Quantitative convergence guarantees for the mean-field dispersion process

We study the dispersion process on the complete graph introduced in the recent work {de_dispersion_2023} under the mean-field framework. In contrast to the probabilistic approach taken in {de_dispersion_2023} and many other related works, our focus is on the investigation of the large time behavior of solutions of the associated kinetic mean-field system of nonlinear ordinary differential equations (ODEs). We establish various analytical and quantitative convergence results for the long time behaviour of the mean-field system and related numerical illustrations are also provided.