Linear analysis of the vectorial network model

In this brief, we analyze the local stochastic dynamics of a recently proposed network-based model of collective behavior in systems of self-propelled particles. In this model, each agent is assimilated to a 2-D unit vector, whose orientation changes in a discrete time setting as a result of noisy interactions with neighboring agents. The process of neighbor selection is stochastic, whereby each agent averages its orientation with a randomly chosen subset of neighbors. We linearize the model in the neighborhood of its ordered state, where all the vectors share the same orientation, and study the effect of noise on the system response. Closed-form results are validated against numerical simulations for small and large networks.