MATH 375T     Uhlenbeck     Computer Assignment  3     Due March 8


Use pplane and dfield to make plots to solve the following problems
on page 200-201.  When the problems says "sketch" you should make a
computer plot.  The programs dfield and pplane are directly available
from the homepage of Professor John Polking at Rice University. To use
them on the math department computers, go into mathlab and type either the
single word dfield, or the single word pplane. Type your equation into
the window that appears and click on the proceed button. Be sure that
you size the window properly to show interesting behavior. If you quit
the plot window, you will also quit dfield or pplane. Just leave it up. 




Problem 1(page 200) :  a)-d).  Use dfield to make plots of typical 
solutions to these equations.


Problem 2(page 200):  Problem 2  a)-d) Find the graphs either
by hand or using the computer. Draw your direction fields (arrows)
along the y axis of the graph (x=0).

 
Problem 7(page 201):  b) d) e) f) Use pplane to plot typical solutions to
these linear  systems of equations.  Explain when zero looks  stable.


Problem 4:   Experiment using pplane with the system of equations 
(for your choices choices of a > 0) 
 
          dx/dt  = 5x - 1.9axy - x^2
          dy/dt  = 5y  - axy - y^2.

Look for solutions in the first quadrant only for various choices of a> 0.
What happens when a is small? What happens when a is largish ( say about 2)
Play with values of a on the  computer to get a rough  estimate of the
bifurcation point between the two behaviors you observe. Suggestion:  Be sure
you see the limit point when a = 0.  This might involve changing the size of
the window.