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Observability is the property that enables to distinguish two differentlocations in $n$-dimensional state space from a reduced number of measuredvariables, usually just one. In high-dimensional systems it is thereforeimportant to make sure that the variable recorded to perform the analysisconveys good observability of the system dynamics. In the case of networkscomposed of neuron models, the observability of the network dependsnontrivially on the observability of the node dynamics and on the topology ofthe network. The aim of this paper is twofold. First, a study of observabilityis conducted using four well-known neuron models by computing three differentobservability coefficients. This not only clarifies observability properties ofthe models but also shows the limitations of applicability of each type ofcoefficients in the context of such models. Second, a multivariate singularspectrum analysis (M-SSA) is performed to detect phase synchronization innetworks 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 isshown that it is possible to detect phase synchronization i)~without having tomeasure all the state variables, but only one from each node, and ii)~withouthaving to estimate the phase.

Observability and Synchronization of Neuron Models