Nuclear University MEPhI","institution_ids":["https://openalex.org/I887846188"]},{"raw_affiliation_string":"Demidov Yaroslavl State University","institution_ids":["https://openalex.org/I198371094"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088106815","display_name":"Valentin Frolov","orcid":null},"institutions":[{"id":"https://openalex.org/I887846188","display_name":"Moscow Engineering Physics Institute","ror":"https://ror.org/04w8z7f34","country_code":"RU","type":"education","lineage":["https://openalex.org/I887846188"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"V. E. Frolov","raw_affiliation_strings":["National Research Nuclear University MEPhI, sh. Kashirskoye 31, Moscow, 115409, Russia","National Research Nuclear University \u201cMEPhI\u201c"],"affiliations":[{"raw_affiliation_string":"National Research Nuclear University MEPhI, sh. Kashirskoye 31, Moscow, 115409, Russia","institution_ids":["https://openalex.org/I887846188"]},{"raw_affiliation_string":"National Research Nuclear University \u201cMEPhI\u201c","institution_ids":["https://openalex.org/I887846188"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110530785"],"corresponding_institution_ids":["https://openalex.org/I198371094","https://openalex.org/I887846188"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.14371903,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"48","issue":"7","first_page":"502","last_page":"515"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.993399977684021,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.764253556728363},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.7006024122238159},{"id":"https://openalex.org/keywords/logistic-function","display_name":"Logistic function","score":0.6842876672744751},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.5211115479469299},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5035869479179382},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.4921998083591461},{"id":"https://openalex.org/keywords/logistic-regression","display_name":"Logistic regression","score":0.48222529888153076},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3308238983154297},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23584094643592834},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17487379908561707},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.12074494361877441},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.10710391402244568},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07259222865104675}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.764253556728363},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.7006024122238159},{"id":"https://openalex.org/C180802074","wikidata":"https://www.wikidata.org/wiki/Q1052379","display_name":"Logistic function","level":2,"score":0.6842876672744751},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.5211115479469299},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5035869479179382},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.4921998083591461},{"id":"https://openalex.org/C151956035","wikidata":"https://www.wikidata.org/wiki/Q1132755","display_name":"Logistic regression","level":2,"score":0.48222529888153076},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3308238983154297},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23584094643592834},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17487379908561707},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.12074494361877441},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.10710391402244568},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07259222865104675},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3103/s0146411614070104","is_oa":false,"landing_page_url":"https://doi.org/10.3103/s0146411614070104","pdf_url":null,"source":{"id":"https://openalex.org/S17203304","display_name":"Automatic Control and Computer Sciences","issn_l":"0146-4116","issn":["0146-4116","1558-108X"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatic Control and Computer Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1485975088","https://openalex.org/W1583311599","https://openalex.org/W1586658033","https://openalex.org/W1605753492","https://openalex.org/W1957083931","https://openalex.org/W1974007280","https://openalex.org/W1978856592","https://openalex.org/W2035610238","https://openalex.org/W2041533330","https://openalex.org/W2081827062","https://openalex.org/W2148744137","https://openalex.org/W2331061927","https://openalex.org/W2799664482","https://openalex.org/W3023996888","https://openalex.org/W4250716583","https://openalex.org/W4297440205","https://openalex.org/W4299993032","https://openalex.org/W4301712079"],"related_works":["https://openalex.org/W2171482902","https://openalex.org/W2129863591","https://openalex.org/W2061411662","https://openalex.org/W2332883973","https://openalex.org/W805945170","https://openalex.org/W1734603769","https://openalex.org/W2922935260","https://openalex.org/W1592131421","https://openalex.org/W3131191061","https://openalex.org/W2920076344"],"abstract_inverted_index":{"We":[0],"studied":[1,47],"the":[2,24,30,38,44,68,84,87,98,109],"dynamics":[3],"of":[4,12,43,62,64,74,82,97,100,103],"finite-difference":[5],"approximation":[6],"with":[7,16],"respect":[8],"to":[9],"spatial":[10],"variables":[11],"a":[13,59],"logistic":[14],"equation":[15],"delay":[17],"and":[18,29,40],"diffusion.":[19],"It":[20,52],"was":[21,46],"assumed":[22],"that":[23,56],"diffusion":[25],"coefficient":[26,32],"is":[27,33,58],"small":[28],"Malthusian":[31],"large.":[34],"The":[35,78],"question":[36],"concerning":[37],"existence":[39],"asymptotic":[41,50,80],"behavior":[42],"attractors":[45,63,89],"using":[48],"special":[49],"methods.":[51],"has":[53],"been":[54],"shown":[55],"there":[57],"rich":[60],"set":[61],"different":[65,104],"types":[66],"in":[67,92,108],"phase":[69],"space:":[70],"guiding":[71],"centers,":[72],"systems":[73],"helicon":[75],"waves,":[76],"etc.":[77],"major":[79],"characteristics":[81],"all":[83],"solutions":[85],"from":[86],"corresponding":[88],"are":[90,106],"adduced":[91],"this":[93],"work.":[94],"Typical":[95],"graphics":[96],"motion":[99],"wave":[101],"fronts":[102],"structures":[105],"represented":[107],"paper.":[110]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}