Modeling synchronization in globally coupled oscillatory systems using model order reduction

Abstract

We construct reduced order models for two classes of globally coupled multi-component oscillatory systems, selected as prototype models that exhibit synchronization. These are the Kuramoto model, considered both in its original formulation and with a suitable change of coordinates, and a model for the circadian clock. The systems of interest possess strong reduction properties, as their dynamics can be efficiently described with a low-dimensional set of coordinates. Specifically, the solution and selected quantities of interest are well approximated at the reduced level, and the reduced models recover the expected transition to synchronized states as the coupling strengths vary. Assuming that the interactions depend only on the averages of the system variables, the surrogate models ensure a significant computational speedup for large systems.

Localized model order reduction and domain decomposition methods for coupled heterogeneous systems

“…Examples include synchronization, resonance, hydrodynamic instabilities and bifurcations arising from variations in the coupling terms or physical parameters. 2 Therefore, it is of interest to develop numerical methods able to capture such phenomena. Given the component-wise structure of the system, domain decomposition methods have proven to be effective in this direction.…”

“…This defines phenomena that cannot be observed while looking at the individual components separately, as they are a result of the interactions of the constituents. Examples include synchronization, resonance, hydrodynamic instabilities and bifurcations arising from variations in the coupling terms or physical parameters 2 . Therefore, it is of interest to develop numerical methods able to capture such phenomena.…”