Cucker-Smale flocking particles with multiplicative noises: Stochastic mean-field limit and phase transition

Young Pil Choi, Samir Salem

Research output: Contribution to journalArticle

Abstract

In this paper, we consider the Cucker-Smale ocking particles which are subject to the same velocity-dependent noise, which exhibits a phase change phenomenon occurs bringing the system from a "non flocking" to a "flocking" state as the strength of noises decreases. We rigorously show the stochastic mean-field limit from the many-particle Cucker-Smale system with multiplicative noises to the Vlasov-type stochastic partial differential equation as the number of particles goes to infinity. More precisely, we provide a quantitative error estimate between solutions to the stochastic particle system and measure-valued solutions to the expected limiting stochastic partial differential equation by using the Wasserstein distance. For the limiting equation, we construct global-in-time measure-valued solutions and study the stability and large-time behavior showing the convergence of velocities to their mean exponentially fast almost surely.

Original languageEnglish
Pages (from-to)573-592
Number of pages20
JournalKinetic and Related Models
Volume12
Issue number3
DOIs
Publication statusPublished - 2019

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation

Fingerprint Dive into the research topics of 'Cucker-Smale flocking particles with multiplicative noises: Stochastic mean-field limit and phase transition'. Together they form a unique fingerprint.

  • Cite this