{"id":"https://openalex.org/W3198390167","doi":"https://doi.org/10.1109/access.2021.3110764","title":"Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method","display_name":"Stability Analysis of Two Kinds of Fractional-Order Neural Networks Based on Lyapunov Method","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3198390167","doi":"https://doi.org/10.1109/access.2021.3110764","mag":"3198390167"},"language":"en","primary_location":{"id":"doi:10.1109/access.2021.3110764","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3110764","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/09530518.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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/ielx7/6287639/6514899/09530518.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102001457","display_name":"Xin Chang","orcid":"https://orcid.org/0000-0001-9558-8422"},"institutions":[{"id":"https://openalex.org/I4210110558","display_name":"Xi'an Technological University","ror":"https://ror.org/01t8prc81","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210110558"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin Chang","raw_affiliation_strings":["Department of Electronics Information and Engineering, Xi\u2019an Technological University, Xi\u2019an City, P.R. China, 710032. (e-mail: cx3020784292@163.com)","Department of Electronics Information and Engineering, Xi\u2019an Technological University, Xi\u2019an, China"],"raw_orcid":"https://orcid.org/0000-0001-9558-8422","affiliations":[{"raw_affiliation_string":"Department of Electronics Information and Engineering, Xi\u2019an Technological University, Xi\u2019an City, P.R. China, 710032. (e-mail: cx3020784292@163.com)","institution_ids":["https://openalex.org/I4210110558"]},{"raw_affiliation_string":"Department of Electronics Information and Engineering, Xi\u2019an Technological University, Xi\u2019an, China","institution_ids":["https://openalex.org/I4210110558"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090593845","display_name":"Qinkun Xiao","orcid":"https://orcid.org/0000-0002-2651-1218"},"institutions":[{"id":"https://openalex.org/I4210110558","display_name":"Xi'an Technological University","ror":"https://ror.org/01t8prc81","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210110558"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qinkun Xiao","raw_affiliation_strings":["Department of Electronics Information and Engineering, Xi\u2019an Technological University, Xi\u2019an City, P.R. China, 710032","Department of Electronics Information and Engineering, Xi\u2019an Technological University, Xi\u2019an, China"],"raw_orcid":"https://orcid.org/0000-0002-2651-1218","affiliations":[{"raw_affiliation_string":"Department of Electronics Information and Engineering, Xi\u2019an Technological University, Xi\u2019an City, P.R. China, 710032","institution_ids":["https://openalex.org/I4210110558"]},{"raw_affiliation_string":"Department of Electronics Information and Engineering, Xi\u2019an Technological University, Xi\u2019an, China","institution_ids":["https://openalex.org/I4210110558"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080858828","display_name":"Yilin Zhu","orcid":"https://orcid.org/0000-0002-5704-4501"},"institutions":[{"id":"https://openalex.org/I4210110558","display_name":"Xi'an Technological University","ror":"https://ror.org/01t8prc81","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210110558"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yilin Zhu","raw_affiliation_strings":["Department of Electronics Information and Engineering, Xi\u2019an Technological University, Xi\u2019an City, P.R. China, 710032","Department of Electronics Information and Engineering, Xi\u2019an Technological University, Xi\u2019an, China"],"raw_orcid":"https://orcid.org/0000-0002-5704-4501","affiliations":[{"raw_affiliation_string":"Department of Electronics Information and Engineering, Xi\u2019an Technological University, Xi\u2019an City, P.R. China, 710032","institution_ids":["https://openalex.org/I4210110558"]},{"raw_affiliation_string":"Department of Electronics Information and Engineering, Xi\u2019an Technological University, Xi\u2019an, China","institution_ids":["https://openalex.org/I4210110558"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079956486","display_name":"Jielei Xiao","orcid":"https://orcid.org/0000-0002-7592-6268"},"institutions":[{"id":"https://openalex.org/I4210130660","display_name":"Xi'an High Tech University","ror":"https://ror.org/03vt7za95","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210130660"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jielei Xiao","raw_affiliation_strings":["Senior High School, Xi\u2019an Tieyi Middle School,Xi\u2019an City, P.R. China, 710000","Senior High School, Xi\u2019an Tieyi Middle School, Xi\u2019an, China"],"raw_orcid":"https://orcid.org/0000-0002-7592-6268","affiliations":[{"raw_affiliation_string":"Senior High School, Xi\u2019an Tieyi Middle School,Xi\u2019an City, P.R. China, 710000","institution_ids":["https://openalex.org/I4210130660"]},{"raw_affiliation_string":"Senior High School, Xi\u2019an Tieyi Middle School, Xi\u2019an, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.1523387,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"9","issue":null,"first_page":"124132","last_page":"124141"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9966999888420105,"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.6801572442054749},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6420327425003052},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.6366286873817444},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.6014666557312012},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5819099545478821},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5764176249504089},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4981577396392822},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4598901867866516},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4356227219104767},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23754966259002686},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