Spectral Coarse Graining and Synchronization in Oscillator Networks

TL;DR

This paper introduces a spectral coarse graining method for oscillator networks that preserves key dynamical properties, enabling simplified yet representative models of complex systems.

Contribution

It presents a novel grouping technique that maintains crucial dynamical features during coarse graining of oscillator networks.

Findings

Coarse graining can preserve synchronization properties.

The method effectively simplifies network analysis.

Applicable to networks with Laplacian-based dynamics.

Abstract

Coarse graining techniques offer a promising alternative to large-scale simulations of complex dynamical systems, as long as the coarse-grained system is truly representative of the initial one. Here, we investigate how the dynamical properties of oscillator networks are affected when some nodes are merged together to form a coarse-grained network. Moreover, we show that there exists a way of grouping nodes preserving as much as possible some crucial aspects of the network dynamics. This coarse graining approach provides a useful method to simplify complex oscillator networks, and more generally any network whose dynamics involves a Laplacian matrix.