{"id":"https://openalex.org/W3089801402","doi":"https://doi.org/10.1109/tcyb.2020.3022024","title":"Practical Exponential Stability of Impulsive Stochastic Reaction\u2013Diffusion Systems With Delays","display_name":"Practical Exponential Stability of Impulsive Stochastic Reaction\u2013Diffusion Systems With Delays","publication_year":2020,"publication_date":"2020-10-01","ids":{"openalex":"https://openalex.org/W3089801402","doi":"https://doi.org/10.1109/tcyb.2020.3022024","mag":"3089801402","pmid":"https://pubmed.ncbi.nlm.nih.gov/33001822"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2020.3022024","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2020.3022024","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Cybernetics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://discovery.dundee.ac.uk/ws/files/56627250/09210593.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048004340","display_name":"Qi Yao","orcid":"https://orcid.org/0000-0001-7680-226X"},"institutions":[{"id":"https://openalex.org/I177639307","display_name":"University of Dundee","ror":"https://ror.org/03h2bxq36","country_code":"GB","type":"education","lineage":["https://openalex.org/I177639307"]},{"id":"https://openalex.org/I59028903","display_name":"Ocean University of China","ror":"https://ror.org/04rdtx186","country_code":"CN","type":"education","lineage":["https://openalex.org/I59028903"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Qi Yao","raw_affiliation_strings":["School of Mathematical Sciences, Ocean University of China, Qingdao, China","Department of Mathematics, University of Dundee, Dundee, U.K"],"raw_orcid":"https://orcid.org/0000-0001-7680-226X","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Ocean University of China, Qingdao, China","institution_ids":["https://openalex.org/I59028903"]},{"raw_affiliation_string":"Department of Mathematics, University of Dundee, Dundee, U.K","institution_ids":["https://openalex.org/I177639307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101831455","display_name":"Ping Lin","orcid":"https://orcid.org/0000-0002-4132-2159"},"institutions":[{"id":"https://openalex.org/I177639307","display_name":"University of Dundee","ror":"https://ror.org/03h2bxq36","country_code":"GB","type":"education","lineage":["https://openalex.org/I177639307"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ping Lin","raw_affiliation_strings":["Department of Mathematics, University of Dundee, Dundee, U.K"],"raw_orcid":"https://orcid.org/0000-0002-4132-2159","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Dundee, Dundee, U.K","institution_ids":["https://openalex.org/I177639307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101693331","display_name":"Linshan Wang","orcid":"https://orcid.org/0000-0002-3183-0352"},"institutions":[{"id":"https://openalex.org/I59028903","display_name":"Ocean University of China","ror":"https://ror.org/04rdtx186","country_code":"CN","type":"education","lineage":["https://openalex.org/I59028903"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Linshan Wang","raw_affiliation_strings":["School of Mathematical Sciences, Ocean University of China, Qingdao, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Ocean University of China, Qingdao, China","institution_ids":["https://openalex.org/I59028903"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101633559","display_name":"Yangfan Wang","orcid":"https://orcid.org/0000-0002-7000-4213"},"institutions":[{"id":"https://openalex.org/I59028903","display_name":"Ocean University of China","ror":"https://ror.org/04rdtx186","country_code":"CN","type":"education","lineage":["https://openalex.org/I59028903"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yangfan Wang","raw_affiliation_strings":["Ministry of Education Key Laboratory of Marine Genetics and Breeding, College of Marine Life Science, Ocean University of China, Qingdao, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ministry of Education Key Laboratory of Marine Genetics and Breeding, College of Marine Life Science, Ocean University of China, Qingdao, China","institution_ids":["https://openalex.org/I59028903"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.281,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.88574599,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"52","issue":"5","first_page":"2687","last_page":"2697"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9980999827384949,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9954000115394592,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9941999912261963,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.596774697303772},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.5528544783592224},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.549436628818512},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5419692397117615},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5096938610076904},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44312241673469543},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41052132844924927},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.33944135904312134},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28423619270324707},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2520182132720947},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23934677243232727},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.13642752170562744}],"concepts":[{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.596774697303772},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.5528544783592224},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.549436628818512},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5419692397117615},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5096938610076904},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44312241673469543},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41052132844924927},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.33944135904312134},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28423619270324707},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2520182132720947},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23934677243232727},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.13642752170562744},{"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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"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":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D004058","descriptor_name":"Diffusion","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D004058","descriptor_name":"Diffusion","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D004058","descriptor_name":"Diffusion","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013269","descriptor_name":"Stochastic Processes","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013269","descriptor_name":"Stochastic Processes","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013269","descriptor_name":"Stochastic Processes","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013997","descriptor_name":"Time