Q1. (a) Identify the stable, unstable and center eigenspaces for the following
system.
x1
3
00
0
x1
x2 1 1 0
0 x2
=
x3 0
0 1 2 x3
x4
0
0 5 1
x4
Then give the normal form equations for this system.
(b) Prove that the following dynamical system in the
MATH3101 BIFURCATION AND CHAOS First Semester Examination, June,
2009
Q1. (a) Identify the stable, unstable and
system.
x1
2
x2 = 0
x3
0
center eigenspaces for the following
0
0
x1
1 3 x2
1 1
x3
Then give the normal form equations for this system.
(8 ma
MATH3101 BIFURCATION AND CHAOS Final Exam, Semester 1, 2010
Q1. Identify the stable, unstable and center eigenspaces for the following system.
2 0 7
x1 (t)
0 x,
x= 0 0
where
x = x2 (t)
10
1
x3 (t)
0
2 what is x(t)?
If initially x(0) =
0
Give the normal