Effect Of Time Delay On Flocking Dynamics - Bae, Hyeong Ohk; Cho, Seung Yeon; Yoo, Jane; Yun, Seok Bae (Networks and Heterogeneous Media, 2022)
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 configu- ration for a two-agent case, in which collective behaviors are accelerated by changes in the delay parameter. Numerical illustrations and financial simula- tions are carried out to verify the validity of the model.
Keywords: 'current; Collective dynamics; Condition; Effect of time; Process information; Return volatilities; Stock returns; Time delayed; Time-delays; Two-agent case