{"id":"https://openalex.org/W1970140901","doi":"https://doi.org/10.1109/tnn.2011.2160987","title":"Generalized Halanay Inequalities and Their Applications to Neural Networks With Unbounded Time-Varying Delays","display_name":"Generalized Halanay Inequalities and Their Applications to Neural Networks With Unbounded Time-Varying Delays","publication_year":2011,"publication_date":"2011-07-21","ids":{"openalex":"https://openalex.org/W1970140901","doi":"https://doi.org/10.1109/tnn.2011.2160987","mag":"1970140901","pmid":"https://pubmed.ncbi.nlm.nih.gov/21775257"},"language":"en","primary_location":{"id":"doi:10.1109/tnn.2011.2160987","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2011.2160987","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"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 Neural Networks","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5115587783","display_name":"\u0411\u043e \u041b\u044e","orcid":"https://orcid.org/0000-0003-3045-628X"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Liu","raw_affiliation_strings":["Key Laboratory of Nonlinear Science, Chinese Ministry of Education, Institute of Mathematics, Fudan University, Shanghai, China. 071018024@fudan.edu.cn","Key Lab. of Nonlinear Sci. of Chinese Minist. of Educ., Fudan Univ., Shanghai, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Nonlinear Science, Chinese Ministry of Education, Institute of Mathematics, Fudan University, Shanghai, China. 071018024@fudan.edu.cn","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Key Lab. of Nonlinear Sci. of Chinese Minist. of Educ., Fudan Univ., Shanghai, China#TAB#","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100813034","display_name":"Wenlian Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenlian Lu","raw_affiliation_strings":["Key Laboratory of Nonlinear Science of Chinese Ministry of Education, Institute of Mathematics, Fudan University, Shanghai, China","Key Lab. of Nonlinear Sci. of Chinese Minist. of Educ., Fudan Univ., Shanghai, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Nonlinear Science of Chinese Ministry of Education, Institute of Mathematics, Fudan University, Shanghai, China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Key Lab. of Nonlinear Sci. of Chinese Minist. of Educ., Fudan Univ., Shanghai, China#TAB#","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062509066","display_name":"Tianping Chen","orcid":"https://orcid.org/0000-0001-6117-6673"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianping Chen","raw_affiliation_strings":["Key Laboratory of Nonlinear Science of Chinese Ministry of Education, Institute of Mathematics, Fudan University, Shanghai, China","Key Lab. of Nonlinear Sci. of Chinese Minist. of Educ., Fudan Univ., Shanghai, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Nonlinear Science of Chinese Ministry of Education, Institute of Mathematics, Fudan University, Shanghai, China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Key Lab. of Nonlinear Sci. of Chinese Minist. of Educ., Fudan Univ., Shanghai, China#TAB#","institution_ids":["https://openalex.org/I24943067"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.657,"has_fulltext":false,"cited_by_count":103,"citation_normalized_percentile":{"value":0.92814569,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"22","issue":"9","first_page":"1508","last_page":"1513"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"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":1.0,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/exponential-stability","display_name":"Exponential stability","score":0.7546184062957764},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.68189537525177},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5768699645996094},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.5508513450622559},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5240878462791443},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.520996630191803},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.5040546655654907},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49913644790649414},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.48971179127693176},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.45563238859176636},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.4503454566001892},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.44899648427963257},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4456534683704376},{"id":"https://openalex.org/keywords/cellular-neural-network","display_name":"Cellular neural network","score":0.42452964186668396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4010661542415619},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.34241175651550293},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.24274447560310364},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21072110533714294},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.21033716201782227},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14333048462867737},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09657758474349976},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08725035190582275}],"concepts":[{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.7546184062957764},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.68189537525177},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5768699645996094},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.5508513450622559},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5240878462791443},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.520996630191803},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.5040546655654907},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49913644790649414},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.48971179127693176},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.45563238859176636},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.4503454566001892},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.44899648427963257},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4456534683704376},{"id":"https://openalex.org/C812465","wikidata":"https://www.wikidata.org/wiki/Q5058375","display_name":"Cellular neural network","level":3,"score":0.42452964186668396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4010661542415619},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.34241175651550293},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.24274447560310364},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21072110533714294},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.21033716201782227},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14333048462867737},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09657758474349976},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08725035190582275},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","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},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1109/tnn.2011.2160987","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2011.2160987","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"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 Neural Networks","raw_type":"journal-article"},{"id":"pmid:21775257","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21775257","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 neural networks","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.550000011920929,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1974469776","https://openalex.org/W2000422023","https://openalex.org/W2025294622","https://openalex.org/W2034001765","https://openalex.org/W2086635487","https://openalex.org/W2094959767","https://openalex.org/W2096783161","https://openalex.org/W2098084981","https://openalex.org/W2116484154","https://openalex.org/W2132552866","https://openalex.org/W2142048021","https://openalex.org/W2150534501","https://openalex.org/W2156002109","https://openalex.org/W4241266039","https://openalex.org/W4300993012"],"related_works":["https://openalex.org/W2134075948","https://openalex.org/W2146846916","https://openalex.org/W2777927656","https://openalex.org/W2085071341","https://openalex.org/W2054869975","https://openalex.org/W2361641056","https://openalex.org/W2074717584","https://openalex.org/W1973113296","https://openalex.org/W2136895532","https://openalex.org/W2155108324"],"abstract_inverted_index":{"In":[0],"this":[1],"brief,":[2],"we":[3,50],"discuss":[4,51],"some":[5,34],"variants":[6],"of":[7,17,21,36],"generalized":[8],"Halanay":[9,38],"inequalities":[10],"that":[11,71],"are":[12,79],"useful":[13],"in":[14],"the":[15,37,45,61,72],"discussion":[16],"dissipativity":[18],"and":[19,27,56],"stability":[20,59],"delayed":[22],"neural":[23,63],"networks,":[24],"integro-differential":[25],"systems,":[26],"Volterra":[28],"functional":[29],"differential":[30],"equations.":[31],"We":[32,68],"provide":[33],"generalizations":[35],"inequality,":[39],"which":[40],"is":[41],"more":[42],"accurate":[43],"than":[44],"existing":[46],"results.":[47],"As":[48],"applications,":[49],"invariant":[52],"set,":[53],"dissipative":[54],"synchronization,":[55],"global":[57],"asymptotic":[58],"for":[60],"Hopfield":[62],"networks":[64],"with":[65,75],"infinite":[66],"delays.":[67],"also":[69],"prove":[70],"dynamical":[73],"systems":[74],"unbounded":[76],"time-varying":[77],"delays":[78],"globally":[80],"asymptotically":[81],"stable.":[82]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":15},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}