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Updated: Mar 8, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Oscillating systems with cointegrated phase processes.

Jacob Østergaard1, Anders Rahbek2, Susanne Ditlevsen3

  • 1Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen Ø, Denmark. ostergaard@math.ku.dk.

Journal of Mathematical Biology
|February 1, 2017
PubMed
Summary
This summary is machine-generated.

Cointegration analysis reveals network structures in oscillating systems. This method accurately identifies feedback direction and coupling strength in biological networks, including EEG data.

Keywords:
CointegrationCoupled oscillatorsEEG signalsInteracting dynamical systemPhase processSynchronizationWinfree oscillator

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Area of Science:

  • Neuroscience
  • Complex Systems
  • Statistical Physics

Background:

  • Oscillating systems are fundamental in biological processes.
  • Understanding network interactions is crucial for system analysis.
  • Existing methods may not fully capture dynamic coupling structures.

Purpose of the Study:

  • To introduce cointegration analysis for inferring network structure in phase-coupled oscillating systems.
  • To demonstrate its applicability to biological network models like Winfree oscillators.
  • To evaluate its effectiveness in identifying directional and proportional coupling strengths.

Main Methods:

  • Defining a class of phase-coupled oscillating systems.
  • Deriving a data-generating process for simulated networks.
  • Applying cointegration analysis to identify network topology.
  • Analyzing simulated Winfree oscillator networks with varying coupling types.
  • Examining electroencephalography (EEG) recordings.

Main Results:

  • Cointegration analysis successfully infers network structure.
  • The method correctly identifies feedback direction and coupling strength.
  • Accurate classification achieved for uni-directional, bi-directional, and all-to-all coupling.
  • Demonstrated capability in analyzing complex biological systems.

Conclusions:

  • Cointegration analysis is a powerful tool for network inference in oscillating systems.
  • The approach offers insights into biological network dynamics.
  • Further application in neuroscience, particularly with EEG data, is promising.