{"id":"https://openalex.org/W3185642989","doi":"https://doi.org/10.1080/00207179.2021.1961167","title":"Practical stability in relation to a part of variables of stochastic pantograph differential equations","display_name":"Practical stability in relation to a part of variables of stochastic pantograph differential equations","publication_year":2021,"publication_date":"2021-07-27","ids":{"openalex":"https://openalex.org/W3185642989","doi":"https://doi.org/10.1080/00207179.2021.1961167","mag":"3185642989"},"language":"en","primary_location":{"id":"doi:10.1080/00207179.2021.1961167","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2021.1961167","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","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/A5100404209","display_name":"Jiaying Li","orcid":"https://orcid.org/0000-0002-2132-3330"},"institutions":[{"id":"https://openalex.org/I4472751","display_name":"Anhui Normal University","ror":"https://ror.org/05fsfvw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I4472751"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiaying Li","raw_affiliation_strings":["Department of Mathematics, Anhui Normal University, Wuhu, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Anhui Normal University, Wuhu, People's Republic of China","institution_ids":["https://openalex.org/I4472751"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017004747","display_name":"Yong Ren","orcid":"https://orcid.org/0000-0002-8353-6788"},"institutions":[{"id":"https://openalex.org/I4472751","display_name":"Anhui Normal University","ror":"https://ror.org/05fsfvw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I4472751"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yong Ren","raw_affiliation_strings":["Department of Mathematics, Anhui Normal University, Wuhu, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0002-8353-6788","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Anhui Normal University, Wuhu, People's Republic of China","institution_ids":["https://openalex.org/I4472751"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5017004747"],"corresponding_institution_ids":["https://openalex.org/I4472751"],"apc_list":null,"apc_paid":null,"fwci":1.3044,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.78326966,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"95","issue":"12","first_page":"3196","last_page":"3201"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9861000180244446,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7626135349273682},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.6640796661376953},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.6502020359039307},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6273247003555298},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.622356653213501},{"id":"https://openalex.org/keywords/pantograph","display_name":"Pantograph","score":0.6074967384338379},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5762557983398438},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4738769233226776},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.4657863676548004},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.45777058601379395},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.45537763833999634},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.297055184841156},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16083645820617676},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08132973313331604},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06995579600334167}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7626135349273682},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.6640796661376953},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.6502020359039307},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6273247003555298},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.622356653213501},{"id":"https://openalex.org/C20756127","wikidata":"https://www.wikidata.org/wiki/Q722757","display_name":"Pantograph","level":2,"score":0.6074967384338379},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5762557983398438},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4738769233226776},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.4657863676548004},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.45777058601379395},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.45537763833999634},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.297055184841156},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16083645820617676},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08132973313331604},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06995579600334167},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207179.2021.1961167","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207179.2021.1961167","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W127321992","https://openalex.org/W298519300","https://openalex.org/W2166856345","https://openalex.org/W2326010876","https://openalex.org/W2809756805","https://openalex.org/W2848899554","https://openalex.org/W2890967797","https://openalex.org/W2914981733","https://openalex.org/W2952593868","https://openalex.org/W2981985592","https://openalex.org/W2993060095","https://openalex.org/W3033153744"],"related_works":["https://openalex.org/W2092831049","https://openalex.org/W2287553547","https://openalex.org/W2112401754","https://openalex.org/W2128093298","https://openalex.org/W2378841998","https://openalex.org/W4298193271","https://openalex.org/W2950517380","https://openalex.org/W2057298754","https://openalex.org/W3160871489","https://openalex.org/W2062608072"],"abstract_inverted_index":{"The":[0],"main":[1],"purpose":[2],"of":[3,17,20,31,37,58,60,75,88],"this":[4],"paper":[5],"is":[6,67],"to":[7,14,55,69,85],"investigate":[8],"the":[9,18,29,35,38,45,71,76,80],"practical":[10,40,47,81],"stability":[11,43,52,82],"in":[12,26,53],"relation":[13,54],"a":[15,56,86],"part":[16,57,87],"variables":[19,59],"stochastic":[21],"pantograph":[22],"differential":[23],"equations":[24],"(SPDEs,":[25],"short).":[27],"With":[28],"aid":[30],"Lyapunov":[32],"function":[33],"method,":[34],"criterions":[36],"global":[39,46],"uniform":[41,48],"asymptotic":[42],"and":[44,73],"p-th":[49],"moment":[50],"exponential":[51],"SPDEs":[61],"are":[62],"established.":[63],"An":[64],"illustrative":[65],"example":[66],"given":[68],"show":[70],"effectiveness":[72],"feasibility":[74],"proposed":[77],"results":[78],"on":[79],"with":[83],"respect":[84],"variables.":[89]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