Factors","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013997","descriptor_name":"Time Factors","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013997","descriptor_name":"Time Factors","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":3,"locations":[{"id":"doi:10.1109/tcyb.2020.3022024","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2020.3022024","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Cybernetics","raw_type":"journal-article"},{"id":"pmid:33001822","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33001822","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on cybernetics","raw_type":null},{"id":"pmh:oai:discovery.dundee.ac.uk:publications/83ace4c0-d519-4343-bbe0-fa1e733ed8c3","is_oa":true,"landing_page_url":"https://discovery.dundee.ac.uk/en/publications/83ace4c0-d519-4343-bbe0-fa1e733ed8c3","pdf_url":"https://discovery.dundee.ac.uk/ws/files/56627250/09210593.pdf","source":{"id":"https://openalex.org/S4306400523","display_name":"Discovery Research Portal (University of Dundee)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177639307","host_organization_name":"University of Dundee","host_organization_lineage":["https://openalex.org/I177639307"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Yao, Q, Lin, P, Wang, L & Wang, Y 2022, 'Practical Exponential Stability of Impulsive Stochastic Reaction-Diffusion Systems With Delays', IEEE Transactions on Cybernetics, vol. 52, no. 5, pp. 2687-2697. https://doi.org/10.1109/TCYB.2020.3022024","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:discovery.dundee.ac.uk:publications/83ace4c0-d519-4343-bbe0-fa1e733ed8c3","is_oa":true,"landing_page_url":"https://discovery.dundee.ac.uk/en/publications/83ace4c0-d519-4343-bbe0-fa1e733ed8c3","pdf_url":"https://discovery.dundee.ac.uk/ws/files/56627250/09210593.pdf","source":{"id":"https://openalex.org/S4306400523","display_name":"Discovery Research Portal (University of Dundee)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177639307","host_organization_name":"University of Dundee","host_organization_lineage":["https://openalex.org/I177639307"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Yao, Q, Lin, P, Wang, L & Wang, Y 2022, 'Practical Exponential Stability of Impulsive Stochastic Reaction-Diffusion Systems With Delays', IEEE Transactions on Cybernetics, vol. 52, no. 5, pp. 2687-2697. https://doi.org/10.1109/TCYB.2020.3022024","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1097322959","display_name":null,"funder_award_id":"32072976","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1791658097","display_name":null,"funder_award_id":"2018YFD0901601","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G3003873415","display_name":null,"funder_award_id":"201906330009","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"},{"id":"https://openalex.org/G3127678264","display_name":"\u968f\u673a\u65f6\u6ede\u53cd\u5e94\u6269\u6563Hopfield\u795e\u7ecf\u7f51\u7edc\u7684\u9002\u5b9a\u6027\u548c\u6e10\u8fd1\u6027\u7814\u7a76","funder_award_id":"11771014","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G444670673","display_name":null,"funder_award_id":"31772844","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4673460526","display_name":null,"funder_award_id":"11861131004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6585082234","display_name":null,"funder_award_id":"2018A07","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7339995587","display_name":null,"funder_award_id":"2018A07","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G8891379759","display_name":null,"funder_award_id":"11771040","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3089801402.pdf","grobid_xml":"https://content.openalex.org/works/W3089801402.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W127321992","https://openalex.org/W1475124599","https://openalex.org/W1480782224","https://openalex.org/W1494628843","https://openalex.org/W1522228969","https://openalex.org/W1533970237","https://openalex.org/W1552503976","https://openalex.org/W1823315528","https://openalex.org/W1966806171","https://openalex.org/W1974306803","https://openalex.org/W1983097489","https://openalex.org/W1987404075","https://openalex.org/W2005315237","https://openalex.org/W2012697508","https://openalex.org/W2012811007","https://openalex.org/W2028712889","https://openalex.org/W2050205048","https://openalex.org/W2055673018","https://openalex.org/W2061015762","https://openalex.org/W2061505796","https://openalex.org/W2062023162","https://openalex.org/W2066680215","https://openalex.org/W2085465150","https://openalex.org/W2109952733","https://openalex.org/W2119032514","https://openalex.org/W2128785176","https://openalex.org/W2140620390","https://openalex.org/W2342805660","https://openalex.org/W2562290404","https://openalex.org/W2587269951","https://openalex.org/W2596904106","https://openalex.org/W2605824083","https://openalex.org/W2751595717","https://openalex.org/W2766523540","https://openalex.org/W2774216483","https://openalex.org/W2803226369","https://openalex.org/W2895858287","https://openalex.org/W2897581946","https://openalex.org/W2907997710","https://openalex.org/W2914624657","https://openalex.org/W2926113039","https://openalex.org/W2948957876","https://openalex.org/W3001048595","https://openalex.org/W3006416751","https://openalex.org/W4211202937","https://openalex.org/W4292366025","https://openalex.org/W4299875178"],"related_works":["https://openalex.org/W1593898832","https://openalex.org/W2142048021","https://openalex.org/W2134075948","https://openalex.org/W2383529437","https://openalex.org/W1790223069","https://openalex.org/W2756324413","https://openalex.org/W2081245100","https://openalex.org/W1973113296","https://openalex.org/W2034561445","https://openalex.org/W2006090893"],"abstract_inverted_index":{"This":[0],"article":[1,91],"studies":[2],"the":[3,20,27,36,50,59,67,78,100],"practical":[4,31,60,103],"exponential":[5,32,51,104],"stability":[6,33,52,61,105],"of":[7,53,80,102,106],"impulsive":[8,68],"stochastic":[9,70],"reaction-diffusion":[10,69],"systems":[11,54],"(ISRDSs)":[12],"with":[13,75,99,108],"delays.":[14,76],"First,":[15],"a":[16],"direct":[17],"approach":[18],"and":[19,34,84,110],"Lyapunov":[21],"method":[22],"are":[23,63,92],"developed":[24],"to":[25,48,66,94],"investigate":[26],"p":[28],"th":[29],"moment":[30],"estimate":[35],"convergence":[37],"rate.":[38],"Note":[39],"that":[40],"these":[41],"two":[42],"methods":[43],"can":[44],"also":[45],"be":[46,95,112],"used":[47],"discuss":[49],"in":[55,89,97],"certain":[56],"conditions.":[57],"Then,":[58],"results":[62,88],"successfully":[64],"applied":[65],"Hopfield":[71],"neural":[72],"networks":[73],"(IRDSHNNs)":[74],"By":[77],"illustration":[79],"four":[81],"numerical":[82],"examples":[83],"their":[85],"simulations,":[86],"our":[87],"this":[90],"proven":[93],"effective":[96],"dealing":[98],"problem":[101],"ISRDSs":[107],"delays,":[109],"may":[111],"regarded":[113],"as":[114],"stabilization":[115],"results.":[116]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":6}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}