A Cucker--Smale Model with Noise and Delay

Handle URI:
http://hdl.handle.net/10754/622022
Title:
A Cucker--Smale Model with Noise and Delay
Authors:
Erban, Radek; Haskovec, Jan; Sun, Yongzheng
Abstract:
A 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
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Erban 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.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Applied Mathematics
Issue Date:
9-Aug-2016
DOI:
10.1137/15M1030467
Type:
Article
ISSN:
0036-1399; 1095-712X
Sponsors:
The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme
Additional Links:
http://epubs.siam.org/doi/10.1137/15M1030467
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorErban, Radeken
dc.contributor.authorHaskovec, Janen
dc.contributor.authorSun, Yongzhengen
dc.date.accessioned2016-12-15T08:40:33Z-
dc.date.available2016-12-15T08:40:33Z-
dc.date.issued2016-08-09en
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.en
dc.identifier.issn0036-1399en
dc.identifier.issn1095-712Xen
dc.identifier.doi10.1137/15M1030467en
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 behavioren
dc.description.sponsorshipThe authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programmeen
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/15M1030467en
dc.rightsArchived with thanks to SIAM Journal on Applied Mathematicsen
dc.subjectCucker-Smale systemen
dc.subjectflockingen
dc.subjectasymptotic behavioren
dc.subjectnoiseen
dc.subjectdelayen
dc.subjectgeometric Brownian motionen
dc.titleA Cucker--Smale Model with Noise and Delayen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalSIAM Journal on Applied Mathematicsen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionMathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, United Kingdomen
dc.contributor.institutionSchool of Sciences, China University of Mining and Technology, Xuzhou, Chinaen
kaust.authorHaskovec, Janen
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