Math 375T Uhlenbeck Name____________________________________ Computer Assignment 2 Due Feb 23 Hand in the code and graphs which answer the question or illustrate the behavior of the equation. 1. Consider the equation x_(n) = .5*x(n-1) + sin(x(n-1)). Use the computer to find the stable fixed points of this equation.Be sure to make plots which approach from above and below the fixed points. 2.Write code to determine the behavior about the fixed point x = 0 of the difference equation x(n) = (x_(n-1))^2. Check solutions which start close to 0 which are both positive and negative. The next two problems assume that you have read and understood sections 2.3 to 2.5 (you don't need to read the part of 2.5 about webbing). The logistics equation is the equation x(n) = r*x(n-1)*(1 - x(n-1)). 3. Choose a value for r for which the logistics equations have a stable fixed point which the solutions oscillate around as they approach it. Use your matlab code to illustrate this with a plot. Now choose a value for r which has a stable points of period 2 and illustrate this with a plot. 4. Same as problem 3, but illustrate a choice of r with stable period points of period greater than 2, and a choice of r in which the behavior of the solutions is chaotic. 5. Use what you learned about writing code for one equation to have the computer plot a solutions of a system x(i) = 2*x(i-1))- .1* x(i-1)*y(i-1) - .01*(x(i-l))^2; y(i) = .9*y(i-1) + .01*x(i-1)*y(i-1); and plot as a curve in the (x,y) plane. Start with initial values near (0,0), close to the fixed point, and large initial values. Explain what happens (you can write this below the plots).