  In two-dimensional space, we investigate the slow dynamics of multiple
localized spots with oscillatory tails in a specific three-component
reaction-diffusion system, whose key feature is that the spots attract or repel
each other alternatively according to their mutual distances, leading to rather
complex patterns. One fundamental pattern is the ring pattern, consisting of
$N$ equally distributed spots on a circle with a certain radius. Depending on
the parameters of the system, stationary or moving (i.e., traveling and
rotating) $N$-spot rings can be observed. In order to understand the emergence
of these patterns, we describe the dynamics of $N$ spots by a set of reduced
ordinary differential equations (ODEs) encoding the information of each spot's
location and velocity. On the basis of the reduced system, we analytically
study the existence and stability of stationary and moving $N$-spot ring
solutions, similar to the collective motion of self-propelled particles.
Numerical simulations are provided to verify our results with fixed parameters.
