Abstract


Flocking models on unit sphere
Sun-ho Choi (NIMS) /
We present several counterparts of the Cucker-Smale type flocking model on unit sphere and provide flocking estimates for the proposed models. Note that Cucker-Smale model is a Newtonian type dynamic equation in $R^3$, For the derivations of the models on unit sphere, we replace the Euclidean sum for the velocity differences in Cucker-Smale model by the sum for the position dependent differences to preserve the modulus of $x_i$. For the flocking estimates of the proposed models, we employ a Lyapunov functional approach.