lorenz.R

parameters <- c(a = -8/3, b = -10, c = 28)

state <- c(X = 1, Y = 1, Z = 1)

Lorenz<-function(t, state, parameters) {
  with(as.list(c(state, parameters)),{
    # rate of change
    dX <- a*X + Y*Z
    dY <- b * (Y-Z)
    dZ <- -X*Y + c*Y - Z
    
    # return the rate of change
    list(c(dX, dY, dZ))
  }) # end with(as.list ...
}

times <- seq(0, 100, by = 0.01)

library(deSolve)
library(ggplot2)
out <- ode(y = state, times = times, func = Lorenz, parms = parameters)

out_df = as.data.frame(out)
ggplot(data = out_df, aes(x = time, X)) + geom_line()
ggplot(data = out_df, aes(x = time, Y)) + geom_line()
ggplot(data = out_df, aes(x = time, Z)) + geom_line()
ggplot(data = out_df, aes(x = X, Z, color = time)) + geom_point()