{"id":"https://openalex.org/W4389317840","doi":"https://doi.org/10.1109/tnnls.2023.3334871","title":"Multistability of State-Dependent Switched Fractional-Order Hopfield Neural Networks With Mexican-Hat Activation Function and Its Application in Associative Memories","display_name":"Multistability of State-Dependent Switched Fractional-Order Hopfield Neural Networks With Mexican-Hat Activation Function and Its Application in Associative Memories","publication_year":2023,"publication_date":"2023-12-04","ids":{"openalex":"https://openalex.org/W4389317840","doi":"https://doi.org/10.1109/tnnls.2023.3334871","pmid":"https://pubmed.ncbi.nlm.nih.gov/38048243"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2023.3334871","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2023.3334871","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/A5069045645","display_name":"Boqiang Cao","orcid":"https://orcid.org/0000-0002-3861-5719"},"institutions":[{"id":"https://openalex.org/I21642278","display_name":"Ningxia University","ror":"https://ror.org/04j7b2v61","country_code":"CN","type":"education","lineage":["https://openalex.org/I21642278"]},{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Boqiang Cao","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, China","Ningxia University, Yinchuan, China"],"raw_orcid":"https://orcid.org/0000-0002-3861-5719","affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]},{"raw_affiliation_string":"Ningxia University, Yinchuan, China","institution_ids":["https://openalex.org/I21642278"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067405953","display_name":"Xiaobing Nie","orcid":"https://orcid.org/0000-0002-8256-6897"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaobing Nie","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-8256-6897","affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108050907","display_name":"Wei Xing Zheng","orcid":"https://orcid.org/0000-0002-0572-5938"},"institutions":[{"id":"https://openalex.org/I63525965","display_name":"Western Sydney University","ror":"https://ror.org/03t52dk35","country_code":"AU","type":"education","lineage":["https://openalex.org/I63525965"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Wei Xing Zheng","raw_affiliation_strings":["School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney, NSW, Australia"],"raw_orcid":"https://orcid.org/0000-0002-0572-5938","affiliations":[{"raw_affiliation_string":"School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I63525965"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017808266","display_name":"Jinde Cao","orcid":"https://orcid.org/0000-0003-3133-7119"},"institutions":[{"id":"https://openalex.org/I193775966","display_name":"Yonsei University","ror":"https://ror.org/01wjejq96","country_code":"KR","type":"education","lineage":["https://openalex.org/I193775966"]},{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN","KR"],"is_corresponding":false,"raw_author_name":"Jinde Cao","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, China","Yonsei Frontier Laboratory, Yonsei University, Seoul, South Korea"],"raw_orcid":"https://orcid.org/0000-0003-3133-7119","affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]},{"raw_affiliation_string":"Yonsei Frontier Laboratory, Yonsei University, Seoul, South Korea","institution_ids":["https://openalex.org/I193775966"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5069045645"],"corresponding_institution_ids":["https://openalex.org/I21642278","https://openalex.org/I76569877"],"apc_list":null,"apc_paid":null,"fwci":6.8863,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.97363903,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"36","issue":"1","first_page":"1213","last_page":"1227"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9991999864578247,"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":0.9991999864578247,"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/T10320","display_name":"Neural Networks and Applications","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9696000218391418,"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/multistability","display_name":"Multistability","score":0.8262344598770142},{"id":"https://openalex.org/keywords/content-addressable-memory","display_name":"Content-addressable memory","score":0.6132214069366455},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.5828697085380554},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.5798581838607788},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5790266394615173},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5640977621078491},{"id":"https://openalex.org/keywords/hopfield-network","display_name":"Hopfield network","score":0.5407874584197998},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5198615193367004},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.506299614906311},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.49375757575035095},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44604483246803284},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.43827566504478455},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4346780776977539},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4091188907623291},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40033239126205444},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.35499995946884155},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.34929731488227844},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24219372868537903},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17110106348991394},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10884737968444824},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.0875844955444336}],"concepts":[{"id":"https://openalex.org/C2776966350","wikidata":"https://www.wikidata.org/wiki/Q6935096","display_name":"Multistability","level":3,"score":0.8262344598770142},{"id":"https://openalex.org/C53442348","wikidata":"https://www.wikidata.org/wiki/Q745101","display_name":"Content-addressable memory","level":3,"score":0.6132214069366455},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.5828697085380554},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.5798581838607788},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5790266394615173},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5640977621078491},{"id":"https://openalex.org/C46421273","wikidata":"https://www.wikidata.org/wiki/Q1407668","display_name":"Hopfield