Observability and synchronization of neuron models

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.