Asymptotic behavior of gradient flows on the unit sphere with various potentials (Q2208439)

In this lengthy paper, a multi-agent system whose dynamics is governed by a gradient flow on the unit sphere associated with the interaction potential between positions of all agents measured by a weighted distance $|x_{i}-x_{j}|^{p+2}$ for any $p\neq 0$, is considered. Employing both attractive and repulsive couplings, the asymptotic behavior of the system accompanied by both $p>0$ (positive range) and $p<0$ (negative range) is studied.