Reconstructing phase dynamics of oscillator networks

TL;DR

This paper presents a method to reconstruct phase dynamics and coupling functions in small networks of coupled oscillators from data, enabling analysis of directed interactions and nonlinear effects.

Contribution

It extends previous methods to small networks, allowing for reconstruction of phase dynamics, coupling functions, and directed coupling quantification from multivariate time series.

Findings

Successfully applied to network motifs of three oscillators

Effective in analyzing random networks of five and nine units

Addresses nonlinear effects in oscillator coupling

Abstract

We generalize our recent approach to reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E, 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from the multivariate time series, we first reconstruct genuine phases and then obtain the coupling functions in terms of these phases. The partial norms of these coupling functions quantify directed coupling between oscillators. We illustrate the method by different network motifs for three coupled oscillators and for random networks of five and nine units. We also discuss nonlinear effects in coupling.