Communications in Mathematical Sciences
Volume 7 (2009)
A simple proof of the Cucker-Smale flocking dynamics and mean-field limit
Pages: 297 – 325
We present a simple proof on the formation of flocking to the Cucker-Smale system based on the explicit construction of a Lyapunov functional. Our results also provide a unified condition on the initial states in which the exponential convergence to flocking state will occur. For large particle systems, we give a rigorous justification for the mean-field limit from the many particle Cucker-Smale system to the Vlasov equation with flocking dissipation as the number of particles goes to infinity.
Flocking; swarming; emergence; self-driven particles system; autonomous agents; Vlasov equation; Lyapunov functional; measure valued solution; Kantorovich-Rubinstein distance
2010 Mathematics Subject Classification
Primary 92C17. Secondary 82C22, 82C40.