Show simple item record

dc.contributor.authorErban, Radek
dc.contributor.authorHaskovec, Jan
dc.contributor.authorSun, Yongzheng
dc.date.accessioned2016-12-15T08:40:33Z
dc.date.available2016-12-15T08:40:33Z
dc.date.issued2016-08-09
dc.identifier.citationErban R, Haškovec J, Sun Y (2016) A Cucker--Smale Model with Noise and Delay. SIAM Journal on Applied Mathematics 76: 1535–1557. Available: http://dx.doi.org/10.1137/15M1030467.
dc.identifier.issn0036-1399
dc.identifier.issn1095-712X
dc.identifier.doi10.1137/15M1030467
dc.identifier.urihttp://hdl.handle.net/10754/622022
dc.description.abstractA generalization of the Cucker-Smale model for collective animal behavior is investigated. The model is formulated as a system of delayed stochastic differential equations. It incorporates two additional processes which are present in animal decision making, but are often neglected in modeling: (i) stochasticity (imperfections) of individual behavior and (ii) delayed responses of individuals to signals in their environment. Sufficient conditions for flocking for the generalized Cucker-Smale model are derived by using a suitable Lyapunov functional. As a by-product, a new result regarding the asymptotic behavior of delayed geometric Brownian motion is obtained. In the second part of the paper, results of systematic numerical simulations are presented. They not only illustrate the analytical results, but hint at a somehow surprising behavior
dc.description.sponsorshipThe authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/15M1030467
dc.rightsArchived with thanks to SIAM Journal on Applied Mathematics
dc.subjectCucker-Smale system
dc.subjectflocking
dc.subjectasymptotic behavior
dc.subjectnoise
dc.subjectdelay
dc.subjectgeometric Brownian motion
dc.titleA Cucker--Smale Model with Noise and Delay
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalSIAM Journal on Applied Mathematics
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionMathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, United Kingdom
dc.contributor.institutionSchool of Sciences, China University of Mining and Technology, Xuzhou, China
kaust.personHaskovec, Jan
refterms.dateFOA2018-06-13T13:59:11Z


Files in this item

Thumbnail
Name:
15m1030467.pdf
Size:
1.026Mb
Format:
PDF
Description:
Main article

This item appears in the following Collection(s)

Show simple item record