Spontaneous Wave Formation in Stochastic Self-Driven Particle Systems

Waves and oscillations are commonly observed in the dynamics of self-driven agents such as pedestrians or vehicles. Interestingly, many factors may perturb stability space homogeneous streaming, leading to spontaneous formation collective related stop-and-go waves, jamiton, phantom jam literature. In this article, we demonstrate that even a minimal additive stochastic noise stable first-order can initiate phenomena. The is not classic white one, but colored described by Gaussian Ornstein-Uhlenbeck process. It turns out joint particles noises forms again (Gaussian) process whose characteristics be explicitly expressed terms parameters model. We analyze its characterize presence waves through oscillation patterns correlation autocorrelation distance spacing between particles. determine exact solutions for functions finite system with periodic boundaries continuum limit when size infinite. Finally, compare experimental trajectories single-file pedestrian motions simulation results.