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Homework 9
Geog210a
Due: December 9, 2011
Problems from text
:
12.6.15, Ch12rev5, 7 & 8
DV Problems:
1.
Find the eigenvalues and eigenvectors for the following matrices.
Please solve these by hand and
check your answers using MATLAB.
For d) use MATLAB only (look at the help page to make
sure you get the eigenvectors right [row vs. column]).
a.
!
=
1
−
2
0
3
b.
!
=
2
0
−
3
1
c.
!
=
4
1
−
2
2
d.
A = [3 2 1 0; 2 4 1 0; 0 0 1 0; 0.5 0.5 0 1];
2.
As we showed in class, the logistic difference system x
n+1
=
ε
x
n
(1 – x
n
) shows stable, periodic and
chaotic behaviors as the value of
ε
changes (see http://en.wikipedia.org/wiki/Logistic_map). The
Ricker difference system also shows transitions among these behaviors but does not have the same
sensitivity to initial conditions (like when x
n
= 1).
The Ricker system is widely used in ecological
and demographic theories to account for density dependence on rates and has the form…
x
n+1
= x
n
exp(
ε
(1 – x
n
))
a)
Plot out examples of the evolution of x
n
for several different values of
ε
(ranging from say 1
to 4) using MATLAB.
Note there is an example of the logistic system available online at
the class website to look at. That said, try to start from the beginning and own it yourself.
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 Fall '09
 Davey

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