You should use pplane5 in MATLAB, or the web based phase plane plotter to do this assignment.

Study the system

You should take the parameters a and b from the tables below, using the last 2 digits of your social security number.

1. Describe the stable trajectory in the phase plane. Note that by graphing the nullclines, you should be able to give a piecewise polynomial which is a very good approximation.

2. Describe the trajectory starting from an arbitrary initial point to the stable trajectory. Again, you should be able to give a piecewise polynomial which is a very good approximation. Note that this will depend upon where you start.

3. Describe the speeds at which the parts of the stable trajectory are traversed. You can do this by looking at the graphs of x and y against time, to determine how long the system spends in each of the sections of the piecewise polynomial you produced in problem 1.

4. What is the period of the oscillation, and what are the x and y amplitudes?

You should be able to estimate the values required to roughly two digits of accuracy.

Include a graph of the phase plane, and of x and y against time for reference.

WARNING: Sometimes the computer is wrong. In particular, it will sometimes stop prematurely, especially when a trajectory is evolving very slowly. Trust consistency. Also, you know the vector field, so can detect some problems from this.

To get the parameters a and B, let A and B be the last two digits in your social security number, (i.e., write it as XXX-XX-XXAB), then use A and B to look up the right values for a and b.