Shot noise in next-generation neural mass models for finite-size networks

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2022. Vol. 106. No. 6. Article L062302.

Vladimir V. Klinshov, Kirillov S.

Neural mass models is a general name for various models describing the collective dynamics of large neural
populations in terms of averaged macroscopic variables. Recently, the so-called next-generation neural mass
models have attracted a lot of attention due to their ability to account for the degree of synchrony. Being exact
in the limit of infinitely large number of neurons, these models provide only an approximate description of
finite-size networks. In the present Letter we study finite-size effects in the collective behavior of neural networks
and prove that these effects can be captured by appropriately modified neural mass models. Namely, we show
that the finite size of the network leads to the emergence of the so-called shot noise appearing as a stochastic
term in the neural mass model. The power spectrum of this shot noise contains pronounced peaks, therefore its
impact on the collective dynamics might be crucial due to resonance effects.

Keywords: нейронные сети, Neural Network