## 2.3 Using R or Matlab to do the exercises.

The best (and easiest) way to simulate these simple models is to create a function which takes as input the parameters ($$Y_0$$, $$r$$) and a variable indicating the length of the time series.

For example for the Linear Map:

# In R
linearMap <- function(Y0 = 0, r = 1, N = 100){

# Initialize Y as an NA vector of size N with as first entry Y0
Y <- c(Y0, rep(NA,N-1))

for(i in 1:N){

Y[i+1] <- # Implement the function here

}

return(Y)
}

# In Matlab
function linearMap(Y0,r,N)
# Implement the function here
end

Creating the time series graphs and the return plot should be easy if the function linearMap returns the time series. Both R and Matlab have a plot() function you can call.1

1. Both R and Matlab have specialized objects to represent timeseries, and functions and packages for timeseries analysis. They are especially convenient for plotting time and date information on the X-axis. See Solutions: Mathematics of Change I