The dynamics of large-scale arrays of coupled resonators

This work describes an analytical framework suitable for the analysis of large-scale arrays of coupled resonators, including those which feature amplitude and phase dynamics, inherent element-level parameter variation, nonlinearity, and/or noise. In particular, this analysis allows for the consideration of coupled systems in which the number of individual resonators is large, extending as far as the continuum limit corresponding to an infinite number of resonators. Moreover, this framework permits analytical predictions for the amplitude and phase dynamics of such systems. The utility of this analytical methodology is explored through the analysis of a system of N non-identical resonators with global coupling, including both reactive and dissipative components, physically motivated by an electromagnetically-transduced microresonator array. In addition to the amplitude and phase dynamics, the behavior of the system as the number of resonators varies is investigated and the convergence of the discrete system to the infinite-N limit is characterized.