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arXiv · 2512.24383

Mean-Field Limits of Deterministic and Stochastic Flocking Models with Nonlinear Velocity Alignment

Vinh Nguyen·Roman Shvydkoy·Changhui Tan
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Abstract

We study the mean-field limit for a class of agent-based models describing flocking with nonlinear velocity alignment. Each agent interacts through a communication protocol $\phi$ and a non-linear coupling of velocities given by the power law $A(\bv) = |\bv|^{p-2}\bv$, $p > 2$. The mean-field limit is proved in two settings -- deterministic and stochastic. We then provide quantitative estimates on propagation of chaos for deterministic case in the case of the classical fat-tailed kernels, showing an improved convergence rate of the $k$-particle marginals to a solution of the corresponding Vlasov equation. The stochastic version is addressed with multiplicative noise depending on the local interaction intensity, which leads to the associated Fokker-Planck-Alignment equation. Our results extend the classical Cucker-Smale theory to the nonlinear framework which has received considerable attention in the literature recently.

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Vinh Nguyen, Roman Shvydkoy, Changhui Tan. 2025-12-30. Mean-Field Limits of Deterministic and Stochastic Flocking Models with Nonlinear Velocity Alignment. https://arxiv.org/abs/2512.24383

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