Assignment 3 – Scripts and Discrete Time Dynamical Systems

Assignment 3 – Scripts and Discrete Time Dynamical Systems
Due Date: September 13, 2011
1. Write a script to simulate the following discrete time dynamical system. One interpretation for
this system is thinking of B as the number of bacteria in your body
. In each time step
half of the bacteria reproduce. However, due to treatment, h
bacteria are killed in each
time step.
2. Let h be 100. Simulate the system for
for 15 time steps. What
happens for both cases and why does there seem to be a problem with the model when
? In this case, what is the equilibrium value?
3. Simulate this dynamical system two more times with different values of h and . Record your
final values, number of time steps, what the system appears to be doing, and the equilibrium
BONUS: Write a line of code in your script that solves for the equilibrium value of the system for
any value of h. Include this line of code in your report for an extra point.
Answer the questions in bold from Lab 3.
Complete the assignment above and be sure to include answers to all questions and all the results from
your simulations.
Think through your answers very carefully. Make sure they are clear and complete.
Note: You do not need to include your actual scripts in this report.