Communication-Rate-Dependent Dynamics of Multi-agent Systems with Heterogeneous Free Will

In this study, we analyze the dynamic characteristics of the Cucker-Smale model with heterogeneous free will (CSF).Most existing research has examined flocking when external perturbations converge to identical values; however, we investigate the case in which agents have different free-will vectors.We first prove that a positive lower bound exists for velocity differences between agents with heterogeneous free will.This implies that flocking cannot occur in the CSF.In particular, in the case of a nontrivial initial velocity and free will, we demonstrate that the distance between agents increases linearly with time.We also obtain an explicit upper bound for the maximum distance between agents when the communication rate is greater than zero and less than 1/2.The maximum distance growth rate depends on the communication rate.Finally, we validate the theoretical results through numerical simulations.