{"id":"https://openalex.org/W1980364829","doi":"https://doi.org/10.1109/tnnls.2015.2415496","title":"Global Exponential Stability for Complex-Valued Recurrent Neural Networks With Asynchronous Time Delays","display_name":"Global Exponential Stability for Complex-Valued Recurrent Neural Networks With Asynchronous Time Delays","publication_year":2015,"publication_date":"2015-04-10","ids":{"openalex":"https://openalex.org/W1980364829","doi":"https://doi.org/10.1109/tnnls.2015.2415496","mag":"1980364829","pmid":"https://pubmed.ncbi.nlm.nih.gov/25872218"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2015.2415496","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2015.2415496","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 and Learning 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/A5051541488","display_name":"Xiwei Liu","orcid":"https://orcid.org/0000-0003-3165-443X"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiwei Liu","raw_affiliation_strings":["Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University, Shanghai, China","Department of Computer Science and Technology, Tongji University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]},{"raw_affiliation_string":"Department of Computer Science and Technology, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]}]},{"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":["School of Computer Sciences and Mathematical Sciences, Fudan University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Sciences and Mathematical Sciences, Fudan University, Shanghai, China","institution_ids":["https://openalex.org/I24943067"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":22.0913,"has_fulltext":false,"cited_by_count":143,"citation_normalized_percentile":{"value":0.99480593,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"27","issue":"3","first_page":"593","last_page":"606"},"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":0.9858999848365784,"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/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9843000173568726,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7847845554351807},{"id":"https://openalex.org/keywords/asynchronous-communication","display_name":"Asynchronous communication","score":0.782569169998169},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.7333142161369324},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.7105063199996948},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.7097554206848145},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6317427158355713},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6114703416824341},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5403220653533936},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5108768343925476},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49577054381370544},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.48593273758888245},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47655633091926575},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.43475398421287537},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37902188301086426},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.32728689908981323},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25471892952919006},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1661492884159088},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1539653241634369},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1423654854297638}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7847845554351807},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.782569169998169},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.7333142161369324},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.7105063199996948},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.7097554206848145},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6317427158355713},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6114703416824341},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5403220653533936},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5108768343925476},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49577054381370544},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.48593273758888245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47655633091926575},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.43475398421287537},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37902188301086426},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.32728689908981323},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25471892952919006},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1661492884159088},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1539653241634369},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1423654854297638},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2015.2415496","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2015.2415496","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 and Learning Systems","raw_type":"journal-article"},{"id":"pmid:25872218","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/25872218","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 and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3297192555","display_name":null,"funder_award_id":"61273211","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6399587625","display_name":null,"funder_award_id":"61203149","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8448526004","display_name":null,"funder_award_id":"61233016","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/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W93167102","https://openalex.org/W1601736658","https://openalex.org/W1967928782","https://openalex.org/W1968728750","https://openalex.org/W1970140901","https://openalex.org/W1973024930","https://openalex.org/W1973690452","https://openalex.org/W1974469776","https://openalex.org/W1979154208","https://openalex.org/W1985287182","https://openalex.org/W1992125110","https://openalex.org/W1999414410","https://openalex.org/W2000273379","https://openalex.org/W2000829143","https://openalex.org/W2010141219","https://openalex.org/W2025294622","https://openalex.org/W2031970152","https://openalex.org/W2037860939","https://openalex.org/W2038428280","https://openalex.org/W2039617089","https://openalex.org/W2043388587","https://openalex.org/W2043757060","https://openalex.org/W2047515252","https://openalex.org/W2048646957","https://openalex.org/W2049176600","https://openalex.org/W2055606008","https://openalex.org/W2056717940","https://openalex.org/W2062210787","https://openalex.org/W2080764377","https://openalex.org/W2081097129","https://openalex.org/W2097557445","https://openalex.org/W2098103010","https://openalex.org/W2101996968","https://openalex.org/W2104404280","https://openalex.org/W2106045980","https://openalex.org/W2111456564","https://openalex.org/W2121752938","https://openalex.org/W2122357350","https://openalex.org/W2123113196","https://openalex.org/W2123168499","https://openalex.org/W2124583036","https://openalex.org/W2126681784","https://openalex.org/W2126944419","https://openalex.org/W2128084896","https://openalex.org/W2132048588","https://openalex.org/W2142389098","https://openalex.org/W2149971042","https://openalex.org/W2150534501","https://openalex.org/W2152646054","https://openalex.org/W2153308713","https://openalex.org/W2157077261","https://openalex.org/W2160121923","https://openalex.org/W3144308317","https://openalex.org/W4229840834","https://openalex.org/W6636193349"],"related_works":["https://openalex.org/W1978738522","https://openalex.org/W2095028518","https://openalex.org/W2377228964","https://openalex.org/W2383827392","https://openalex.org/W2059311322","https://openalex.org/W2782159350","https://openalex.org/W2536963663","https://openalex.org/W2057482994","https://openalex.org/W1989732506","https://openalex.org/W1988317900"],"abstract_inverted_index":{"In":[0],"this":[1,48],"paper,":[2],"we":[3,74,102],"investigate":[4],"the":[5,76,81,86,95,108,115,136,160],"global":[6,111],"exponential":[7,77,96,112],"stability":[8,113],"for":[9,107,118],"complex-valued":[10,20,120],"recurrent":[11],"neural":[12,121],"networks":[13,21],"with":[14,50],"asynchronous":[15],"time":[16,54],"delays":[17,55,60],"by":[18,38],"decomposing":[19],"to":[22,158],"real":[23],"and":[24,27,72,83,110,138],"imaginary":[25],"parts":[26],"construct":[28],"an":[29],"equivalent":[30],"real-valued":[31],"system.":[32],"The":[33],"network":[34],"model":[35,69],"is":[36,89],"described":[37],"a":[39,91],"continuous-time":[40],"equation.":[41],"There":[42],"are":[43,64,128,156],"two":[44],"main":[45],"differences":[46],"of":[47,85,94,114,132,135,146,162],"paper":[49],"previous":[51,144],"works:":[52],"1)":[53],"can":[56,149],"be":[57,150],"asynchronous,":[58],"i.e.,":[59],"between":[61,141],"different":[62],"nodes":[63],"different,":[65],"which":[66],"make":[67],"our":[68,126,133,163],"more":[70],"general":[71],"2)":[73],"prove":[75],"convergence":[78],"directly,":[79],"while":[80],"existence":[82],"uniqueness":[84,109],"equilibrium":[87,116],"point":[88,117],"just":[90],"direct":[92],"consequence":[93],"convergence.":[97],"Using":[98],"three":[99],"generalized":[100],"norms,":[101],"present":[103],"some":[104,153],"sufficient":[105],"conditions":[106,124],"delayed":[119],"networks.":[122],"These":[123],"in":[125],"results":[127],"less":[129],"restrictive":[130],"because":[131],"consideration":[134],"excitatory":[137],"inhibitory":[139],"effects":[140],"neurons;":[142],"so":[143],"works":[145],"other":[147],"researchers":[148],"extended.":[151],"Finally,":[152],"numerical":[154],"simulations":[155],"given":[157],"demonstrate":[159],"correctness":[161],"obtained":[164],"results.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":22},{"year":2017,"cited_by_count":29},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
