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Recurrence quantification analysis for the identification of burst phase synchronisation.

E L Lameu1, S Yanchuk2, E E N Macau1

  • 1National Institute for Space Research, São José dos Campos, São Paulo 12227-010, Brazil.

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Spatial recurrence quantification analysis (RQA) effectively identifies chaotic burst phase synchronization in neural networks. This method reveals synchronized neuron groups and their sizes in both single and clustered network structures.

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Area of Science:

  • Computational Neuroscience
  • Complex Systems Analysis
  • Network Science

Background:

  • Chaotic bursting neurons are crucial in neural dynamics.
  • Understanding phase synchronization in complex neural networks is challenging.
  • Existing methods may not fully capture spatial synchronization patterns.

Purpose of the Study:

  • To apply spatial recurrence quantification analysis (RQA) for identifying chaotic burst phase synchronization.
  • To analyze synchronization in a single small-world neural network and a network of small-world subnetworks.
  • To determine the capability of spatial RQA in detecting synchronized neuron groups and their sizes.

Main Methods:

  • Utilized the Rulkov map to model chaotic bursting neuron dynamics.
  • Employed spatial recurrence quantification analysis (RQA) on network structures.
  • Derived an analytical expression for spatial recurrence rate using Gaussian approximation for single networks.
  • Investigated clustered networks composed of small-world subnetworks.

Main Results:

  • Spatial RQA successfully identified groups of synchronized neurons and quantified their sizes.
  • An analytical expression for spatial recurrence rate was obtained for single networks.
  • Phase synchronization within and between subnetworks was identified in clustered networks.
  • Demonstrated the effectiveness of spatial RQA in complex network topologies.

Conclusions:

  • Spatial RQA is a powerful tool for detecting and analyzing chaotic burst phase synchronization in neural networks.
  • The method is applicable to both single complex networks and networks of networks.
  • Spatial RQA provides insights into the spatial organization of synchronized neuronal activity.