M331 Introduction to Mathematical Modeling

Problem Set 2: Modeling with Difference Equations

Please type all problems with extensive verbal anwers. Due Friday September 22, 2000.

1. Section 3.2 Problem 1.
2. Section 3.2 Problem 4.
3. Section 3.2 Problem 8.
4. Section 3.2 Problem 11.
5. Determine the general solution to the second order difference equation
   $$x_{n+2} = x_{n+1} + x_n +1$$
   Are there any equilibrium points? Are they stable?
6. Consider the difference equation model
   $$x_{n+1} = x_n + 10x_n(5-x_n)(10-x_n)$$
   What are the equilibrium points? Argue whether they are stable or not by plotting $\Delta x_n$ versus $x_n$.