network","level":3,"score":0.5407874584197998},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5198615193367004},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.506299614906311},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.49375757575035095},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44604483246803284},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.43827566504478455},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4346780776977539},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4091188907623291},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40033239126205444},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.35499995946884155},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.34929731488227844},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24219372868537903},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17110106348991394},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10884737968444824},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0875844955444336},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2023.3334871","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2023.3334871","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:38048243","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38048243","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/G4585534567","display_name":null,"funder_award_id":"61833005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G68194271","display_name":null,"funder_award_id":"61673111","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W1623819170","https://openalex.org/W1939048443","https://openalex.org/W1975003303","https://openalex.org/W1979981924","https://openalex.org/W1991848143","https://openalex.org/W2016054987","https://openalex.org/W2020625830","https://openalex.org/W2020731033","https://openalex.org/W2034828267","https://openalex.org/W2059162909","https://openalex.org/W2069671775","https://openalex.org/W2072434871","https://openalex.org/W2087661690","https://openalex.org/W2169006540","https://openalex.org/W2306429512","https://openalex.org/W2474785193","https://openalex.org/W2476959674","https://openalex.org/W2501582773","https://openalex.org/W2566966489","https://openalex.org/W2582971624","https://openalex.org/W2732117597","https://openalex.org/W2781354505","https://openalex.org/W2790719793","https://openalex.org/W2885704392","https://openalex.org/W2894286678","https://openalex.org/W2894411297","https://openalex.org/W2896879375","https://openalex.org/W2901472487","https://openalex.org/W2914428788","https://openalex.org/W2946743559","https://openalex.org/W2947795685","https://openalex.org/W2966024432","https://openalex.org/W2966558131","https://openalex.org/W2986128400","https://openalex.org/W3004112379","https://openalex.org/W3008610884","https://openalex.org/W3010720225","https://openalex.org/W3048458742","https://openalex.org/W3089040279","https://openalex.org/W3105862385","https://openalex.org/W3120219852","https://openalex.org/W3123065208","https://openalex.org/W3132211664","https://openalex.org/W3159546681","https://openalex.org/W3164053552","https://openalex.org/W3168014694","https://openalex.org/W3188110435","https://openalex.org/W3203583012","https://openalex.org/W4211045621","https://openalex.org/W4220758892","https://openalex.org/W4378530903"],"related_works":["https://openalex.org/W2144581752","https://openalex.org/W1536116856","https://openalex.org/W4321273133","https://openalex.org/W2147932521","https://openalex.org/W1977722518","https://openalex.org/W2883844359","https://openalex.org/W1560986979","https://openalex.org/W2072147513","https://openalex.org/W3087113781","https://openalex.org/W1863343919"],"abstract_inverted_index":{"The":[0],"multistability":[1],"and":[2,37,55,84,104,125,130,132,153,182],"its":[3],"application":[4],"in":[5,10,63,68,93,117,162],"associative":[6,149],"memories":[7,150],"are":[8,47,74],"investigated":[9],"this":[11],"article":[12],"for":[13,151],"state-dependent":[14,105],"switched":[15],"fractional-order":[16,41,102],"Hopfield":[17],"neural":[18],"networks":[19],"(FOHNNs)":[20],"with":[21,114,136,164],"Mexican-hat":[22],"activation":[23],"function":[24],"(AF).":[25],"Based":[26],"on":[27],"the":[28,33,38,51,64,70,79,82,94,97,115,118,120,138,165,171,179,186,189],"Brouwer's":[29],"fixed":[30],"point":[31],"theorem,":[32],"contraction":[34],"mapping":[35],"principle":[36],"theory":[39],"of":[40,58,66,86,123,174,188],"differential":[42],"equations,":[43],"some":[44],"sufficient":[45],"conditions":[46],"established":[48],"to":[49,131,147],"ensure":[50],"existence,":[52],"exact":[53],"existence":[54,83],"local":[56],"stability":[57,85],"multiple":[59],"equilibrium":[60],"points":[61],"(EPs)":[62],"sense":[65],"Filippov,":[67],"which":[69],"positively":[71],"invariant":[72],"sets":[73],"also":[75,177],"estimated.":[76],"In":[77],"particular,":[78],"analysis":[80],"concerning":[81],"EPs":[87,124,127],"is":[88,145,192],"quite":[89],"different":[90],"from":[91,129],"those":[92],"literature":[95],"because":[96],"considered":[98],"system":[99,139,180],"involves":[100],"both":[101],"derivative":[103],"switching.":[106],"It":[107],"should":[108],"be":[109],"pointed":[110],"out":[111],"that,":[112],"compared":[113],"results":[116,191],"literature,":[119],"total":[121],"number":[122],"stable":[126],"increases":[128],",":[133],"respectively,":[134],"where":[135],"being":[137],"dimension.":[140],"Besides,":[141],"a":[142,158],"new":[143],"method":[144],"designed":[146],"realize":[148],"grayscale":[152],"color":[154],"images":[155],"by":[156,194],"introducing":[157],"deviation":[159],"vector,":[160],"which,":[161],"comparison":[163],"existing":[166],"works,":[167],"not":[168],"only":[169],"improves":[170],"utilization":[172],"efficiency":[173],"EPs,":[175],"but":[176],"reduces":[178],"dimension":[181],"computational":[183],"burden.":[184],"Finally,":[185],"effectiveness":[187],"theoretical":[190],"illustrated":[193],"four":[195],"numerical":[196],"simulations.":[197]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":21},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}