This is code simulates the dynamics of neuronal ensembles using the model of FREs and QIF neurons.
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:
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. https://doi.org/10.1103/PhysRevX.5.021028