Linear analysis of the vectorial network model in the presence of leaders

In this work, we study the collective behavior of a multi-agent system of stochastically interacting leaders and followers. In this time-varying network, the nodes update their states through a noisy interaction with a randomly selected subset of neighbors, including leaders whose average orientation is not updated in time. By linearizing the system dynamics in the vicinity of the leaders’ common trajectory, we establish a toolbox of closed-form expressions that aid in the understanding of the influence of noise, number of connected neighbors, network size, and proportion of leaders on the group coordination.