Author
Erban, R
Haskovec, J
Sun, Y
Journal title
SIAM Journal on Applied Mathematics
Last updated
2024-03-27T14:14:36.347+00:00
Abstract
A generalization of the Cucker-Smale model for collective animal behaviour 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 modelling: (i)
stochasticity (imperfections) of individual behaviour; 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 byproduct, a new result regarding the
asymptotic behaviour 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 behaviour of the system - namely, that an introduction of
intermediate time delay may facilitate flocking.
Symplectic ID
532061
Download URL
http://arxiv.org/abs/1507.04432v1
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Publication type
Journal Article
Publication date
09 Aug 2016
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