Phase reduction explains chimera shape: when multi-body interaction matters

TL;DR

This paper extends the Kuramoto-Sakaguchi model to include second-order phase interactions, demonstrating that high-order phase reduction accurately captures chimera state shapes influenced by multi-body interactions in oscillator networks.

Contribution

The paper introduces a second-order phase reduction for non-identical Stuart-Landau oscillators, linking coupling matrices to multi-body interactions and improving chimera state modeling.

Findings

Second-order phase model reproduces chimera shape dependence on coupling strength.

High-order phase reduction captures effects missed by first-order models.

Explicit relation established between coupling matrix and multi-body interactions.

Abstract

We present an extension of the Kuramoto-Sakaguchi model for networks, deriving the second-order phase approximation for a paradigmatic model of oscillatory networks - an ensemble of non-identical Stuart-Landau oscillators coupled pairwisely via an arbitrary coupling matrix. We explicitly demonstrate how this matrix translates into the coupling structure in the phase equations. To illustrate the power of our approach and the crucial importance of high-order phase reduction, we tackle a trendy setup of non-locally coupled oscillators exhibiting a chimera state. We reveal that our second-order phase model reproduces the dependence of the chimera shape on the coupling strength that is not captured by the typically used first-order Kuramoto-like model. Our derivation contributes to a better understanding of complex networks' dynamics, establishing a relation between the coupling matrix and multi-body interaction terms in the high-order phase model.