Flocking of the hybrid Cucker–Smale model

Abstract

In recent years, both the continuous-time and discrete-time Cucker–Smale models have been widely studied. However, in the practical systems, the dynamics of the agents coupled with each others can be hybrid. Thus, we consider the asymptotic flocking behavior of the hybrid Cucker–Smale model, which is composed of continuous-time dynamic agents and discrete-time dynamic agents. Firstly by some technical lemmas, a super-linear inequality of the derivative of velocity variance is established. Then, we eventually show that the hybrid model can achieve asymptotic flocking for the long-range communication weight1 case. At last, the simulation examples are given to verify the theoretical results.