Strong stochastic flocking with noise under long-range fat tail communication

Abstract

Consider the reality that flocking behavior is affected by random noise. We study the Cucker–Smale-type systems with multiplicative noise where the communication weight satisfies the long-range fat tail condition. By comparing with the related deterministic system, we show that the noise intensity of the stochastic system mainly affects the convergence speed of the flocking. Specifically, we demonstrate that the system can achieve a stochastic finite-time flocking when the noise intensity is small, and almost surely asymptotic flocking when the noise intensity is large. Some numerical simulations are given to show our theoretical results. In addition, the method in this work can improve the results of previous studies.