Document Type


Publication Date



Coupled -- Oscillator Arrays, Flocking


We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles. The model considers asymmetric, linear, decentralized dynamics, where the acceleration of each vehicle depends on the relative positions and velocities between itself and a set of local neighbors. We first derive necessary and sufficient conditions for asymptotic stability, then derive expressions for the phase velocity of propagation of disturbances in velocity through this system. We show that the high frequencies exhibit damping, which implies existence of well-defined signal velocities c+>0 and c−f(x−c+t) in the direction of increasing agent numbers and f(x−c−t) in the other.


This is the author’s version of a work that was accepted for publication in European Physical Journal: Special Topics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Physical Journal: Special Topics, Vol 225, Issue 6/7, 2016 and can be found online at:



Persistent Identifier