Secular condition for the McKean system

In this paper, we study the McKean kinetic system for two groups of particles with periodic initial data in the weight space. The system is reduced to an integro-differential operator containing nonintegrable terms. We find a secularity condition that allows one to eliminate the nondissipative part and hence reduce the problem to a nonlinear equation in a Hilbert space; this is the main step towards proving the stabilization of the solution.