Cucker-Smale model with normalized communication weights and time delay

Handle URI:
http://hdl.handle.net/10754/623816
Title:
Cucker-Smale model with normalized communication weights and time delay
Authors:
Choi, Young-Pil; Haskovec, Jan
Abstract:
We study a Cucker-Smale-type system with time delay in which agents interact with each other through normalized communication weights. We construct a Lyapunov functional for the system and provide sufficient conditions for asymptotic flocking, i.e., convergence to a common velocity vector. We also carry out a rigorous limit passage to the mean-field limit of the particle system as the number of particles tends to infinity. For the resulting Vlasov-type equation we prove the existence, stability and large-time behavior of measure-valued solutions. This is, to our best knowledge, the first such result for a Vlasov-type equation with time delay. We also present numerical simulations of the discrete system with few particles that provide further insights into the flocking and oscillatory behaviors of the particle velocities depending on the size of the time delay.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Haskovec J, Choi Y-P (2017) Cucker-Smale model with normalized communication weights and time delay. Kinetic and Related Models 10: 1011–1033. Available: http://dx.doi.org/10.3934/krm.2017040.
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Kinetic and Related Models
KAUST Grant Number:
1000000193
Issue Date:
6-Mar-2017
DOI:
10.3934/krm.2017040
Type:
Article
ISSN:
1937-5093
Sponsors:
YPC was supported by Engineering and Physical Sciences Research Council (EP/K00804/1) and ERC-Starting grant HDSPCONTR
Additional Links:
http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=13816
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorChoi, Young-Pilen
dc.contributor.authorHaskovec, Janen
dc.date.accessioned2017-05-31T11:23:07Z-
dc.date.available2017-05-31T11:23:07Z-
dc.date.issued2017-03-06en
dc.identifier.citationHaskovec J, Choi Y-P (2017) Cucker-Smale model with normalized communication weights and time delay. Kinetic and Related Models 10: 1011–1033. Available: http://dx.doi.org/10.3934/krm.2017040.en
dc.identifier.issn1937-5093en
dc.identifier.doi10.3934/krm.2017040en
dc.identifier.urihttp://hdl.handle.net/10754/623816-
dc.description.abstractWe study a Cucker-Smale-type system with time delay in which agents interact with each other through normalized communication weights. We construct a Lyapunov functional for the system and provide sufficient conditions for asymptotic flocking, i.e., convergence to a common velocity vector. We also carry out a rigorous limit passage to the mean-field limit of the particle system as the number of particles tends to infinity. For the resulting Vlasov-type equation we prove the existence, stability and large-time behavior of measure-valued solutions. This is, to our best knowledge, the first such result for a Vlasov-type equation with time delay. We also present numerical simulations of the discrete system with few particles that provide further insights into the flocking and oscillatory behaviors of the particle velocities depending on the size of the time delay.en
dc.description.sponsorshipYPC was supported by Engineering and Physical Sciences Research Council (EP/K00804/1) and ERC-Starting grant HDSPCONTRen
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.relation.urlhttp://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=13816en
dc.subjectCucker-Smale modelen
dc.subjectVlasov equarionen
dc.subjectnormalized communication weightsen
dc.subjecttime delayen
dc.subjectasymptotic behavioren
dc.subjectflockingen
dc.titleCucker-Smale model with normalized communication weights and time delayen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalKinetic and Related Modelsen
dc.contributor.institutionDepartment of Mathematics, Inha University, Incheon, 402-751, South Koreaen
kaust.authorHaskovec, Janen
kaust.grant.number1000000193en
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