Research Paper#Flocking Models, Mean-Field Limit, Nonlinear Velocity Alignment, Cucker-Smale🔬 ResearchAnalyzed: Jan 3, 2026 15:35
Mean-Field Analysis of Flocking Models with Nonlinear Velocity Alignment
Published:Dec 30, 2025 17:51
•1 min read
•ArXiv
Analysis
This paper extends the classical Cucker-Smale theory to a nonlinear framework for flocking models. It investigates the mean-field limit of agent-based models with nonlinear velocity alignment, providing both deterministic and stochastic analyses. The paper's significance lies in its exploration of improved convergence rates and the inclusion of multiplicative noise, contributing to a deeper understanding of flocking behavior.
Key Takeaways
- •Proves the mean-field limit for deterministic and stochastic flocking models with nonlinear velocity alignment.
- •Provides quantitative estimates on propagation of chaos, improving convergence rates in the deterministic case.
- •Addresses the stochastic version with multiplicative noise, leading to a Fokker-Planck-Alignment equation.
- •Extends the classical Cucker-Smale theory to a nonlinear framework.
Reference
“The paper provides quantitative estimates on propagation of chaos for the deterministic case, showing an improved convergence rate.”