{"id":"https://openalex.org/W4306728956","doi":"https://doi.org/10.1109/tnnls.2022.3210551","title":"Almost Sure Stability of Complex-Valued Complex Networks: A Noise-Based Delayed Coupling Under Random Denial-of-Service Attacks","display_name":"Almost Sure Stability of Complex-Valued Complex Networks: A Noise-Based Delayed Coupling Under Random Denial-of-Service Attacks","publication_year":2022,"publication_date":"2022-11-03","ids":{"openalex":"https://openalex.org/W4306728956","doi":"https://doi.org/10.1109/tnnls.2022.3210551","pmid":"https://pubmed.ncbi.nlm.nih.gov/36251901"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2022.3210551","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2022.3210551","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/A5100444231","display_name":"Sen Li","orcid":"https://orcid.org/0000-0001-7747-4253"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sen Li","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, Shandong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, Shandong, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114246480","display_name":"Xueqing Gao","orcid":"https://orcid.org/0009-0008-3610-6217"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xueqing Gao","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, Shandong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, Shandong, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101413899","display_name":"Xiaohua Ding","orcid":null},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaohua Ding","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, Shandong, China"],"raw_orcid":"https://orcid.org/0000-0001-6172-1539","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, Shandong, China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I204983213"],"apc_list":null,"apc_paid":null,"fwci":1.336,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.81438292,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"35","issue":"5","first_page":"6520","last_page":"6530"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9957000017166138,"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":0.9957000017166138,"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":0.9840999841690063,"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/T10241","display_name":"Functional Brain Connectivity Studies","score":0.941100001335144,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5930160284042358},{"id":"https://openalex.org/keywords/denial-of-service-attack","display_name":"Denial-of-service attack","score":0.5186623334884644},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5099750757217407},{"id":"https://openalex.org/keywords/lyapunov-stability","display_name":"Lyapunov stability","score":0.4740169644355774},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4713893532752991},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4650719165802002},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45792680978775024},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.45770761370658875},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.45035016536712646},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.42482998967170715},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40509361028671265},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.34001249074935913},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.18022724986076355},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14477673172950745},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.12940090894699097},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11414709687232971},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09290757775306702}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5930160284042358},{"id":"https://openalex.org/C38822068","wikidata":"https://www.wikidata.org/wiki/Q131406","display_name":"Denial-of-service attack","level":3,"score":0.5186623334884644},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5099750757217407},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.4740169644355774},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4713893532752991},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4650719165802002},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45792680978775024},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.45770761370658875},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.45035016536712646},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.42482998967170715},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40509361028671265},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.34001249074935913},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.18022724986076355},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14477673172950745},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.12940090894699097},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11414709687232971},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09290757775306702},{"id":"https://openalex.org/C110875604","wikidata":"https://www.wikidata.org/wiki/Q75","display_name":"The