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Delayed Cucker-Smale model with and without noise revisited. (arXiv:1810.01084v1 [math.CA])
来源于:arXiv
Delay in information processing has been incorporated in many models that
describe emergence in biological systems. In particular, different versions of
the Cucker-Smale model have been considered with processing delay in previous
works. In this paper, we study the delayed Cucker-Smale-type system proposed by
Erban, Haskovec and Sun \cite{ErHaSu}, in which all terms in the communication
weight and the velocity coupling have a positive constant delay $\tau>0$. %We
give an affirmative answer to an open question We show that flocking occurs for
the communication weight originally proposed by Cucker and Smale,
$\psi(r)=(1+r^{2})^{-\beta}$, $r \geq 0$, if $0<\beta <\frac{1}{2}$ and the
delay $\tau$ is sufficiently small. In addition, we prove that the delayed
system with multiplicative white noises exhibits flocking behavior if the
intensity of the noise is sufficiently small. Both results rely on stability
estimates for the Cucker-Smale delayed flow. 查看全文>>