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dc.contributor.authorHaskovec, Jan
dc.date.accessioned2021-02-15T08:48:15Z
dc.date.available2020-06-17T10:46:09Z
dc.date.available2021-02-15T08:48:15Z
dc.date.issued2021-01-21
dc.date.submitted2020-05-28
dc.identifier.citationHaskovec, J. (2021). A Simple Proof of Asymptotic Consensus in the Hegselmann--Krause and Cucker--Smale Models with Normalization and Delay. SIAM Journal on Applied Dynamical Systems, 20(1), 130–148. doi:10.1137/20m1341350
dc.identifier.issn1536-0040
dc.identifier.doi10.1137/20m1341350
dc.identifier.urihttp://hdl.handle.net/10754/663638
dc.description.abstractWe present a simple proof of asymptotic consensus in the discrete Hegselmann--Krause model and flocking in the discrete Cucker--Smale model with normalization and variable delay. This proof utilizes the convexity of the normalized communication weights and a Gronwall--Halanay-type inequality. The main advantage of our method, compared to previous approaches to the delay Hegselmann--Krause model, is that it does not require any restriction on the maximal time delay, or the initial data, or decay rate of the influence function. From this point of view the result is optimal. For the Cucker--Smale model it provides an analogous result in the regime of unconditonal flocking with sufficiently slowly decaying communication rate, but still without any restriction on the length of the maximal time delay. Moreover, we demonstrate that the method can be easily extended to the mean-field limits of both the Hegselmann--Krause and Cucker--Smale systems, using appropriate stability results on the measure-valued solutions.
dc.description.sponsorshipThis work was supported by KAUST.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttps://epubs.siam.org/doi/10.1137/20M1341350
dc.rightsArchived with thanks to SIAM Journal on Applied Dynamical Systems
dc.titleA Simple Proof of Asymptotic Consensus in the Hegselmann--Krause and Cucker--Smale Models with Normalization and Delay
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalSIAM Journal on Applied Dynamical Systems
dc.eprint.versionPost-print
dc.identifier.volume20
dc.identifier.issue1
dc.identifier.pages130-148
dc.identifier.arxivid2005.13589
kaust.personHaskovec, Jan
dc.date.accepted2020-12-07
refterms.dateFOA2020-06-17T10:46:35Z
kaust.acknowledged.supportUnitKAUST baseline fund
dc.date.published-online2021-01-21
dc.date.published-print2021-01
dc.date.posted2020-05-27


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