Flocking and non-flocking behavior in a stochastic Cucker-Smale system

TL;DR

This paper introduces a stochastic Cucker-Smale model incorporating randomness in communication, proves solution existence, and demonstrates how noise levels influence flocking behavior, supported by numerical examples.

Contribution

It presents a new stochastic model for flocking, establishes solution existence and uniqueness, and analyzes how noise impacts emergent flocking behavior.

Findings

Large noise inhibits flocking behavior

Small noise allows flocking to occur

Numerical examples illustrate theoretical results

Abstract

We first present a new stochastic version of the Cucker-Smale model of the emergent behavior in flocks in which the mutual communication between individuals is affected by random factor. Then, the existence and uniqueness of global solution to this system are verified. We show a result which agrees with natural fact that under the effect of large noise, there is no flocking. In contrast, if noise is small, then flocking may occur. Paper ends with some numerical examples.