Large scale brain networks are understood nowadays to underlie the emergence of cognitive functions, though the detailed mechanisms are hitherto unknown. The challenges in the study of large scale brain networks are amongst others their high dimensionality requiring significant computational efforts, the complex connectivity across brain areas and the associated transmission delays, as well as the stochastic nature of neuronal processes. To decrease the computational effort, neurons are clustered into neural masses, which then are approximated by reduced descriptions of population dynamics. Here, we implement a neural population mode approach (Assisi et al. in Phys. Rev. Lett. 94(1):018106, 2005; Stefanescu and Jirsa in PLoS Comput. Biol. 4(11):e1000219, 2008), which parsimoniously captures various types of population behavior. We numerically demonstrate that the reduced population mode system favorably captures the high-dimensional dynamics of neuron networks with an architecture involving homogeneous local connectivity and a large-scale, fiber-like connection with time delay.