Effects of Measurement Noise on Flocking Dynamics of Cucker–Smale Systems

Abstract

Understanding the emergence of coordination behavior is of paramount importance in science and engineering. Environmental noise may have important impact on the coordination. In this brief, we consider a variation of the standard Cucker-Smale system in which individuals can not measure the states of others exactly. We present sufficient conditions on group size, noise intensity and communication rate to guarantee the almost surely exponential convergence toward flocking. We challenge the prevailing paradigm that noise suppressing the emergence of collective motion and report that noise may facilitate the emergence of ordered flocking behavior. We also find that group with high density can reach the ordered state more rapidly.