Math 3321
Homework 7
1. Find the steady states of each of the following systems, and classify each one as a
sink, a source, a saddle, or neither.
a.
()
()
'4
'5 2
uu uv
vv uv
=โโ
=โโ
b.
()
()
'93
'5
uu uv
vv uv
=โโ
=โโ
c. 2
'3
'
uvu
vuv
=โ
=โ
2. Create a phase plot for each of the systems in the problem above. Make sure your
plots include sufficient information to see the behavior near all steady states of the
systems. The software at http://math.rice.edu/~dfield/dfpp.html might be helpful.
3. Do a complete analysis of the behavior of steady states for the Brusselator (given
in class) depending upon the parameter values a and b.
4. Section 6.1 โ Problems 2-26 even.
5. Section 3.5 โ Problems 2-10 even.
6. Section 3.6 โ Problems 2, 4, 5, 6, 8.
