{"id":"https://openalex.org/W2124566079","doi":"https://doi.org/10.1142/s0218127414400173","title":"Dynamics of the Logistic Equation with Delay and Delay Control","display_name":"Dynamics of the Logistic Equation with Delay and Delay Control","publication_year":2014,"publication_date":"2014-08-01","ids":{"openalex":"https://openalex.org/W2124566079","doi":"https://doi.org/10.1142/s0218127414400173","mag":"2124566079"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127414400173","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414400173","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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":"National Research Nuclear University MEPhI","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":["Math Department, P. G. Demidov Yaroslavl State University, Sovietskaya 14, Yaroslavl 150000, Russia","National Research Nuclear University MEPhI, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Math Department, P. G. Demidov Yaroslavl State University, Sovietskaya 14, Yaroslavl 150000, Russia","institution_ids":["https://openalex.org/I198371094"]},{"raw_affiliation_string":"National Research Nuclear University MEPhI, Russia","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":0.8059,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.78990622,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","issue":"08","first_page":"1440017","last_page":"1440017"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.995199978351593,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9894999861717224,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.7349982857704163},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6460256576538086},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6201373338699341},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6004059910774231},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5954511761665344},{"id":"https://openalex.org/keywords/logistic-function","display_name":"Logistic function","score":0.5843631029129028},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4756214916706085},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.45369839668273926},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.446353554725647},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42457646131515503},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34067797660827637},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26605886220932007},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.14223769307136536},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11256518959999084},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06172516942024231}],"concepts":[{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.7349982857704163},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6460256576538086},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6201373338699341},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6004059910774231},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5954511761665344},{"id":"https://openalex.org/C180802074","wikidata":"https://www.wikidata.org/wiki/Q1052379","display_name":"Logistic function","level":2,"score":0.5843631029129028},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4756214916706085},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.45369839668273926},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.446353554725647},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42457646131515503},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34067797660827637},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26605886220932007},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.14223769307136536},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11256518959999084},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06172516942024231},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","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},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127414400173","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127414400173","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W102324627","https://openalex.org/W111157985","https://openalex.org/W1586658033","https://openalex.org/W1827537164","https://openalex.org/W1974473930","https://openalex.org/W1986710554","https://openalex.org/W2035695789","https://openalex.org/W2038291611","https://openalex.org/W2057634036","https://openalex.org/W2068551947","https://openalex.org/W2079871064","https://openalex.org/W2080389444","https://openalex.org/W2096966061","https://openalex.org/W2122264076","https://openalex.org/W2145417199","https://openalex.org/W2148088470","https://openalex.org/W2799664482","https://openalex.org/W2897568761","https://openalex.org/W3023996888","https://openalex.org/W4210960242","https://openalex.org/W4232701107","https://openalex.org/W4246667848","https://openalex.org/W4285719527","https://openalex.org/W4299993032"],"related_works":["https://openalex.org/W2115030441","https://openalex.org/W2147578878","https://openalex.org/W2159990075","https://openalex.org/W2799149877","https://openalex.org/W2187808779","https://openalex.org/W2614149677","https://openalex.org/W1496660757","https://openalex.org/W2171331836","https://openalex.org/W2371802546","https://openalex.org/W2124566079"],"abstract_inverted_index":{"Asymptotic":[0],"methods":[1],"investigate":[2],"the":[3,7,20,23,36,40,43,53,62],"dynamic":[4],"properties":[5],"of":[6,22,34,42,52,66,70],"logistic":[8],"equation":[9,55],"with":[10,56],"delay":[11,13],"and":[12],"control.":[14],"The":[15,49],"possibility":[16],"to":[17,61],"effectively":[18],"control":[19,45],"characteristics":[21],"relaxation":[24],"cycle":[25],"has":[26,58],"been":[27,59],"illustrated.":[28],"We":[29],"introduce":[30],"a":[31,71],"new":[32],"method":[33],"studying":[35],"dynamics,":[37],"provided":[38],"that":[39],"ratio":[41],"delayed":[44],"is":[46],"large":[47],"enough.":[48],"original":[50],"problem":[51],"dynamics":[54,65],"delays":[57],"reduced":[60],"nonlocal":[63],"special":[64],"nonlinear":[67],"boundary-value":[68],"problems":[69],"parabolic":[72],"type.":[73]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}