主从Cucker-Smale模型的有限时间群体运动行为

Finite-time flocking behavior of leader-following Cucker-Smale model

研究主从Cucker-Smale模型在有限时间内发生群体运动行为。通过构造具体的Lyapunov泛函,得到当0≤β≤1/2时,无条件群体运动行为在有限时间内发生;当β>1/2时,条件群体运动行为在有限时间内发生,其中发生条件仅依赖于初始值。最后,通过几个数值仿真来说明理论结果的有效性。

This paper proves that the flocking of leader-follower Cucker-Smale model occurs in finite time.Based on the explicit construction of Lyapunov functionals,we obtained that for 0≤β≤1/2,unconditional flocking occurs in finite time,whereas conditional flocking would occur for β>1/2 in finite time,and the conditions of flocking occurrence depend on initial data. Finally,we illustrate our theoretical results by numerical simulations.