@article{Bae2022, 
author = {Hyeong-Ohk Bae and Seung Yeon Cho and Jane Yoo and Seok-Bae Yun},
title = {Effect of time delay on flocking dynamics},
year = {2022},
journal = {Networks and Heterogeneous Media},
volume = {17},
number = {5},
pages = {803-825},
keywords = {Cucker–Smale model, flocking, volatility, time delay},
url = {https://www.sciopen.com/article/10.3934/nhm.2022027},
doi = {10.3934/nhm.2022027},
abstract = {We propose a time-delayed Cucker-Smale type model(CS model), which can be applied to modeling (1) collective dynamics of self-propelling agents and (2) the dynamical system of stock return volatility in a financial market. For both models, we assume that it takes a certain amount of time to collect/process information about the current position/return configuration until velocity/volatility adjustment is made. We provide a sufficient condition under which flocking phenomena occur. We also identify the initial configuration for a two-agent case, in which collective behaviors are accelerated by changes in the delay parameter. Numerical illustrations and financial simulations are carried out to verify the validity of the model.}
}