Calculus for the Life Science I
MAT1330A , MAT1330B, MAT1330E
Assignment 6
Due date: Oct. 28
Instructor (circle one):
Jing Li
,
Catalin Rada
,
Frithjof Lutscher
DGD (circle one):
1
,
2
,
3
,
4
Student Name (printed):
Student ID Number:
Question 1
An animal species is described by the discrete dynamical system
N
i
+1
= 1
.
5
N
i
(1

N
i
)

hN
i
,
i
= 0
,
1
,
2
,
3
, . . . ,
where
N
i
is the fraction of the maximal population after
i
years.
h
is the
harvesting
effort of
the predators.
a
)
Find the equilibrium points. One of these points will depend of
h
.
Equilibrium points :
b
)
Given the largest interval for
h
such that the equilibrium points in (
a
) have a biological
meaning.
Interval for
h
:
c
)
Find the
equilibrium
harvest
R
for this species as a function of
h
.
R
=
d
)
Determine the harvesting effort
h
that will maximize the equilibrium harvest.
h
=
e
)
Give the maximal equilibrium harvest.
R
=
f
)
Is the maximal equilibrium harvest stable or unstable ?
The maximal equilibrium harvest is (circle one)
stable
or
unstable
because
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 Rad
 Chemistry, Calculus, Chemical reaction

Click to edit the document details