I would introduce the population density approach under mean-field approximation for networks of spiking neurons, talking about the derivation of a general firing rate equation and its descriptive power even when the system is far from an equilibrium state. Starting from this I will conclude presenting a self-consistent mean-field approach which allows to describe in the same conditions the stochastic dynamics of networks composed of a finite number of nervous cells.
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Mattia, M., and Del Giudice, P. (2004). Finite-size dynamics of inhibitory and excitatory interacting spiking neurons. Phys. Rev. E 70, 052903.
Gigante, G., Mattia, M., and Del Giudice, P. (2007). Diverse population-bursting modes of adapting spiking neurons. Phys. Rev. Lett. 98, 148101.
Vinci, G. V, Benzi, R., and Mattia, M. (2023). Self-consistent stochastic dynamics for finite-size networks of spiking neurons. Phys. Rev. Lett. 130, 097402.