Predicting oscillations in complex networks with delayed feedback

TL;DR

This paper develops an analytic framework to predict oscillations in complex networks caused by structural complexity and delayed feedback, validated through experiments and data-driven prediction methods.

Contribution

It introduces a theoretical dimension reduction approach and a reservoir computing pipeline to analyze and predict oscillations in complex systems with delay.

Findings

Oscillations emerge when structural complexity and delay exceed critical thresholds.

Greater connectivity reduces the delay needed for oscillation onset.

The framework accurately predicts oscillation onset from timeseries data.

Abstract

Oscillatory dynamics are common features of complex networks, often playing essential roles in regulating function. Across scales from gene regulatory networks to ecosystems, delayed feedback mechanisms are key drivers of system-scale oscillations. The analysis and prediction of such dynamics are highly challenging, however, due to the combination of high-dimensionality, non-linearity and delay. Here, we systematically investigate how structural complexity and delayed feedback jointly induce oscillatory dynamics in complex systems, and introduce an analytic framework comprising theoretical dimension reduction and data-driven prediction. We reveal that oscillations emerge from the interplay of structural complexity and delay, with reduced models uncovering their critical thresholds and showing that greater connectivity lowers the delay required for their onset. Our theory is empirically tested in an experiment on a programmable electronic circuit, where oscillations are observed once structural complexity and feedback delay exceeded the critical thresholds predicted by our theory. Finally, we deploy a reservoir computing pipeline to accurately predict the onset of oscillations directly from timeseries data. Our findings deepen understanding of oscillatory regulation and offer new avenues for predicting dynamics in complex networks.