Self-consistent stochastic dynamics for finite-size networks of spiking neurons
arxiv(2021)
摘要
Despite the huge number of neurons composing a brain network, ongoing
activity of local cell assemblies composing cortical columns is intrinsically
stochastic. Fluctuations in their instantaneous rate of spike firing ν(t)
scale with the size of the assembly and persist in isolated network, i.e., in
absence of external source of noise. Although deterministic chaos due to the
quenched disorder of the synaptic couplings likely underlies this seemingly
stochastic dynamics, an effective theory for the network dynamics of a finite
ensemble of spiking neurons is lacking. Here, we fill this gap by extending the
so-called population density approach including an activity- and size-dependent
stochastic source in the Fokker-Planck equation for the membrane potential
density. The finite-size noise embedded in this stochastic partial derivative
equation is analytically characterized leading to a self-consistent and
non-perturbative description of ν(t) valid for a wide class of spiking
neuron networks. Its power spectra of ν(t) are found in excellent agreement
with those from detailed simulations both in the linear regime and across a
synchronization phase transition, when a size-dependent smearing of the
critical dynamics emerges.
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