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Observability and synchronization of neuron models.

Luis A Aguirre1, Leonardo L Portes2, Christophe Letellier3

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Summary
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This study investigates how to best observe complex neuron networks. It introduces a method to detect phase synchronization using minimal measurements from each neuron model.

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Area of Science:

  • Computational Neuroscience
  • Complex Systems Analysis
  • Dynamical Systems Theory

Background:

  • Observability is crucial for understanding high-dimensional dynamical systems, especially networks of neuron models.
  • Network observability depends on individual neuron model dynamics and network topology.
  • Current methods for analyzing neuron network synchronization often require extensive measurements.

Purpose of the Study:

  • To assess the observability of four well-known neuron models using different observability coefficients.
  • To investigate the emergence of phase synchronization in networks of neuron models.
  • To introduce and validate a novel method for detecting phase synchronization with minimal data.

Main Methods:

  • Calculation of three distinct observability coefficients for four neuron models.
  • Application of multivariate singular spectrum analysis (MSSA) to neuron networks.
  • Analysis of synchronization using single-variable measurements from each node.

Main Results:

  • The study clarifies the observability properties and limitations of different coefficients for specific neuron models.
  • Multivariate singular spectrum analysis is demonstrated as a viable tool for analyzing neuron networks.
  • Phase synchronization in neuron networks can be detected using minimal measurements (one variable per node) and without phase estimation.

Conclusions:

  • The choice of observability coefficient impacts the understanding of neuron model dynamics.
  • Multivariate singular spectrum analysis offers a powerful, data-efficient approach for studying synchronization in neuron networks.
  • Effective network state recovery and synchronization detection are achievable with strategically selected single-variable measurements.