Asymptotic properties of various stochastic Cucker-Smale dynamics

Laure Pédèches

doi:10.3934/dcds.2018115

Article Contents

2018, Volume 38, Issue 6: 2731-2762. Doi: 10.3934/dcds.2018115

This issue Previous Article Partially hyperbolic sets with a dynamically minimal lamination Next Article Remarks on the critical coupling strength for the Cucker-Smale model with unit speed

Asymptotic properties of various stochastic Cucker-Smale dynamics

Laure Pédèches

Institut de Mathématiques de Toulouse, 118, route de Narbonne, F-31062 Toulouse Cedex 9, France

Received: March 2017

Revised: December 2017

Published: June 2018

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Abstract

Starting from the stochastic Cucker-Smale model introduced in [14], we look into its asymptotic behaviours for different kinds of interaction. First in term of ergodicity, when $t$ goes to infinity, seeking invariant probability measures and using Lyapunov functionals. Second, when the number $N$ of particles becomes large, leading to results about propagation of chaos.

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Mathematics Subject Classification: Primary: 60K35; Secondary: 60H10, 82C22.

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Figure 1. Case $\gamma = 0.2$, with $D = 0.1$, $\lambda = 5$, $\beta = 2$ and $K_{\gamma} = 8.3$

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Figure 2. Case $\gamma = 2$, with $D = 0.1$, $\lambda = 5$, $\beta = 2$ and $K_{\gamma} = 17$

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