In Example 1 we used Lotka-Volterra equations to model populations of rabbits and wolves. Let's modify those equations as follows: dR dt dW dt Answer= 0.07R(1-0.00025R) - 0.001 RW -0.04W+0.00004 RW Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R, W), where R is the number of rabbits and W the number of wolves. For example, if you found three equilibrium solutions, one with 100 rabbits and 10 wolves, one with 200 rabbits and 20 wolves, and one with 300 rabbits and 30 wolves, you would enter (100, 10), (200, 20), (300, 30). Do not round fractional answers to the nearest integer.
In Example 1 we used Lotka-Volterra equations to model populations of rabbits and wolves. Let's modify those equations as follows: dR dt dW dt Answer= 0.07R(1-0.00025R) - 0.001 RW -0.04W+0.00004 RW Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R, W), where R is the number of rabbits and W the number of wolves. For example, if you found three equilibrium solutions, one with 100 rabbits and 10 wolves, one with 200 rabbits and 20 wolves, and one with 300 rabbits and 30 wolves, you would enter (100, 10), (200, 20), (300, 30). Do not round fractional answers to the nearest integer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I put answer also with different variable. Just give me answer by putting my question variable. Thanku
![Given:
Step 2
de
dt
57
57
dR
dt
Equilibrium solutions
dw
dt
dw
dt
and
20
(ii) when
2 0.IR 1-0.0001 R ) - 0.003 RW
(R, W) =
= -0.01 W + 0.00004 RW
dk
d+
(i) when w=0
Hence,
0.00004 RW
0.01 W=0
W / 0.00004 R -0.01) =0
W =0
=>
-7
=>
30.
occur at the points.
(0,0) and (10,000, 0);
R = 250
=> R=0 d
0.00004 R = 0.01
R =
1000
។
0.1 R0.00001 RY -0.003 RW =0
0.1 R0.00001 RV =0
R (0.1-0.00001 R) =0
=7
(250, 32.5)
=> 0.1(250) - 0.00001(250) -0.003 (250) 0 =0
0.75 W = 24.375
W = 32.5
equilibrium
where
[de =0]
0.00001 R = 0.1
=> R = 10,000.
solutions
= 250.
are
(0,0), (10,000,0) and (250, 32.5)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81d21141-6551-4f5f-aede-0a79467fdc0f%2F3596e5fd-fd6c-49c9-969f-223937a35202%2Fsseuvj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given:
Step 2
de
dt
57
57
dR
dt
Equilibrium solutions
dw
dt
dw
dt
and
20
(ii) when
2 0.IR 1-0.0001 R ) - 0.003 RW
(R, W) =
= -0.01 W + 0.00004 RW
dk
d+
(i) when w=0
Hence,
0.00004 RW
0.01 W=0
W / 0.00004 R -0.01) =0
W =0
=>
-7
=>
30.
occur at the points.
(0,0) and (10,000, 0);
R = 250
=> R=0 d
0.00004 R = 0.01
R =
1000
។
0.1 R0.00001 RY -0.003 RW =0
0.1 R0.00001 RV =0
R (0.1-0.00001 R) =0
=7
(250, 32.5)
=> 0.1(250) - 0.00001(250) -0.003 (250) 0 =0
0.75 W = 24.375
W = 32.5
equilibrium
where
[de =0]
0.00001 R = 0.1
=> R = 10,000.
solutions
= 250.
are
(0,0), (10,000,0) and (250, 32.5)
Transcribed Image Text:In Example 1 we used Lotka-Volterra equations to model populations of rabbits and wolves. Let's modify those equations
as follows:
dR
dt
dW
dt
Answer=
0.07R(1-0.00025R) - 0.001 RW
-0.04W+0.00004 RW
Find all of the equilibrium solutions.
Enter your answer as a list of ordered pairs (R, W), where R is the number of rabbits and W the number of wolves. For
example, if you found three equilibrium solutions, one with 100 rabbits and 10 wolves, one with 200 rabbits and 20 wolves,
and one with 300 rabbits and 30 wolves, you would enter (100, 10), (200, 20), (300, 30). Do not round fractional answers
to the nearest integer.
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