Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(5): 1327-1339

Online first article September 22, 2016      Printed September 30, 2016

https://doi.org/10.4134/BKMS.b150629

Copyright © The Korean Mathematical Society.

Flocking and pattern motion in a modified Cucker-Smale model

Xiang Li, Yicheng Liu, and Jun Wu

National University of Defense Technology, National University of Defense Technology, Changsha University of Science Technology

Abstract

Self-organizing systems arise very naturally in artificial intelligence, and in physical, biological and social sciences. In this paper, we modify the classic Cucker-Smale model at both microscopic and macroscopic levels by taking the target motion pattern driving forces into consideration. Such target motion pattern driving force functions are properly defined for the line-shaped motion pattern and the ball-shaped motion pattern. For the modified Cucker-Smale model with the prescribed line-shaped motion pattern, we have analytically shown that there is a flocking pattern with an asymptotic flocking velocity. This is illustrated by numerical simulations using both symmetric and non-symmetric pairwise influence functions. For the modified Cucker-Smale model with the prescribed ball-shaped motion pattern, our simulations suggest that the solution also converges to the prescribed motion pattern.

Keywords: flocking pattern, self-organizing system, motion pattern, influence function, asymptotic flocking velocity

MSC numbers: 34A34, 34D05

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