Energy exchange in globally coupled mechanical phase oscillators

TL;DR

This paper analyzes energy exchange dynamics in a mean-field coupled oscillator ensemble with friction and external forcing, revealing regimes with controllable power transfer influenced by system parameters.

Contribution

It provides analytical expressions for energy exchange rates in different dynamical regimes of coupled oscillators, highlighting nontrivial parameter dependencies.

Findings

Energy exchange rates depend on entrainment levels.

Non-monotonic behavior of energy transfer with friction.

Power transfer can be manipulated via oscillator parameters.

Abstract

We study the stationary dynamics of energy exchange in an ensemble of phase oscillators, coupled through a mean-field mechanical interaction and added with friction and an external periodic excitation. The degree of entrainment between different parts of the ensemble and the external forcing determines three dynamical regimes, each of them characterized by specific rates of energy exchange. Using suitable approximations, we are able to obtain analytical expressions for those rates, which are in satisfactory agreement with results from numerical integration of the equations of motion. In some of the dynamical regimes, the rates of energy exchange show nontrivial dependence on the friction coefficients --in particular, non-monotonic behavior and sign switching. This suggests that, even in this kind of stylized model, power transfer between different parts of the ensemble and to the environment can be manipulated by a convenient choice of the individual oscillator parameters.