User:Egm6341.s10.Team4.roni/HW7/7.4

= Problem 4: Discrete Population Dynamics - Logistic Map - Chaotic System - Period Doubling =

Given
Class notes and Pages 454-456 King et al 2003 - An Introduction to Chaotic Systems.

Given factor r -represents the growth from generation to the next [[media:Egm6341.s10.mtg39.djvu|39-3]]

Find
Run the given Code to reproduce plots 15.6 and 15.7 in King et al 2003.

Solution
 original Code

 Matlab Code: 

Plot 1 shows the results from running the original code



 Modification to the original Code

 Matlab Code: 

Plot 2 shows the results from running the modified code



Discussion:

From Plot 2 One can see that when r=4, a small change in the input of the initial x value would give apparently a random nature of solution and divergence after about 50 iterations. The 0 marker in blue are for x=0.1 starting point and the x markers in green are for x=0.1+1e-16. Initially (up to about 50 iterations) the x and o symbols fall one on to of the other (giving same solution) and diverging after about 50 iterations.

Author
Solved and typed by - Egm6341.s10.Team4.roni 18:49, 18 April 2010 (UTC) Proof read by -