{"id":"https://openalex.org/W2090830274","doi":"https://doi.org/10.1142/s0129065703001534","title":"Global Convergence of Delayed Neural Network Systems","display_name":"Global Convergence of Delayed Neural Network Systems","publication_year":2003,"publication_date":"2003-06-01","ids":{"openalex":"https://openalex.org/W2090830274","doi":"https://doi.org/10.1142/s0129065703001534","mag":"2090830274","pmid":"https://pubmed.ncbi.nlm.nih.gov/12884452"},"language":"en","primary_location":{"id":"doi:10.1142/s0129065703001534","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129065703001534","pdf_url":null,"source":{"id":"https://openalex.org/S197665576","display_name":"International Journal of Neural Systems","issn_l":"0129-0657","issn":["0129-0657","1793-6462"],"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 Neural Systems","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/A5030103251","display_name":"Wenlian Lu","orcid":"https://orcid.org/0000-0003-1880-6240"},"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":["Laboratory of Nonlinear Science,  Institute of Mathematics, Fudan University, Shanghai,  200433, P.R. China","Laboratory of Nonlinear Science, Institute of Mathematics, Fudan University, Shanghai, 200433, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Nonlinear Science,  Institute of Mathematics, Fudan University, Shanghai,  200433, P.R. China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Laboratory of Nonlinear Science, Institute of Mathematics, Fudan University, Shanghai, 200433, P.R. China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034031384","display_name":"Libin Rong","orcid":"https://orcid.org/0000-0002-1464-6078"},"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":"Libin Rong","raw_affiliation_strings":["Laboratory of Nonlinear Science,  Institute of Mathematics, Fudan University, Shanghai,  200433, P.R. China","Laboratory of Nonlinear Science, Institute of Mathematics, Fudan University, Shanghai, 200433, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Nonlinear Science,  Institute of Mathematics, Fudan University, Shanghai,  200433, P.R. China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Laboratory of Nonlinear Science, Institute of Mathematics, Fudan University, Shanghai, 200433, P.R. China","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":["Laboratory of Nonlinear Science,  Institute of Mathematics, Fudan University, Shanghai,  200433, P.R. China","Laboratory of Nonlinear Science, Institute of Mathematics, Fudan University, Shanghai, 200433, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Nonlinear Science,  Institute of Mathematics, Fudan University, Shanghai,  200433, P.R. China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Laboratory of Nonlinear Science, Institute of Mathematics, Fudan University, Shanghai, 200433, P.R. China","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":9.1936,"has_fulltext":false,"cited_by_count":73,"citation_normalized_percentile":{"value":0.9787935,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"13","issue":"03","first_page":"193","last_page":"204"},"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/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9930999875068665,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7919694185256958},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.7427595257759094},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.7353876829147339},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6301945447921753},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6051620841026306},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.5993213653564453},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5968295335769653},{"id":"https://openalex.org/keywords/activation-function","display_name":"Activation function","score":0.5946146845817566},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5593791007995605},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.54655522108078},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5426320433616638},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.504468560218811},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.4896738827228546},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.45642396807670593},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4439735412597656},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.42130395770072937},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4134482443332672},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2661471366882324},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20383143424987793},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1345595121383667},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.12739220261573792},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.122958242893219}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7919694185256958},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.7427595257759094},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.7353876829147339},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6301945447921753},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6051620841026306},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.5993213653564453},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5968295335769653},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.5946146845817566},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5593791007995605},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.54655522108078},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5426320433616638},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.504468560218811},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.4896738827228546},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.45642396807670593},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4439735412597656},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.42130395770072937},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4134482443332672},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2661471366882324},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20383143424987793},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1345595121383667},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.12739220261573792},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.122958242893219},{"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},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","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":2,"locations":[{"id":"doi:10.1142/s0129065703001534","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129065703001534","pdf_url":null,"source":{"id":"https://openalex.org/S197665576","display_name":"International Journal of Neural Systems","issn_l":"0129-0657","issn":["0129-0657","1793-6462"],"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 Neural Systems","raw_type":"journal-article"},{"id":"pmid:12884452","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/12884452","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":"International journal of neural systems","raw_type":null}],"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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1586658033","https://openalex.org/W1973545255","https://openalex.org/W2014960375","https://openalex.org/W2018089249","https://openalex.org/W2025294622","https://openalex.org/W2036270456","https://openalex.org/W2056717940","https://openalex.org/W2064924023","https://openalex.org/W2075256837","https://openalex.org/W2076215153","https://openalex.org/W2084820442","https://openalex.org/W2089808022","https://openalex.org/W2094307076","https://openalex.org/W2095425517","https://openalex.org/W2098103010","https://openalex.org/W2100337613","https://openalex.org/W2107344562","https://openalex.org/W2111926818","https://openalex.org/W2116484154","https://openalex.org/W2119772282","https://openalex.org/W2121003919","https://openalex.org/W2121752938","https://openalex.org/W2150551708","https://openalex.org/W2152189682","https://openalex.org/W2153308713","https://openalex.org/W2154102142","https://openalex.org/W2158872585","https://openalex.org/W2160121923","https://openalex.org/W2166588786","https://openalex.org/W2373941911","https://openalex.org/W3210839039","https://openalex.org/W4210925605","https://openalex.org/W4292365908"],"related_works":["https://openalex.org/W2893539081","https://openalex.org/W3024877706","https://openalex.org/W3022392884","https://openalex.org/W4385451479","https://openalex.org/W4210854505","https://openalex.org/W3012219884","https://openalex.org/W4295036712","https://openalex.org/W4375958661","https://openalex.org/W2811324119","https://openalex.org/W4211198594"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"without":[3],"assuming":[4],"the":[5,12,23,41,49,60,65,77,84,87],"boundedness,":[6],"strict":[7],"monotonicity":[8],"and":[9,44],"differentiability":[10],"of":[11,26,29,48,64],"activation":[13,88],"functions,":[14],"we":[15],"utilize":[16],"a":[17,27],"new":[18,37],"Lyapunov":[19],"function":[20],"to":[21],"analyze":[22],"global":[24,45],"convergence":[25],"class":[28],"neural":[30],"networks":[31],"models":[32],"with":[33,72],"time":[34],"delays.":[35],"A":[36],"sufficient":[38],"condition":[39,78],"guaranteeing":[40],"existence,":[42],"uniqueness":[43],"exponential":[46],"stability":[47,55],"equilibrium":[50],"point":[51],"is":[52,70],"derived.":[53],"This":[54],"criterion":[56],"imposes":[57],"constraints":[58],"on":[59],"feedback":[61],"matrices":[62],"independently":[63],"delay":[66],"parameters.":[67],"The":[68],"result":[69],"compared":[71],"some":[73],"previous":[74],"works.":[75],"Furthermore,":[76],"may":[79],"be":[80],"less":[81],"restrictive":[82],"in":[83],"case":[85],"that":[86],"functions":[89],"are":[90],"hyperbolic":[91],"tangent.":[92]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
