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Simulations of the dynamics of neuronal ensembles using the model of FREs and QIF neurons.
R Mathematica C++ Python
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FREs and QIF neurons simulations

This is code simulates the dynamics of neuronal ensembles using the model of FREs and QIF neurons.

FREs (macroscopic model)

The macroscopic dynamics of neuronal ensembles are studied using the the firing-rate equations (FREs). The equations and model descriptions can be found in [1].

The code, fre_ode_solve.R, plots the firing rate r, the mean membrane potential v, and the external current stimulus I(t). Below we can see both the system behaviour under a square and a sinusoidal external current:

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QIF (microscopic model)

The quadratic integrate-and-fire (QIF) neurons is the canonical model for class I neurons, and, thus, generically describes their dynamics near the spiking threshold. Our aim here is to derive the FREs corresponding to a heterogeneous all-to-all coupled population of N QIF neurons.

The code, qif_solve_cpp_from_file.R (which can used precompiled QIF neurons using C++; or compile them from qif_solve.cpp), plots the mean membrane potential v and mean fire-rate r (from the FREs); the instantaneous membrane potential and fire-rate (QIF neurons simulation); a raster plot of 300 randomly selected QIF neurons; and the external current stimulus I(t):



[1]: Montbrió, E., Pazó, D., & Roxin, A. (2015). Macroscopic description for networks of spiking neurons. Physical Review X,: 5(2), 1–14.

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