Abstract
We study the asymptotic behavior of a second-order swarm model on the unit sphere in both particle and kinetic regimes for the identical cases. For the emergent behaviors of the particle model, we show that a solution to the particle system with identical oscillators always converge to the equilibrium by employing the gradient-like flow approach. Moreover, we establish the uniform-in-time \begin{document}$ \ell_2 $\end{document} -stability using the complete aggregation estimate. By applying such uniform stability result, we can perform a rigorous mean-field limit, which is valid for all time, to derive the Vlasov-type kinetic equation on the phase space. For the proposed kinetic equation, we present the global existence of measure-valued solutions and emergent behaviors.
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