2061755657196045},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.20044580101966858},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13043534755706787}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6801572442054749},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6420327425003052},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.6366286873817444},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.6014666557312012},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5819099545478821},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5764176249504089},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4981577396392822},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4598901867866516},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4356227219104767},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23754966259002686},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2061755657196045},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.20044580101966858},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13043534755706787},{"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/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":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2021.3110764","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3110764","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/09530518.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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:dfc9ed664c2049c5b5eeb39bec75e47d","is_oa":true,"landing_page_url":"https://doaj.org/article/dfc9ed664c2049c5b5eeb39bec75e47d","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 9, Pp 124132-124141 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2021.3110764","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3110764","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/6514899/09530518.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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.6000000238418579}],"awards":[{"id":"https://openalex.org/G5827775281","display_name":"\u57fa\u4e8e\u56fe\u6a21\u578b\u7684\u52a8\u6001\u7acb\u4f53\u573a\u666f\u68c0\u7d22\u7814\u7a76","funder_award_id":"60972095","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6844821413","display_name":"\u57fa\u4e8e\u89c6\u89c9\u53ca\u56fe\u6a21\u578b\u7684\u8fde\u7eed\u624b\u8bed\u8bc6\u522b\u7814\u7a76","funder_award_id":"61671362","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7879472498","display_name":null,"funder_award_id":"62071366","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8060576399","display_name":"\u57fa\u4e8e\u56fe\u6a21\u578b\u7684\u4eba\u4f53\u8fd0\u52a8\u6355\u83b7\u6570\u636e\u68c0\u7d22\u7814\u7a76","funder_award_id":"61271362","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3198390167.pdf","grobid_xml":"https://content.openalex.org/works/W3198390167.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W608208035","https://openalex.org/W1979594386","https://openalex.org/W1992271136","https://openalex.org/W2003560775","https://openalex.org/W2020625830","https://openalex.org/W2049570254","https://openalex.org/W2050580331","https://openalex.org/W2053751819","https://openalex.org/W2056904916","https://openalex.org/W2286622088","https://openalex.org/W2474785193","https://openalex.org/W2482509550","https://openalex.org/W2554775479","https://openalex.org/W2594234726","https://openalex.org/W2768845549","https://openalex.org/W2794044373","https://openalex.org/W2807722645","https://openalex.org/W2809898024","https://openalex.org/W2904182550","https://openalex.org/W2945854435","https://openalex.org/W2953563516","https://openalex.org/W2956855079","https://openalex.org/W2995312257","https://openalex.org/W3005132778","https://openalex.org/W3007442310","https://openalex.org/W3008354675","https://openalex.org/W3014378035","https://openalex.org/W3029755157","https://openalex.org/W3034111674","https://openalex.org/W3038484279","https://openalex.org/W3044422455","https://openalex.org/W3087579456","https://openalex.org/W3094992824","https://openalex.org/W3119014068","https://openalex.org/W3130098536","https://openalex.org/W3130601514","https://openalex.org/W3134977171","https://openalex.org/W3153424191","https://openalex.org/W3156734385","https://openalex.org/W4246331082","https://openalex.org/W6791500132"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W4301247218","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W2164703465","https://openalex.org/W2168383058","https://openalex.org/W2143247663","https://openalex.org/W2050693590","https://openalex.org/W2060195842"],"abstract_inverted_index":{"At":[0],"present,":[1],"the":[2,12,17,41,44,56,66,87,98,118,122,126,130],"theory":[3,78],"and":[4,30,47,68,79,83,101],"application":[5],"of":[6,20,43,70,106,120],"fractional-order":[7,21,60,111],"neural":[8,22,61,112],"networks":[9,23,62,113],"remain":[10],"in":[11],"exploratory":[13],"stage.":[14],"We":[15],"study":[16],"asymptotic":[18,36,107],"stability":[19,37,108],"with":[24,63],"Riemann-Liouville":[25],"(R-L)":[26],"derivatives.":[27],"For":[28],"non-delayed":[29],"delayed":[31],"systems,":[32],"we":[33],"propose":[34],"an":[35],"criterion":[38],"based":[39,85],"on":[40,86,97],"combination":[42],"Lyapunov":[45,92],"method":[46],"linear":[48],"matrix":[49,76],"inequality":[50,99],"(LMI)":[51],"method.":[52],"The":[53],"highlights":[54],"include":[55],"following:":[57],"(1)":[58],"for":[59,110],"time":[64],"delay,":[65],"existence":[67],"uniqueness":[69],"solutions":[71],"are":[72,114,132],"proven":[73],"by":[74,125],"using":[75,134],"analysis":[77],"contraction":[80],"mapping":[81],"theorem,":[82],"(2)":[84],"unique":[88],"solution,":[89],"a":[90],"suitable":[91],"functional":[93],"is":[94],"constructed.":[95],"Based":[96],"theorem":[100],"LMI":[102],"method,":[103],"two":[104],"sets":[105],"criteria":[109],"proven,":[115],"which":[116],"avoids":[117],"difficulty":[119],"solving":[121],"fractional":[123],"derivative":[124],"Leibniz":[127],"law.":[128],"Finally,":[129],"results":[131],"verified":[133],"numerical":[135],"simulations.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}