Flocking and asymptotic velocity of the Cucker-Smale model with processing delay

摘要

The processing delay is incorporated into the influence function of the well-known Cucker-Smale model for self-organized systems with multiple agents. Both symmetric and non-symmetric pairwise influence functions are considered, and a Lyapunov functional approach is developed to establish the existence of flocking solutions for the proposed delayed Cucker-Smale model. An analytic formula is given to calculate the asymptotic flocking velocity in terms of model parameters and the variation of the position during the initial time interval.