Math 427K-H   Homework 9    Due Thrusday April 16, 2009



1.  Find and classify the fixed points for the system


  x' = (2 - x)(y-x),  y' = (4-x)(y+x).


2. Find and classify the fixed points for the system

   x' = (1 - y), y' = x^2 - y^2.



3. The system

  x' = -y, y' = -ay - x(x - .15)(x-2)

results from an approximation of the Hodgkin-Huxley equations for nerve
impulses.


Find the fixed points and classify their stability.


4. Find the fixed points for the system

x' = 2(y/(1+y))x - x.

y' = -(y/(1+y)) x - y + 2.


5.  Classify the fixed points that you found in problem 4.  (Note that this
is a model for a chemostat.)