The European Physical Journal Special Topics
Boundary value problems, Autonomous vehicles -- Mathematical models, Transients (Dynamics) -- Mathematical models, Linear oscillators
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.
Cantos, C. E., Hammond, D. K., & Veerman, J. J. P. (2016). Transients in the synchronization of asymmetrically coupled oscillator arrays. The European Physical Journal Special Topics, 225(6-7), 1199-1209.