An analytical theory for spiking neurons driven by colored noise
Existing mean field theories of spiking neural networks largely neglect the second order statistics of spike trains. This approximation hampers the understanding of real network dynamics, which can indeed be strongly influenced by related phenomena, like slow fluctuations. We develop an analytical theory for the spike train auto-covariance of leaky integrate-and-fire neurons driven by colored noise. A recently developed expansion in terms of the eigenfunctions of the corresponding Fokker–Planck equation is extended to the case of colored noise input, modeled by a Markov embedding. This theory constitutes a big step towards a self-consistent description of network dynamics including its covariance structure.
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