A nonlinear functional approach for mono-cluster flocking to the discrete Cucker-Smale model

Abstract

We present a nonlinear functional approach for the discrete Cucker-Smale (C-S) model with a general communication weight, and using the monotonicity of this functional, we provide a simple sufficient condition for the emergence of a mono-cluster flocking in terms of initial data, communication weight function and system parameters. Our proposed nonlinear functionals are the discrete analogues of the continuous nonlinear functionals introduced in [S.-Y. Ha and J.-G. Liu, Commun. Math. Sci., 7:297-325, 2009]. © 2019 International Press.