Research

Paper

TESTING March 04, 2026

Predicting oscillations in complex networks with delayed feedback

Authors

Shijie Liu, Jinliang Han, Tim Rogers, Yongzheng Sun

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.

Metadata

arXiv ID: 2603.04251
Provider: ARXIV
Primary Category: cond-mat.dis-nn
Published: 2026-03-04
Fetched: 2026-03-05 06:06

Related papers

Raw Data (Debug)
{
  "raw_xml": "<entry>\n    <id>http://arxiv.org/abs/2603.04251v1</id>\n    <title>Predicting oscillations in complex networks with delayed feedback</title>\n    <updated>2026-03-04T16:39:11Z</updated>\n    <link href='https://arxiv.org/abs/2603.04251v1' rel='alternate' type='text/html'/>\n    <link href='https://arxiv.org/pdf/2603.04251v1' rel='related' title='pdf' type='application/pdf'/>\n    <summary>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.</summary>\n    <category scheme='http://arxiv.org/schemas/atom' term='cond-mat.dis-nn'/>\n    <category scheme='http://arxiv.org/schemas/atom' term='q-bio.PE'/>\n    <published>2026-03-04T16:39:11Z</published>\n    <arxiv:primary_category term='cond-mat.dis-nn'/>\n    <author>\n      <name>Shijie Liu</name>\n    </author>\n    <author>\n      <name>Jinliang Han</name>\n    </author>\n    <author>\n      <name>Tim Rogers</name>\n    </author>\n    <author>\n      <name>Yongzheng Sun</name>\n    </author>\n  </entry>"
}