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The collective motion of self-driven agents is a phenomenon of great interestin interacting particle systems. In this paper, we develop and analyze a modelof agent motion in one dimension with periodic boundaries using a stochasticport-Hamiltonian system (PHS). The interaction model is symmetric and based onnearest neighbors. The distance-based terms and kinematic relations correspondto the skew-symmetric Hamiltonian structure of the PHS, while the velocitydifference terms make the system dissipative. The originality of the approacheslies in the stochastic noise that plays the role of an external input. It turnsout that the stochastic PHS with a quadratic potential is an Ornstein-Uhlenbeckprocess, for which we explicitly determine the distribution for any time $t\ge0$ and in the limit $t\to\infty$.  We characterize the collective motion by showing that the agents' meanvelocity is Brownian noise whose fluctuations increase with time, while thevariance of the agents' velocities and distances, which quantify thecoordination of the agents' motion, converge. The motion model does not specifya preferred direction of motion. However, assuming a equilibrium uniformstarting configuration, the results show that the noise triggers rapidlycoordinated agent motion determined by the Brownian behavior of the meanvelocity. Interestingly, simulation results show that some theoreticalproperties obtained with the Ornstein-Uhlenbeck process also hold for thenonlinear model with general interaction potential.

The Collective Dynamics of a Stochastic Port-Hamiltonian Self-Driven Agent Model in One Dimension