Energy exchange in globally coupled mechanical phase oscillators

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.

Energy flow and dissipation in heterogeneous ensembles of coupled phase oscillators

“…As discussed in our previous publication [11], the present system is expected to exhibit three qualitatively different stationary regimes of collective behavior, depending on the parameters which control the dynamics. These regimes are characterized by diverse degrees of synchronization with the external excitation.…”

“…This is the equation of motion for a mechanical oscillator of phase Θ subjected to friction and an external harmonic force of unitary frequency. It can be readily shown [2,11] that, for long times, its solution becomes synchronized to the force if k > γ . Thus, this is the second condition that defines the regime of full synchronization in our oscillator ensemble.…”

“…In a recent contribution [11], we have studied energy exchange in an ensemble of globally coupled mechanical oscillators, in a situation where the system is excited by an external harmonic force applied to one of the oscillators. Friction forces, whose intensity varied from oscillator to oscillator, made it possible to reach a state of stationary motion where we characterized the flow of energy between different oscillators and with the environment.…”

P36 - Untersuchung der dynamischen Energieverteilung in ko-resonant gekoppelten Cantilever-Sensoren

“…die Ausbildung effektiver Sensorparameter, Amplitudenverstärkung und die Linearität / Stabilität der Schwingung [6]. Diese Effekte können auf fundamentaler Ebene durch den Energieaustausch zwischen Oszillatoren beschrieben werden [7,8]. Um dies für das ko-resonante System zu untersuchen, wurde ein entsprechendes Modell in der finite Elemente Software Comsol Multiphysics implementiert und dort hinsichtlich der Energieverteilungen für verschiedenen Anpassungsgrade und Anregungsfrequenzen für harmonische Anregung im Zeitbereich analysiert.…”