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.
Xiang Li, Yicheng Liu, and Jun Wu
National University of Defense Technology, National University of Defense Technology, Changsha University of Science Technology
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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