MATLAB Code

The Logistic Map (y=h*y*(1-y))

Conduct 4000 runs of the logistic map going through 1000 timesteps each, with each run using a different h parameter value from 0 to 4 in steps of .001 From each run, save the last 40 values of y (which will be kept track of with variable x). And then plot them all to show the classic bifurcation plot of the logistic map.

The following English instructions should be translated into matlab code:

clear all variables

start a for loop where h goes from

1 to 4000,

set your saved- value counter, x, to zero

set the iterated value, y, to start at a random number between 0 and 1

start a for loop where t (for timestep) goes from 1 to 1000

iterate the new value of y using the logistic map equation

(e.g.,y=h*y*(1-y)) (but make sure h is scaled to a range of .001 to 4, not 1 to 4000)

if the timestep variable is greater than 960, increment x up by 1 because we're saving these y values

save y in a matrix with h rows and x columns

bring if statement to an end

bring timestep loop to an end

bring h loop to an end

plot the matrix with all h rows and all x columns

(you may need to adjust the MarkerSize to get small dots)