Behavior of $n$ Infinite Chains of Kinematic Points With the Immediate-Neighbors Interaction Dynamics

Consider n doubly infinite chains of kinematic points, where kinematic points can move in a two-dimensional plane; these kinematic points could be vehicles/drones modeled as point masses. In this paper, we analyze the behavior, under bounded perturbations, of such n infinite chains of kinematic points with respect to the immediate-neighbors interaction dynamics. We show that if the initial perturbations are bounded, then such an autonomous system converges to an equilibrium point. Furthermore, under some additional conditions, the autonomous system converges to the same equilibrium point in which it was before the perturbations.