{"id":"https://openalex.org/W2911033484","doi":"https://doi.org/10.1109/access.2019.2891721","title":"Global $\\mu$ -Stability of Quaternion-Valued Neural Networks With Unbounded and Asynchronous Time-Varying Delays","display_name":"Global $\\mu$ -Stability of Quaternion-Valued Neural Networks With Unbounded and Asynchronous Time-Varying Delays","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2911033484","doi":"https://doi.org/10.1109/access.2019.2891721","mag":"2911033484"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2891721","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2891721","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08606049.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08606049.pdf","any_repository_has_fulltext":true},"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":["Department of Computer Science and Technology, Tongji University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0003-3165-443X","affiliations":[{"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/A5100398107","display_name":"Zhonghua Li","orcid":"https://orcid.org/0009-0008-0395-2820"},"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":"Zhonghua Li","raw_affiliation_strings":["Department of Computer Science and Technology, Tongji University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I116953780"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":3.3765,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.92907351,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"7","issue":null,"first_page":"9128","last_page":"9141"},"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":0.9805999994277954,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9459999799728394,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.79604172706604},{"id":"https://openalex.org/keywords/cauchys-convergence-test","display_name":"Cauchy's convergence test","score":0.6508350968360901},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.6471654176712036},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6443278193473816},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.5568726658821106},{"id":"https://openalex.org/keywords/asynchronous-communication","display_name":"Asynchronous communication","score":0.5414964556694031},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5405266880989075},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.5092055201530457},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4815116822719574},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4406810402870178},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4402575194835663},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4391309320926666},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42046689987182617},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4202154874801636},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.358185350894928},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21905595064163208},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.16506657004356384},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14973270893096924},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1407206952571869},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.13899025321006775},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13313958048820496},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.0752517580986023}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.79604172706604},{"id":"https://openalex.org/C76835800","wikidata":"https://www.wikidata.org/wiki/Q859102","display_name":"Cauchy's convergence test","level":5,"score":0.6508350968360901},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.6471654176712036},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6443278193473816},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.5568726658821106},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.5414964556694031},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5405266880989075},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.5092055201530457},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4815116822719574},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4406810402870178},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4402575194835663},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4391309320926666},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42046689987182617},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4202154874801636},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.358185350894928},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21905595064163208},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.16506657004356384},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14973270893096924},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1407206952571869},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.13899025321006775},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13313958048820496},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.0752517580986023},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C106947605","wikidata":"https://www.wikidata.org/wiki/Q3278575","display_name":"Cauchy boundary condition","level":4,"score":0.0},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2019.2891721","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2891721","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08606049.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e2ce008d83e14fbdaab14b0df7e5c13d","is_oa":true,"landing_page_url":"https://doaj.org/article/e2ce008d83e14fbdaab14b0df7e5c13d","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 7, Pp 9128-9141 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2891721","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2891721","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08606049.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"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/G7027707469","display_name":null,"funder_award_id":"61673298","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7469888421","display_name":null,"funder_award_id":"17ZR1445700","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"},{"id":"https://openalex.org/G846901025","display_name":null,"funder_award_id":"17QA1404500","funder_id":"https://openalex.org/F4320327803","funder_display_name":"Shanghai Rising-Star Program"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309612","display_name":"Natural Science Foundation of Shanghai","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322449","display_name":"Tongji University","ror":"https://ror.org/03rc6as71"},{"id":"https://openalex.org/F4320327803","display_name":"Shanghai Rising-Star Program","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2911033484.pdf","grobid_xml":"https://content.openalex.org/works/W2911033484.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W55809570","https://openalex.org/W80623023","https://openalex.org/W285212305","https://openalex.org/W599808240","https://openalex.org/W1519761144","https://openalex.org/W1974469776","https://openalex.org/W1980364829","https://openalex.org/W2000273379","https://openalex.org/W2025294622","https://openalex.org/W2025808664","https://openalex.org/W2043757060","https://openalex.org/W2056717940","https://openalex.org/W2091060625","https://openalex.org/W2101996968","https://openalex.org/W2150534501","https://openalex.org/W2157077261","https://openalex.org/W2160121923","https://openalex.org/W2210164727","https://openalex.org/W2251287495","https://openalex.org/W2279590403","https://openalex.org/W2281015479","https://openalex.org/W2316379303","https://openalex.org/W2345882720","https://openalex.org/W2391671645","https://openalex.org/W2515469213","https://openalex.org/W2520103018","https://openalex.org/W2524790587","https://openalex.org/W2555231795","https://openalex.org/W2591262746","https://openalex.org/W2591865209","https://openalex.org/W2601065450","https://openalex.org/W2609992716","https://openalex.org/W2728012017","https://openalex.org/W2766270357","https://openalex.org/W2793034572"],"related_works":["https://openalex.org/W3127350447","https://openalex.org/W3108700312","https://openalex.org/W4225472102","https://openalex.org/W2382948573","https://openalex.org/W2887325221","https://openalex.org/W2084651007","https://openalex.org/W2184550115","https://openalex.org/W3121191907","https://openalex.org/W2391028436","https://openalex.org/W4213061425"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,54],"investigate":[4],"the":[5,29,34,39,44,48,51,56,60,66,71,77,88,104,107],"global":[6],"\u03bc-stability":[7,75],"problem":[8],"of":[9,22,38,42,50,76,90,106],"quaternion-valued":[10],"neural":[11],"networks":[12],"(QVNNs)":[13],"with":[14],"unbounded":[15],"and":[16,59,74,92],"asynchronous":[17],"time-varying":[18],"delays.":[19],"The":[20,80],"decomposition":[21],"QVNNs":[23],"is":[24,100],"proposed":[25],"first":[26],"based":[27],"on":[28],"Hamilton":[30],"rules":[31],"to":[32,64,87,102],"avoid":[33],"non-communicative":[35],"multiplication":[36],"feature":[37],"quaternion.":[40],"Instead":[41],"establishing":[43],"Lyapunov-Krasovskii":[45],"functional":[46],"in":[47],"form":[49],"Hermitian":[52],"matrix,":[53],"combine":[55],"{\u03be,":[57],"\u221e}-norm":[58],"Cauchy":[61],"convergence":[62],"principle":[63],"derive":[65],"sufficient":[67],"conditions":[68],"that":[69],"guarantee":[70],"existence,":[72],"uniqueness,":[73],"equilibrium":[78],"point.":[79],"obtained":[81,108],"criteria":[82],"here":[83],"are":[84],"milder,":[85],"owing":[86],"consideration":[89],"inhibitory":[91],"excitatory":[93],"between":[94],"neurons.":[95],"Finally,":[96],"a":[97],"specified":[98],"example":[99],"presented":[101],"verify":[103],"correctness":[105],"results.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2019-01-25T00:00:00"}
