MAT 431 - WINTER 2012
Project 1
Ryan Szypowski
Due February 12, 2013
Instructions
In this project, you will study a particular model of a shery. The mathematical details are
given in Strogatz question
MAT 431 - WINTER 2013
Homework 4 Solutions
Ryan Szypowski
Due March 7, 2013
1. Prove that the system
x = x y x(x2 + y 2 )
y = x + y y(x2 + y 2 )
has a closed orbit for any > 0 using the Poincar-Bendix
MAT 431 - WINTER 2012
Project 2
Ryan Szypowski
Due March 14, 2013
Instructions
In this project, you will study a particular model of a chemical oscillator. The mathematical
details are given in Stroga
MAT 431 - WINTER 2013
Homework 3 Solutions
Ryan Szypowski
Due Feb 26, 2013
1. Let f : R2 R be dened by
f (x, y) = x4 2x2 + y 4 2y 2 .
(a) Find and classify all xed points of the system
f
x
f
y =
y
x
MAT 431 - WINTER 2013
Homework 4
Ryan Szypowski
Due March 7, 2013
1. Prove that the system
x = x y x(x2 + y 2 )
y = x + y y(x2 + y 2 )
has a closed orbit for any > 0 using the Poincar-Bendixson theore
MAT 431 - WINTER 2012
Homework 1 Solutions
Ryan Szypowski
Due January 24, 2013
1. For each of the following, nd and classify all xed points. Use both linear stability
analysis (in the cases where it w
MAT 431 - WINTER 2012
Homework 2
Ryan Szypowski
Due Feb 5, 2013
1. For each of the following linear systems, classify the single xed point at the origin.
Then, sketch a few solution curves in the phas
MAT 431 - WINTER 2013
Homework 2 Solution
Ryan Szypowski
Due Feb 5, 2013
1. For each of the following linear systems, classify the single xed point at the origin.
Then, sketch a few solution curves in
MAT 431 - WINTER 2012
Homework 3
Ryan Szypowski
Due Feb 26, 2013
1. Let f : R2 R be dened by
f (x, y) = x4 2x2 + y 4 2y 2 .
(a) Find and classify all xed points of the system
f
x
f
y =
y
x =
then sk
MAT 431 - WINTER 2012
Homework 1
Ryan Szypowski
Due January 24, 2013
1. For each of the following, nd and classify all xed points. Use both linear stability
analysis (in the cases where it works), as