R/data.R

In magi: MAnifold-Constrained Gaussian Process Inference

#' Dataset of noisy observations from the FitzHugh-Nagumo (FN) equations
#'
#' @description 
#' The classic FN equations model the spike potentials of neurons, where system components \eqn{V} and \eqn{R} are the voltage and recovery variables, respectively.
#' 
#' \eqn{V} and \eqn{R} are governed by the following differential equations:
#'
#' \deqn{ \frac{dV}{dt} = c(V-\frac{V^3}{3}+R) }
#' \deqn{ \frac{dR}{dt} = -\frac{1}{c}(V-a+bR) }
#' 
#' where \eqn{\theta = (a,b,c)} are system parameters.
#' This dataset was generated by first numerically solving these ODEs from \eqn{t=0} to \eqn{t=20}, with initial conditions \eqn{V(0) = -1} and \eqn{R(0) = 1} and parameters \eqn{\theta = (0.2, 0.2, 3)}.
#' The system components were taken to be measured at 28 observation time points (as indicated in \code{time} column) with additive Gaussian noise (standard deviation 0.2).
#'
#' @format A data frame with 28 rows and 3 columns (time, \eqn{V}, \eqn{R}).
#' @references
#' FitzHugh, R (1961). Impulses and Physiological States in Theoretical Models of Nerve Membrane. \emph{Biophysical Journal}, 1(6), 445–466.
#'
#' @usage
#' data(FNdat)

"FNdat"