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Updated: May 12, 2025

Modeling the Functional Network for Spatial Navigation in the Human Brain
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Applicability of spatial early warning signals to complex network dynamics.

Neil G MacLaren1, Kazuyuki Aihara2, Naoki Masuda1,3,4

  • 1Department of Mathematics, State University of New York at Buffalo, New York, NY 14260-2900, USA.

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|May 6, 2025
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Summary

Spatial early warning signals (EWSs) can predict tipping points in complex systems. This study found that spatial EWSs, particularly coefficient of variation and spatial skewness, perform better on complex networks than traditional lattice networks.

Keywords:
complex networksdynamics on networksearly warning signalstipping points

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Area of Science:

  • Complex Systems Science
  • Dynamical Systems Theory
  • Network Science

Background:

  • Early warning signals (EWSs) are crucial for anticipating tipping points in dynamical systems.
  • Traditional temporal EWSs require extensive time-series data, limiting their practical application.
  • Spatial EWSs offer a promising alternative by utilizing single spatial samples.

Purpose of the Study:

  • To investigate the performance of six major spatial EWSs on diverse network structures.
  • To address the knowledge gap regarding spatial EWS effectiveness on general complex networks beyond regular lattices.

Main Methods:

  • Evaluation of six spatial EWSs across various network types, including regular lattices and complex networks.
  • Comparison of EWS performance under different tipping scenarios.
  • Analysis of spatial EWS behavior and reliability on square lattices versus complex networks.

Main Results:

  • The optimal spatial EWS is dependent on the specific tipping scenario.
  • Coefficient of variation and spatial skewness generally outperformed other spatial EWSs.
  • Spatial EWSs exhibited significantly different behavior and increased reliability on complex networks compared to square lattices.

Conclusions:

  • Spatial EWSs are a viable and potentially more reliable method for detecting tipping points in complex systems.
  • The findings highlight the importance of network structure in the performance of spatial EWSs.
  • Further research into spatial EWSs on complex networks is warranted.