Victor Camocho
math2250fall2011-2
WeBWorK assignment number Homework 14 is due : 12/08/2011 at 11:00pm MST.
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1. (1 pt) hw14/p1.pg
Find all critical points of the following system. List them in ascending order by x-value and then by y-value. Find the Jacobian
matrix of the system about each equilibrium and calculate the
eigenvalues of each to determine the type of each equilibrium
point.
dx
dt
dy
dt
1.
(
,
) ?
2.
(
,
) ?
3.
(
,
) ?
3. (1 pt) hw14/p3.pg
In the following system there are an infinite number of critical
points. However, there are only two types of critical points that
appear. What are the two types? (Note: List your answers in
alphabetical order).
= 6x − 5y + x2
= 2x − y + y2
dx
dt
dy
dt
1.
?
2.
4.
(
,
= y2 − y
= − sin(x)
?
) ?
4. (1 pt) hw14/p6.pg
The following system models a predator-prey system where x(t)
is the prey population over time and y(t) is the predator population over time.
2. (1 pt) hw14/p2.pg
Find all critical points of the following system. List them in ascending order by x-value and then by y-value. Find the Jacobian
matrix of the system about each equilibrium and calculate the
eigenvalues of each to determine the type of each equilibrium
point.
dx
dt
dy
dt
1.
(
,
) ?
2.
(
,
) ?
3.
(
,
) ?
dx
dt
dy
dt
=
x + y − xy2
= −3x − y + x2 y
= 200x − 4xy
= −400y + 2xy
Find the critical points and the types of each critical point
for this system. Record the critical points in ascending order by
x-value.
1.
1
(
,
) ?
2.
(
,
) ?
What will happen to the species in this system over time? ?
c
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