Pawesuppressl Lorek, University of Ottawa, MAT 1330D, Winter 2009
Assignment 2, due March 4, 17:30 in class
Student Name
Student Number
Problem 1:
[4 points] Consider the following DTDS:
M
t
+1
=
8
M
2
t
15 +
M
2
t
Analyze this DTDS, i.e., determine the biologically relevant fixed points (i.e. equilibria)
and their stability. Draw the updating function and use cobwebbing to illustrate and
confirm your analytical results.
Problem 2:
[8 points]
Consider the following nonlinear DTDS for growing population with harvesting:
x
t
+1
=
f
(
x
t
) = 4
x
t
(3

x
t
)

hx
t
,
where
h
≥
0 denotes the intensity of harvesting.
(a) [4p] Analyze this DTDS, i.e., determine the biologically relevant fixed points and
their stability. Summarize your results in the form of a little table:
range of
h
fixed point(s)
stability
(b) [2p] Draw the updating function and use cobwebbing for
h
= 10
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 Fall '08
 DUMITRISCU
 Calculus, Logic, Critical Point, Derivative, Mathematical analysis, Pawel Lorek, relevant ﬁxed points

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