Dynamic properties of chasers in a moving queue based on a delayed chasing model

A delayed chasing model is proposed to simulate the chase behavior in the queue, where each member regards the closest one ahead as the target, and the leader is attracted to a target point with slight fluctuation. When the initial distances between neighbors possess an identical low value, the fluctuating target of the leader can cause an amplified disturbance in the queue. After a long period of time, the queue recovers the stable state from the disturbance, forming a straight-line-like pattern again, but distances between neighbors grow. Whether the queue can keep stable or not depends on initial distance, desired velocity, and relaxation time. Furthermore, we carry out convergence analysis to explain the divergence transformation behavior and confirm the convergence conditions, which is in approximate agreement with simulations. (paper)