## Stability of entrainment of a continuum of coupled oscillators

Published in *Chaos: An Interdisciplinary Journal of Nonlinear Science*, 2017

Complex natural and engineered systems are ubiquitous, and their behavior is challenging to characterize and control. We examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can result in each oscillator attaining the frequency of the driving signal, with a phase offset determined by its natural frequency. We consider a special case of interacting oscillators in which the coupling tends to destabilize the phase configuration to which the driving signal would send the collection in the absence of coupling. In this setting, we derive stability results that characterize the trade-off between the effects of driving and coupling, and compare these results to the well-known Kuramoto model of a collection of freerunning coupled oscillators. ** Read more**

Recommended citation: Jordan Snyder, Anatoly Zlotnik, Aric Hagberg, "Stability of entrainment of a continuum of coupled oscillators." Chaos: An Interdisciplinary Journal of Nonlinear Science, 2017. __http://aip.scitation.org/doi/10.1063/1.4994567__