[AMath 383] Homework Comments
Dear class,
A few comments about the homework due next week.
For the Romeo and Juliet model, when you nondimensionalize, be sure
that you pay attention to the wording. Use the same characteristic
scale for both R and J:
R = c_L R_tilde
J = C_L J_tilde
This is quite a lot like the example we did in class.
For the competition model problem, I was hoping to have pushed a little
further today in class. What I wanted to say is the following:
The x-nullcline consists of two lines, call them A and B. The
y-nullcline consists of two more lines, call them C and D. There are
four possible equilibria cases:
A intersects C
A intersects D
B intersects C
B intersects D
For the competition model, three of these are incredibly easy. But one
is not so easy, although it is still a simple linear system. Feel free
to use a computer to solve this system, either by solving the linear
system or by finding an approximate graphical solution. However, you
NEED to SHOW YOUR WORK. Don't just list the four equilibria--explain
which lines intersecting they come from.
Also, feel free to use the computer graphing tools to help you
understand and explore stability. At the same time, you need to EXPLAIN
and SHOW YOUR WORK why the equilibria are stable or unstable. (At this
point, you should be able to determine stability by identifying whether
all directions point toward the equilibrium or whether there is some
point nearby with a direction pointing away. You can use the Jacobian,
but you don't need to yet.)
Best wishes, and have a good weekend.
D. Brian Walton
AMath 383 Instructor
Guggenheim 408C
(206) 685-9298