MATH 4309: Mathematical Biology
Quiz 7
Due Date: February 27 by 5pm
Send to josic@math.uh.edu
Use subject MATH 4309: Quiz 7
1. Use pplane to examine the phase portrait for the Morris-Lecar model at the
parameter values given in Exercise 5.9.
2. Draw three phase planes corresponding to values of mu< 0, mu =0, and mu > 0
for the system given by Eq. 5.22 in the book. You can use pplane to examine this
system.
3. Consider a 2 by 2 matrix, and let T stand for the trace of the matrix, and D for the
determinant. Show that eigenvalues of the matrix are roots of the polynomial
x^2 – T x + D
4. Consider the linear system x’ = Ax, where A is the 2x2 matrix given below. How
does the phase diagram change a is increased from 1 to 3? You can use pplane to
explore this – however, you need to give a written explanation for the changes you
observe.
5. What part of the reading did you find the most confusing?