https://doi.org/10.1140/epjst/e2016-02665-0
Regular Article
Signal velocity in oscillator arrays
1 Maseeh Department of Mathematics & Statistics, Portland State University, Portland, USA
2 Maseeh Department of Mathematics & Statistics, Portland State University, Portland, USA
CQCN, Dept. of Physics, University of Crete, Heraklion, Greece
3 Applied Mathematics Department, Oregon Institute of Technology, Wilsonville, USA
a e-mail: ccantos@pdx.edu
b e-mail: veerman@pdx.edu
c e-mail: david.hammond@oit.edu
Received: 28 March 2016
Revised: 26 July 2016
Published online: 30 September 2016
We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles where the acceleration of each vehicle depends on the relative positions and velocities between itself and a set of local neighbors. After describing necessary and sufficient conditions for asymptotic stability, we 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 velocitiesc+ > 0 and c− < 0 such that low frequency disturbances travel through the flock as f+(x − c+t) in the direction of increasing agent numbers and f−(x − c−t) in the other.
© EDP Sciences, Springer-Verlag, 2016
