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ArticleDate
2016-08-09Online Publication Date
2016-08-09Print Publication Date
2016-01Permanent link to this record
http://hdl.handle.net/10754/622022
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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 behaviorCitation
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.Sponsors
The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programmearXiv
1507.04432Additional Links
http://epubs.siam.org/doi/10.1137/15M1030467ae974a485f413a2113503eed53cd6c53
10.1137/15M1030467