  Recently, the so-called next-generation neural mass models have received a
lot of attention of the researchers in the field of mathematical neuroscience.
The ability of these models to account for the degree of synchrony in neural
populations proved useful in many contexts such as the modeling of brain
rhythms, working memory and spatio-temporal patterns of activity. In the
present Letter we study the effects of finite size on the collective behaviour
of neural networks and show that they can be captured by appropriately modified
neural mass models. Namely, the finite size of the network leads to the
emergence of the shot noise appearing as a stochastic term in the neural mass
model. We calculate the power spectrum of the shot noise and show that it might
demonstrate pronounced peaks in the frequencies comparable to the mean firing
rate. Although the shot noise is weak in large massively connected networks,
its impact on the collective dynamics might be crucial due to resonance
effects.
