{"id":"https://openalex.org/W7224895191","doi":"https://doi.org/10.3390/fractalfract10110763","title":"Finite-Time Synchronization of Discontinuous Fractional-Order Multi-Layer Coupled Neural Networks via Aperiodic Intermittent Control","display_name":"Finite-Time Synchronization of Discontinuous Fractional-Order Multi-Layer Coupled Neural Networks via Aperiodic Intermittent Control","publication_year":2026,"publication_date":"2026-10-30","ids":{"openalex":"https://openalex.org/W7224895191","doi":"https://doi.org/10.3390/fractalfract10110763"},"language":"en","primary_location":{"id":"doi:10.3390/fractalfract10110763","doi":"https://doi.org/10.3390/fractalfract10110763","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract10110763","pdf_url":null,"source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractal and Fractional","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/fractalfract10110763","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074262611","display_name":"Bibo Zheng","orcid":"https://orcid.org/0009-0002-7130-3909","observed_orcids":["https://orcid.org/0009-0002-7130-3909"]},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bibo Zheng","raw_affiliation_strings":["School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5160177957","display_name":"Yunqiu Xu","orcid":"https://orcid.org/0009-0004-7365-5005","observed_orcids":["https://orcid.org/0009-0004-7365-5005"]},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunqiu Xu","raw_affiliation_strings":["School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China"],"raw_orcid":"https://orcid.org/0009-0004-7365-5005","affiliations":[{"raw_affiliation_string":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5139260601","display_name":"Wei Dai","orcid":"https://orcid.org/0000-0003-3057-7225","observed_orcids":["https://orcid.org/0000-0003-3057-7225","https://orcid.org/0009-0002-4827-3924"]},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wei Dai","raw_affiliation_strings":["School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China","institution_ids":["https://openalex.org/I25757504"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5139260601"],"corresponding_institution_ids":["https://openalex.org/I25757504"],"apc_list":{"value":2700,"currency":"CHF","value_usd":3258},"apc_paid":{"value":2700,"currency":"CHF","value_usd":3258},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.86947008,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"11","first_page":"763","last_page":"763"},"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/T10244","display_name":"Chaos control and synchronization","score":0.0,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/finite-time-synchronization","display_name":"finite-time synchronization","score":1.0},{"id":"https://openalex.org/keywords/fractional-order-neural-networks","display_name":"fractional-order neural networks","score":0.9210000038146973},{"id":"https://openalex.org/keywords/aperiodic-intermittent-control","display_name":"aperiodic intermittent control","score":0.906000018119812},{"id":"https://openalex.org/keywords/discontinuous-activation-functions","display_name":"discontinuous activation functions","score":0.9369999766349792},{"id":"https://openalex.org/keywords/settling-time-estimation","display_name":"settling time estimation","score":0.9200000166893005},{"id":"https://openalex.org/keywords/non-smooth-dynamics","display_name":"non-smooth dynamics","score":0.7229999899864197}],"concepts":[{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.9031000137329102},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.7628999948501587},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.755299985408783},{"id":"https://openalex.org/C2778179450","wikidata":"https://www.wikidata.org/wiki/Q17146472","display_name":"Intermittent control","level":2,"score":0.6078000068664551},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.5784000158309937},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5741999745368958},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5504999756813049},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.49540001153945923},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4657999873161316},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41449999809265137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41040000319480896},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.40059998631477356},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.3847000002861023},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.30550000071525574},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.304500013589859},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.28790000081062317},{"id":"https://openalex.org/C2984730371","wikidata":"https://www.wikidata.org/wiki/Q6501221","display_name":"Feedback controller","level":3,"score":0.2766999900341034},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C14781684","wikidata":"https://www.wikidata.org/wiki/Q3983320","display_name":"Settling time","level":3,"score":0.25679999589920044}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/fractalfract10110763","doi":"https://doi.org/10.3390/fractalfract10110763","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract10110763","pdf_url":null,"source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractal and Fractional","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/fractalfract10110763","doi":"https://doi.org/10.3390/fractalfract10110763","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract10110763","pdf_url":null,"source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractal and Fractional","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2938767275","https://openalex.org/W4319866182","https://openalex.org/W7163635908","https://openalex.org/W4408665704","https://openalex.org/W2994715859","https://openalex.org/W2470397023","https://openalex.org/W4415259448","https://openalex.org/W2615137854","https://openalex.org/W2621255396","https://openalex.org/W2901483232"],"abstract_inverted_index":{"This":[0,112],"paper":[1],"is":[2,25,67,93,166],"mainly":[3],"concentrated":[4],"on":[5,142],"finite-time":[6],"synchronization":[7,52],"(FTS)":[8],"for":[9,120,124,153],"discontinuous":[10,22,158],"fractional-order":[11,90],"multi-layer":[12],"coupled":[13],"neural":[14,38,80],"networks":[15],"(FMCNNs)":[16],"under":[17,109],"aperiodic":[18,60,110],"intermittent":[19,61],"control.":[20],"The":[21],"activation":[23],"function":[24,102],"introduced":[26],"to":[27,95,168],"capture":[28],"abrupt":[29],"transitions":[30],"and":[31,51,106,126,146],"switching":[32],"phenomena":[33],"widely":[34],"observed":[35],"in":[36],"practical":[37],"dynamics.":[39],"However,":[40],"such":[41],"nonsmooth":[42,79],"behaviors":[43],"significantly":[44],"increase":[45],"the":[46,70,97,100,104,128,133,136,140,143,155,161,170,173],"complexity":[47],"of":[48,78,99,157,172],"controller":[49,62],"design":[50],"analysis.":[53],"To":[54],"cope":[55],"with":[56,63,132],"these":[57],"problems,":[58],"an":[59],"a":[64,88,116,148,163],"simple":[65],"structure":[66],"developed":[68],"within":[69],"Filippov":[71],"differential":[72,91],"inclusion":[73],"framework,":[74],"ensuring":[75],"effective":[76],"handling":[77],"dynamics":[81],"while":[82],"reducing":[83],"control":[84,105],"cost.":[85],"More":[86],"importantly,":[87],"piecewise":[89],"inequality":[92,113],"established":[94],"characterize":[96],"evolution":[98],"Lyapunov":[101],"over":[103],"rest":[107],"intervals":[108],"switching.":[111],"serves":[114],"as":[115],"fundamental":[117],"analytical":[118,151],"tool":[119,152],"deriving":[121],"sufficient":[122],"conditions":[123],"FTS":[125,156],"estimating":[127],"settling":[129],"time.":[130],"Compared":[131],"existing":[134],"results,":[135],"proposed":[137,174],"framework":[138],"relaxes":[139],"restrictions":[141],"power":[144],"exponent":[145],"provides":[147],"more":[149],"general":[150],"investigating":[154],"FMLCNNs.":[159],"In":[160],"end,":[162],"simulation":[164],"example":[165],"provided":[167],"show":[169],"validity":[171],"method.":[175]},"counts_by_year":[],"updated_date":"2026-11-01T11:40:01.658920","created_date":"2026-10-31T00:00:00"}