USING MATLAB: Use the logistic equation, given by: OR to demonstrate the followi

Question

USING MATLAB:

Use the logistic equation, given by:

OR

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

Explanation / Answer

A normal distribution, sometimes called the bell curve, is a distribution that occurs naturally in many situations. For example, the bell curve is seen in tests like the SAT and GRE. The bulk of students will score the average (C), while smaller numbers of students will score a B or D. An even smaller percentage of students score an F or an A. This creates a distribution that resembles a bell (hence the nickname). The bell curve is symmetrical. Half of the data will fall to the left of the mean; half will fall to the right.
Many groups follow this type of pattern. That’s why it’s widely used in business, statistics and in government bodies like the FDA:

The empirical rule tells you what percentage of your data falls within a certain number of standard deviations from the mean:
• 68% of the data falls within one standard deviation of the mean.
• 95% of the data falls within two standard deviations of the mean.
• 99.7% of the data falls within three standard deviations of the mean.

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