Internet","level":2,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2022.3210551","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2022.3210551","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:36251901","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36251901","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1494628843","https://openalex.org/W1972523481","https://openalex.org/W2003530067","https://openalex.org/W2016812413","https://openalex.org/W2028027246","https://openalex.org/W2068740779","https://openalex.org/W2070722739","https://openalex.org/W2107396783","https://openalex.org/W2134799554","https://openalex.org/W2337446187","https://openalex.org/W2474875956","https://openalex.org/W2592852902","https://openalex.org/W2611391190","https://openalex.org/W2743408846","https://openalex.org/W2798142547","https://openalex.org/W2799494644","https://openalex.org/W2801010298","https://openalex.org/W2807820314","https://openalex.org/W2883863415","https://openalex.org/W2900301110","https://openalex.org/W2900729111","https://openalex.org/W2911308244","https://openalex.org/W2916555858","https://openalex.org/W2955151645","https://openalex.org/W2981984657","https://openalex.org/W2982097845","https://openalex.org/W2988685755","https://openalex.org/W3012422265","https://openalex.org/W3018652411","https://openalex.org/W3027099475","https://openalex.org/W3037295153","https://openalex.org/W3039187353","https://openalex.org/W3045234274","https://openalex.org/W3045256736","https://openalex.org/W3082335512","https://openalex.org/W3084004264","https://openalex.org/W3085896112","https://openalex.org/W3096856936","https://openalex.org/W3110577543","https://openalex.org/W3171702065","https://openalex.org/W3175848738","https://openalex.org/W3194099120","https://openalex.org/W3198765278","https://openalex.org/W3199416654","https://openalex.org/W4220875728","https://openalex.org/W4229706427","https://openalex.org/W4235816940"],"related_works":["https://openalex.org/W4386482731","https://openalex.org/W2765763546","https://openalex.org/W4385302085","https://openalex.org/W2360429410","https://openalex.org/W4256682929","https://openalex.org/W335511927","https://openalex.org/W2471811227","https://openalex.org/W2217591390","https://openalex.org/W4390188535","https://openalex.org/W2157496457"],"abstract_inverted_index":{"This":[0],"article":[1],"is":[2,47,83,122,147,190,251],"concerned":[3],"with":[4,104,167],"stability":[5,24,38,89,139,193,231],"for":[6,191],"stochastic":[7,26,132],"complex-valued":[8,27,91,243],"delayed":[9,74],"complex":[10],"networks":[11,245],"under":[12,225],"random":[13],"denial-of-service":[14],"(RDoS)":[15],"attacks.":[16],"Different":[17],"from":[18],"the":[19,23,51,57,64,78,88,94,128,143,157,180,182,185,187,192,195,200,213,218,222,226,230,233,236,255,258],"existing":[20],"literature":[21],"on":[22,31],"of":[25,66,80,90,101,109,127,142,160,194,199,221,228,232,257],"systems":[28,53],"that":[29,179,207],"concentrate":[30],"moment":[32,161],"stability,":[33],"we":[34,203],"investigate":[35],"almost":[36,136],"sure":[37,137],"(ASS),":[39],"where":[40,93],"noise":[41,176,183],"plays":[42],"a":[43,69,98,151],"stabilizing":[44],"role.":[45],"It":[46],"noted":[48],"that,":[49],"besides":[50],"vertex":[52],"influenced":[54],"by":[55,149],"noise,":[56],"interactions":[58],"among":[59],"vertices":[60],"are":[61,115,239],"also":[62],"at":[63,106,118],"mercy":[65],"noise.":[67],"As":[68],"consequence,":[70],"an":[71,135,205,248],"innovative":[72],"noise-based":[73],"coupling":[75,223],"(NDC)":[76],"in":[77],"presence":[79],"RDoS":[81,95,112,170],"attacks":[82,96,113],"proposed":[84],"first":[85],"to":[86,211,241,253],"accomplish":[87],"networks,":[92],"have":[97],"certain":[99],"probability":[100],"triumphantly":[102],"interfering":[103],"communications":[105],"active":[107,119],"intervals":[108],"attackers.":[110],"Namely,":[111],"considered":[114],"randomly":[116],"launched":[117],"periods,":[120],"which":[121],"more":[123],"realistic.":[124],"In":[125,197],"terms":[126],"Lyapunov":[129],"method":[130],"and":[131,175,217,247],"analysis":[133],"theory,":[134],"exponential":[138],"(ASES)":[140],"criterion":[141,164,201],"system":[144],"discussed":[145],"straightforwardly":[146],"developed":[148],"constructing":[150],"delay-free":[152],"auxiliary":[153],"system,":[154],"while":[155],"removing":[156],"traditional":[158],"assumption":[159],"stability.":[162],"The":[163],"strongly":[165],"linked":[166],"topological":[168],"structure,":[169],"frequency,":[171],"attack":[172,215],"successful":[173],"probability,":[174],"intensity":[177],"reveals":[178],"higher":[181],"intensity,":[184],"faster":[186],"convergence":[188],"rate":[189],"network.":[196,234],"light":[198],"established,":[202],"present":[204],"algorithm":[206],"can":[208],"be":[209],"employed":[210],"analyze":[212],"tolerable":[214],"parameters":[216],"upper":[219],"bound":[220],"delays,":[224],"prerequisite":[227],"guaranteeing":[229],"Eventually,":[235],"theoretical":[237,259],"results":[238],"applied":[240],"inertial":[242],"neural":[244],"(ICNNs)":[246],"illustrative":[249],"example":[250],"presented":[252],"substantiate":[254],"efficiency":[256],"works.":[260]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}