Complete Cluster Predictability of the Cucker–Smale Flocking Model on the Real Line

Title
Complete Cluster Predictability of the Cucker–Smale Flocking Model on the Real Line
Author
박진영
Keywords
SELF-DRIVEN PARTICLES; ASYMPTOTIC FLOCKING; DYNAMICS; EMERGENCE; LIMIT; BEHAVIOR
Issue Date
2019-01
Publisher
SPRINGER
Citation
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, v. 231, NO. 1, Page. 319-365
Abstract
We present the complete predictability of clustering for the Cucker–Smale (C–S) model on the line. Emergence of multi-cluster flocking is often observed in numerical simulations for the C–S model with short-range interactions. However, the explicit computation of the number of emergent multi-clusters a priori is a challenging problem for the Cucker–Smale flocking model. In this paper, we present an explicit criterion and algorithm to calculate the number of clusters and their bulk velocities in terms of initial configuration, coupling strength and communication weight function in a one-dimensional setting. We present a finite increasing sequence of coupling strengths in which the number of asymptotic clusters has a jump. We also provide several numerical examples and compare them with analytical results.
URI
https://link.springer.com/article/10.1007%2Fs00205-018-1281-xhttp://repository.hanyang.ac.kr/handle/20.500.11754/107311
ISSN
0003-9527; 1432-0673
DOI
10.1007/s00205-018-1281-x
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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