Network inference applicable to both synchronous and desynchronous systems from oscillatory signals

TL;DR

This paper introduces a novel method for inferring interaction networks from oscillatory signals, applicable to both synchronized and desynchronized systems, supported by phase reduction theory and validated on simulated data.

Contribution

It extends network inference techniques to synchronized oscillators, overcoming previous limitations and enabling analysis of a broader class of oscillatory systems.

Findings

Effective inference from limited data

Validated on simulated limit-cycle oscillators

Applicable to both synchronized and desynchronized systems

Abstract

Synchronization is ubiquitous in nature, which is mathematically described by coupled oscillators. Synchronization strongly depends on the interaction network, and the network plays a crucial role in controlling the dynamics. To understand and control synchronization dynamics in the real world, it is essential to identify the network from the observed data. While previous studies have developed the methods for inferring the network of asynchronous systems, it remains challenging to infer the network of well-synchronized oscillators. In this study, we develop a method for inferring the network of synchronized and desynchronized oscillators from time series. Our method expands the applicability of network inference to a wider class of oscillatory systems. The proposed method discards a large part of data used for inference, which may seem counterintuitive. However, the effectiveness of the method is supported by the phase reduction theory, a well-established theory for weakly coupled oscillators. We verify the proposed method by applying it to simulated data of the limit-cycle oscillators. This study provides an important step towards understanding synchronization in real-world systems from a network perspective.