Low-dimensional firing rate dynamics of spiking neuron networks

Maurizio Mattia

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arXiv · 1609.08855

Low-dimensional firing rate dynamics of spiking neuron networks

Maurizio Mattia

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Abstract

Starting from a spectral expansion of the Fokker-Plank equation for the membrane potential density in a network of spiking neurons, a low-dimensional dynamics of the collective firing rate is derived. As a result a $n$-order ordinary differential equation for the network activity can be worked out by taking into account the slowest $n$ modes of the expansion. The resulting low-dimensional dynamics naturally takes into account the strength of the synaptic couplings under the hypothesis of a not too fast changing membrane potential density. By considering only the two slowest modes, the firing rate dynamics is equivalent to the one of a damped oscillator in which the angular frequency and the relaxation time are state-dependent. The presented results apply to a wide class of networks of one-compartment neuron models.

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Maurizio Mattia. 2016-09-28. Low-dimensional firing rate dynamics of spiking neuron networks. https://arxiv.org/abs/1609.08855

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