Sunday, January 6, 2019

Lorenz model describes the dynamics of three state variables, -R

Lorenz model describes the dynamics of three state variables, X, Y and Z

> Lorenz <- function (t, y, parms) {
+     with(as.list(c(y, parms)), {
+         dX <- a * X + Y * Z
+         dY <- b * (Y - Z)
+         dZ <- -X * Y + c * Y - Z
+         return(list(c(dX, dY, dZ)))
+     })
+ }
> parms <- c(a = -8/3, b = -10, c = 28)
> yini <- c(X = 1, Y = 1, Z = 1)
> times <- seq(from = 0, to = 100, by = 0.01)
> out <- ode(y = yini, times = times, func = Lorenz, parms = parms)
>
> plot(out, lwd = 2)
> plot(out[,"X"], out[,"Y"],
+      type = "l", xlab = "X",
+      ylab = "Y", main = "butterfly")

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