Flocking of the hybrid Cucker-Smale model with normalized communication weight

In recent years, the Cucker-Smale model has been widely studied by researchers. However, the dynamics of coupling between agents can be hybrid and the normalized pre-actor 1/N has certain shortcomings. We consider the asymptotic flocking problem of the hybrid C-S model with a normalized weight function, which is composed of the continuous-time dynamic agents and the discrete-time dynamic agents. The use of the normalized weight function destroys the symmetry of the model. Therefore, in order to get the conclusion that the model is asymptotically flocking, firstly we will give the estimation of velocity difference derivative through classification discussion. Secondly, an auxiliary lemma is given. Then combined with the above estimation, we can get that the hybrid model is asymptotically flocking. Finally, the theoretical calculation results are verified by simulation examples.