American Institute of Mathematical Sciences

June  2018, 38(6): 2731-2762. doi: 10.3934/dcds.2018115

Asymptotic properties of various stochastic Cucker-Smale dynamics

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

Received  March 2017 Revised  December 2017 Published  April 2018

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.

Citation: Laure Pédèches. Asymptotic properties of various stochastic Cucker-Smale dynamics. Discrete & Continuous Dynamical Systems - A, 2018, 38 (6) : 2731-2762. doi: 10.3934/dcds.2018115
References:

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References:
Case $\gamma = 0.2$, with $D = 0.1$, $\lambda = 5$, $\beta = 2$ and $K_{\gamma} = 8.3$
Case $\gamma = 2$, with $D = 0.1$, $\lambda = 5$, $\beta = 2$ and $K_{\gamma} = 17$
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