2019-10-18T14:16:40Z
https://digital.csic.es/dspace-oai/request
oai:digital.csic.es:10261/140032
2018-06-25T12:24:38Z
com_10261_37
com_10261_4
col_10261_290
00925njm 22002777a 4500
dc
Montbrió, Ernest
author
Pazó, Diego
author
Roxin, Alex
author
2015
A major goal of neuroscience, statistical physics, and nonlinear dynamics is to understand how brain function arises from the collective dynamics of networks of spiking neurons. This challenge has been chiefly addressed through large-scale numerical simulations. Alternatively, researchers have formulated mean-field theories to gain insight into macroscopic states of large neuronal networks in terms of the collective firing activity of the neurons, or the firing rate. However, these theories have not succeeded in establishing an exact correspondence between the firing rate of the network and the underlying microscopic state of the spiking neurons. This has largely constrained the range of applicability of such macroscopic descriptions, particularly when trying to describe neuronal synchronization. Here, we provide the derivation of a set of exact macroscopic equations for a network of spiking neurons. Our results reveal that the spike generation mechanism of individual neurons introduces an effective coupling between two biophysically relevant macroscopic quantities, the firing rate and the mean membrane potential, which together govern the evolution of the neuronal network. The resulting equations exactly describe all possible macroscopic dynamical states of the network, including states of synchronous spiking activity. Finally, we show that the firing-rate description is related, via a conformal map, to a low-dimensional description in terms of the Kuramoto order parameter, called Ott-Antonsen theory. We anticipate that our results will be an important tool in investigating how large networks of spiking neurons self-organize in time to process and encode information in the brain.
Physical Review X 5(2): 021028 (2015)
http://hdl.handle.net/10261/140032
10.1103/PhysRevX.5.021028
http://dx.doi.org/10.13039/501100003329
Macroscopic description for networks of spiking neurons