Asymptotic behavior of a second-order swarm sphere model and its kinetic limit (Q2178478)

The authors investigate the asymptotic behavior of a second-order swarm model in both particle and kinetic levels. A solution to the particle system with identical oscillators always converge to the equilibrium due to the gradient-like flow approach. The uniform-in-time stability is established by using the complete aggregation estimate. The mean field kinetic equation and the global-in-time existence of a measure-valued solution are obtained. The work of the authors provides an important contribution to the research of complex behaviors of swarm models.