Phase transitions in the time synchronization model

There are two types $i=1,2$ of particles on the line $R$, with $N_i$ particles of type $i$. Each particle of type $i$ moves with constant velocity $v_i$. Moreover, any particle of type $i=1,2$ jumps to any particle of type $j=1,2$ with rates $N_{j}^{-1}\alpha _{ij}$. We find phase transitions in the clusterization (synchronization) behavior of this system of particles on different time scales $t=t(N)$ relative to $N=N_1+N_2$.