#' The duffing map.
#'
#' @param n Number of points in the time series.
#' @param xi The initial value for x
#' @param yi The initival value for y
#' @param a The value of the parameter a
#' @param b The value of the parameter b
#' @param add.timestep Add a column indicating the time step?
#' @param plot Plot the time series?
#' @return A n-by-2 data frame containing the values of the x and y components.
#' @export
duffing_map <- function(n = 1000,
xi = 1,
yi = 1,
a = 2.75,
b = 0.2,
add.timestep = FALSE,
plot = FALSE) {
x = vector(length = n)
y = vector(length = n)
x[1] = xi
y[1] = yi
for (i in 2:n) {
x[i] = y[i - 1]
y[i] = -b * x[i - 1] + a * y[i - 1] - y[i - 1]^3
}
if (add.timestep) {
timestep = 1:n
df = data.frame(timestep, x, y)
names(df) = c("t", "x", "y")
} else {
df = data.frame(x, y)
names(df) = c("x", "y")
}
if (plot & add.timestep) {
p = ggplot2::ggplot() +
ggplot2::geom_line(data = df, mapping = ggplot2::aes(x = t, y = x, col = "x")) +
ggplot2::geom_line(data = df, mapping = ggplot2::aes(x = t, y = y, col = "y")) +
ggplot2::theme_bw() +
ggplot2::ylab("value") +
ggplot2::ggtitle("Duffing map (forced oscillator with nonlinear elasticity)")
print(p)
} else if (plot & !add.timestep) {
warning("cannot plot without adding timestep.")
}
return(df)
}
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