# Observability and Synchronization of Neuron Models

## TL;DR

This paper investigates the observability of neuron model networks and introduces a novel application of multivariate singular spectrum analysis to detect phase synchronization using minimal measurements.

## Contribution

It compares observability coefficients across neuron models and applies M-SSA to identify phase synchronization without full state measurement or phase estimation.

## Key findings

- Observability varies with neuron model and network topology.
- M-SSA effectively detects phase synchronization with limited data.
- Different observability coefficients have distinct applicability limitations.

## Abstract

Observability is the property that enables to distinguish two different locations in $n$-dimensional state space from a reduced number of measured variables, usually just one. In high-dimensional systems it is therefore important to make sure that the variable recorded to perform the analysis conveys good observability of the system dynamics. In the case of networks composed of neuron models, the observability of the network depends nontrivially on the observability of the node dynamics and on the topology of the network. The aim of this paper is twofold. First, a study of observability is conducted using four well-known neuron models by computing three different observability coefficients. This not only clarifies observability properties of the models but also shows the limitations of applicability of each type of coefficients in the context of such models. Second, a multivariate singular spectrum analysis (M-SSA) is performed to detect phase synchronization in networks composed by neuron models. This tool, to the best of the authors' knowledge has not been used in the context of networks of neuron models. It is shown that it is possible to detect phase synchronization i)~without having to measure all the state variables, but only one from each node, and ii)~without having to estimate the phase.