Emergent behaviors in group ring flocks

We present a first-order aggregation model on group ring, and study its asymptotic dynamics. In positive coupling strength regime, we show that the flow generated by proposed tends to an equilibrium manifold asymptotically. For this, introduce Lyapunov functional which is non-increasing along flow, using temporal decay of nonlinear LaSalle invariance principle, converges toward also structure strongly dependent underlying group.