{"id":"https://openalex.org/W3117067538","doi":"https://doi.org/10.3934/nhm.2021002","title":"Periodic consensus in network systems with general distributed processing delays","display_name":"Periodic consensus in network systems with general distributed processing delays","publication_year":2020,"publication_date":"2020-12-31","ids":{"openalex":"https://openalex.org/W3117067538","doi":"https://doi.org/10.3934/nhm.2021002","mag":"3117067538"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2021002","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2021002","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/nhm.2021002","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101706512","display_name":"Yicheng Liu","orcid":"https://orcid.org/0000-0003-0318-7870"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yicheng Liu","raw_affiliation_strings":["College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, 410073, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, 410073, P. R. China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101431251","display_name":"Yipeng Chen","orcid":"https://orcid.org/0000-0001-5838-9387"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yipeng Chen","raw_affiliation_strings":["College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, 410073, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, 410073, P. R. China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060932290","display_name":"Jun Wu","orcid":"https://orcid.org/0000-0003-3493-3522"},"institutions":[{"id":"https://openalex.org/I56934997","display_name":"Changsha University of Science and Technology","ror":"https://ror.org/03yph8055","country_code":"CN","type":"education","lineage":["https://openalex.org/I56934997"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Wu","raw_affiliation_strings":["College of Mathematics and Statistics, Changsha University of Science Technology, Changsha, 410076, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Changsha University of Science Technology, Changsha, 410076, P. R. China","institution_ids":["https://openalex.org/I56934997"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100411459","display_name":"Xiao Wang","orcid":"https://orcid.org/0000-0002-2672-5443"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao Wang","raw_affiliation_strings":["College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, 410073, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, 410073, P. R. China","institution_ids":["https://openalex.org/I170215575"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101706512"],"corresponding_institution_ids":["https://openalex.org/I170215575"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21223688,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"1","first_page":"139","last_page":"153"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998999834060669,"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":0.9998999834060669,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9986000061035156,"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/social-connectedness","display_name":"Social connectedness","score":0.8425852060317993},{"id":"https://openalex.org/keywords/consensus","display_name":"Consensus","score":0.5940433144569397},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5410626530647278},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5165568590164185},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.4658758342266083},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45912042260169983},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45690667629241943},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.4529187083244324},{"id":"https://openalex.org/keywords/uniform-consensus","display_name":"Uniform consensus","score":0.419162392616272},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3745826780796051},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2505238652229309},{"id":"https://openalex.org/keywords/multi-agent-system","display_name":"Multi-agent system","score":0.21770992875099182},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10095825791358948},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09529179334640503}],"concepts":[{"id":"https://openalex.org/C201943243","wikidata":"https://www.wikidata.org/wiki/Q7551008","display_name":"Social connectedness","level":2,"score":0.8425852060317993},{"id":"https://openalex.org/C107107730","wikidata":"https://www.wikidata.org/wiki/Q2994424","display_name":"Consensus","level":3,"score":0.5940433144569397},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5410626530647278},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5165568590164185},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.4658758342266083},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45912042260169983},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45690667629241943},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.4529187083244324},{"id":"https://openalex.org/C80966040","wikidata":"https://www.wikidata.org/wiki/Q7885028","display_name":"Uniform consensus","level":4,"score":0.419162392616272},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3745826780796051},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2505238652229309},{"id":"https://openalex.org/C41550386","wikidata":"https://www.wikidata.org/wiki/Q529909","display_name":"Multi-agent system","level":2,"score":0.21770992875099182},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10095825791358948},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09529179334640503},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/nhm.2021002","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2021002","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:741eea0aa6c74dcaad6891372fa0efed","is_oa":false,"landing_page_url":"https://doaj.org/article/741eea0aa6c74dcaad6891372fa0efed","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 16, Iss 1, Pp 139-153 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2021002","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2021002","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1998692453","https://openalex.org/W2146890818","https://openalex.org/W3100384848"],"related_works":["https://openalex.org/W1788591815","https://openalex.org/W4229449431","https://openalex.org/W2112337480","https://openalex.org/W2166189192","https://openalex.org/W2766105656","https://openalex.org/W2106670435","https://openalex.org/W2017057923","https://openalex.org/W2148488729","https://openalex.org/W2783501646","https://openalex.org/W1537624148"],"abstract_inverted_index":{"How":[0],"to":[1,104],"understand":[2],"the":[3,27,34,47,60,67,70,93,106,116,123,139,144,150],"dynamical":[4],"consensus":[5,35,54,57,82,85,109],"patterns":[6,36],"in":[7,14,25,37,110],"network":[8,39,49,71],"systems":[9],"is":[10,102],"of":[11,29,69,80,112,146],"particular":[12],"significance":[13],"both":[15,52],"theories":[16],"and":[17,55,66,83,115,133,142],"applications.":[18],"In":[19,76],"this":[20],"paper,":[21],"we":[22,44,121,137],"are":[23,90],"interested":[24],"investigating":[26],"influences":[28,145],"distributed":[30],"processing":[31],"delay":[32],"on":[33,149],"a":[38,63],"model.":[40],"As":[41],"new":[42],"observations,":[43],"show":[45],"that":[46],"desired":[48],"model":[50,113],"undergoes":[51],"weak":[53,81],"periodic":[56,84,108],"behaviors":[58],"when":[59],"parameters":[61,114],"reach":[62],"threshold":[64,124],"value":[65],"connectedness":[68],"system":[72],"may":[73],"be":[74],"absent.":[75],"results,":[77],"some":[78,127],"criterions":[79],"with":[86],"exponential":[87],"convergent":[88],"rate":[89],"established":[91],"by":[92],"standard":[94],"functional":[95],"differential":[96],"equations":[97],"analysis.":[98],"An":[99],"analytic":[100],"formula":[101],"given":[103],"calculate":[105],"asymptotic":[107],"terms":[111],"initial":[117],"time":[118],"interval.":[119],"Also,":[120],"post":[122],"values":[125],"for":[126],"typical":[128],"distributions":[129],"included":[130],"uniform":[131],"distribution":[132],"Gamma":[134],"distribution.":[135],"Finally,":[136],"give":[138],"numerical":[140],"simulation":[141],"analyse":[143],"different":[147],"delays":[148],"consensus.":[151]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}