FNdat {magi}R Documentation

Dataset of noisy observations from the FitzHugh-Nagumo (FN) equations

Description

The classic FN equations model the spike potentials of neurons, where system components VV and RR are the voltage and recovery variables, respectively.

VV and RR are governed by the following differential equations:

dVdt=c(VV33+R) \frac{dV}{dt} = c(V-\frac{V^3}{3}+R)

dRdt=1c(Va+bR) \frac{dR}{dt} = -\frac{1}{c}(V-a+bR)

where θ=(a,b,c)\theta = (a,b,c) are system parameters. This dataset was generated by first numerically solving these ODEs from t=0t=0 to t=20t=20, with initial conditions V(0)=1V(0) = -1 and R(0)=1R(0) = 1 and parameters θ=(0.2,0.2,3)\theta = (0.2, 0.2, 3). The system components were taken to be measured at 28 observation time points (as indicated in time column) with additive Gaussian noise (standard deviation 0.2).

Usage

data(FNdat)

Format

A data frame with 28 rows and 3 columns (time, VV, RR).

References

FitzHugh, R (1961). Impulses and Physiological States in Theoretical Models of Nerve Membrane. Biophysical Journal, 1(6), 445–466.


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