USING MATLAB:

Use the logistic equation, given by:

Ti ari-1 ari 1) [x(i) = ax(i-1)(1-x(i-1))]

OR

x_t = ax_{t-1}(1-x_{t-1}) [x(t) = ax(t-1)(1-x(t-1))]

to demonstrate the following properties (using Matlab).

a. Sensitivity to a (very) small change in initial condition (in the Chaotic Regime)

b. Quantify how the average of 10 randomly selected paths of close neighboring initial points diverges in different regimes (i.e. check this for values of parameter a < 3, between 3 and 3.4495, and above this value). Plot the average divergence against the value of parameter a.

c. Failure of autocorrelation in detecting a relationship

d. Success of the return plot in detecting a relationship

e. Interpret your findings