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Dynamical network markers for heterogeneous hierarchical networks.

Yuto Saito¹, Hampei Sasahara², Jun-Ichi Imura¹

¹Graduate School of Engineering, Institute of Science Tokyo, Tokyo, 152-8552, Japan.

Scientific Reports

|July 2, 2025

Summary

This summary is machine-generated.

This study extends dynamical network marker (DNM) theory to complex hierarchical networks, enabling earlier prediction of critical transitions (CTs). Stronger network interactions improve DNM node identification for better early-warning signals.

Keywords:

Critical transition Dynamical network marker Dynamical system Early-warning signal Hierarchical network

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Area of Science:

Complex Systems Science
Network Theory
Dynamical Systems

Background:

Early-warning signals (EWS) are vital for predicting critical transitions (CTs) in complex systems.
Dynamical network marker (DNM) theory uses network fluctuations for EWS, but is limited to simple networks.

Purpose of the Study:

To extend DNM theory to heterogeneous hierarchical networks.
To analyze network behavior before CTs in these complex structures.

Main Methods:

Theoretical analysis of DNM in hierarchical networks.
Numerical simulations to validate the extended theory.
Characterization of DNM nodes via network eigenvectors.

Main Results:

Extended DNM theory accurately predicts CTs in hierarchical networks.
Stronger network interactions require more subnetworks but enhance DNM node precision.
Identified critical role of sampling strategies in CT detection.

Conclusions:

The extended DNM theory provides a more comprehensive framework for analyzing complex hierarchical systems.
This work advances the prediction of critical transitions in real-world networks, including biological systems.