TEXAS A&M UNIVERSITY
DEPARTMENT OF MATHEMATICS
MATH 308H
Test 3 (take home, due 11:10 on Dec 1)
On my honor, as an Aggie, I have neither given nor received unauthorized aid on this work.
Name (print):
1.
Analyse the nonlinear system
(
x0 = x(3 − x − y),
y 0 = y(x − 1).
(a) Find all critical points of the system.
(b) By linearizing the system around each critical point, find the type of each CP (stable/unstable, node/saddle/spiral/center). If you found any saddle points, find their
stable/unstable directions (eigenvectors).
(c) Sketch (by hand) the global phase portrait of the system (positive quadrant only).
(d) Use Matlab to plot the direction field and few representative solutions.
2.
Perform the same analysis for the system
(
x0 = x(4 − x − 2y),
y 0 = y(7 − y − 3x).