Eur. Phys. J. Special Topics 225, 1199-1209 (2016)
https://doi.org/10.1140/epjst/e2016-02658-y

Regular Article

Transients in the synchronization of asymmetrically coupled oscillator arrays

¹ Maseeh Department of Mathematics & Statistics, Portland State University, Portland, USA
² Applied Mathematics Department, Oregon Institute of Technology, Wilsonville, USA
³ Maseeh Department of Mathematics & Statistics, Portland State University, Portland, USA, CQCN, Dept of Physics, University of Crete, Heraklion, Greece

^a e-mail: ccantos@pdx.edu
^b e-mail: david.hammond@oit.edu
^c e-mail: veerman@pdx.edu

Received: 28 March 2016
Revised: 26 July 2016
Published online: 30 September 2016

Abstract

We consider the transient behavior of a large linear array of coupled linear damped harmonic oscillators following perturbation of a single element. Our work is motivated by modeling the behavior of flocks of autonomous vehicles. We first state a number of conjectures that allow us to derive an explicit characterization of the transients, within a certain parameter regime Ω. As corollaries we show that minimizing the transients requires considering non-symmetric coupling, and that within Ω the computed linear growth in N of the transients is independent of (reasonable) boundary conditions.