Duffing oscillator
$begingroup$
I have to draw the phase space of this modification of Duffing oscillator:
begin{align}
dot x &= y,\
dot y &= x - x^3 - ay - (x^2)y quad text{ when } quad a=1 ; text{ and } ;a=5.
end{align}
I know that critical points are $(0, 0)$, $(-1, 0)$, and $(1, 0),$ and I have demonstrated that when $a =1$ I have a spiral the form $(pm1,0)$ and when $a = 5$ not.
Does someone know how to draw it?
Thank you.
ordinary-differential-equations
edited Jan 15 at 16:07
LutzL
60k42057
asked Jan 15 at 14:30
CastiCasti
61
$endgroup$
add a comment |
$begingroup$
I have to draw the phase space of this modification of Duffing oscillator:
begin{align}
dot x &= y,\
dot y &= x - x^3 - ay - (x^2)y quad text{ when } quad a=1 ; text{ and } ;a=5.
end{align}
I know that critical points are $(0, 0)$, $(-1, 0)$, and $(1, 0),$ and I have demonstrated that when $a =1$ I have a spiral the form $(pm1,0)$ and when $a = 5$ not.
Does someone know how to draw it?
Thank you.
ordinary-differential-equations
edited Jan 15 at 16:07
LutzL
60k42057
asked Jan 15 at 14:30
CastiCasti
61
$endgroup$
$begingroup$
Improve your question, pls.
$endgroup$
– Word Shallow
Jan 15 at 14:33
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Why did you revert back the edit made by Key Flex?
$endgroup$
– BigbearZzz
Jan 15 at 14:50
$begingroup$
Do you mean draw with a computer program or do a sketch by hand if no computer is available?
$endgroup$
– LutzL
Jan 15 at 16:11
add a comment |
$begingroup$
I have to draw the phase space of this modification of Duffing oscillator:
begin{align}
dot x &= y,\
dot y &= x - x^3 - ay - (x^2)y quad text{ when } quad a=1 ; text{ and } ;a=5.
end{align}
I know that critical points are $(0, 0)$, $(-1, 0)$, and $(1, 0),$ and I have demonstrated that when $a =1$ I have a spiral the form $(pm1,0)$ and when $a = 5$ not.
Does someone know how to draw it?
Thank you.
ordinary-differential-equations
edited Jan 15 at 16:07
LutzL
60k42057
asked Jan 15 at 14:30
CastiCasti
61
$endgroup$
I have to draw the phase space of this modification of Duffing oscillator:
begin{align}
dot x &= y,\
dot y &= x - x^3 - ay - (x^2)y quad text{ when } quad a=1 ; text{ and } ;a=5.
end{align}
I know that critical points are $(0, 0)$, $(-1, 0)$, and $(1, 0),$ and I have demonstrated that when $a =1$ I have a spiral the form $(pm1,0)$ and when $a = 5$ not.
Does someone know how to draw it?
Thank you.
ordinary-differential-equations
ordinary-differential-equations
edited Jan 15 at 16:07
LutzL
60k42057
asked Jan 15 at 14:30
CastiCasti
61
edited Jan 15 at 16:07
LutzL
60k42057
asked Jan 15 at 14:30
CastiCasti
61
edited Jan 15 at 16:07
LutzL
60k42057
edited Jan 15 at 16:07
LutzL
60k42057
edited Jan 15 at 16:07
LutzL
60k42057
60k42057
asked Jan 15 at 14:30
CastiCasti
61
asked Jan 15 at 14:30
CastiCasti
61
asked Jan 15 at 14:30
CastiCasti
61
61
$begingroup$
Improve your question, pls.
$endgroup$
– Word Shallow
Jan 15 at 14:33
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Why did you revert back the edit made by Key Flex?
$endgroup$
– BigbearZzz
Jan 15 at 14:50
$begingroup$
Do you mean draw with a computer program or do a sketch by hand if no computer is available?
$endgroup$
– LutzL
Jan 15 at 16:11
add a comment |
$begingroup$
Improve your question, pls.
$endgroup$
– Word Shallow
Jan 15 at 14:33
$begingroup$
Why did you revert back the edit made by Key Flex?
$endgroup$
– BigbearZzz
Jan 15 at 14:50
$begingroup$
Do you mean draw with a computer program or do a sketch by hand if no computer is available?
$endgroup$
– LutzL
Jan 15 at 16:11
$begingroup$
Improve your question, pls.
$endgroup$
– Word Shallow
Jan 15 at 14:33
$begingroup$
Improve your question, pls.
$endgroup$
– Word Shallow
Jan 15 at 14:33
$begingroup$
Why did you revert back the edit made by Key Flex?
$endgroup$
– BigbearZzz
Jan 15 at 14:50
$begingroup$
Why did you revert back the edit made by Key Flex?
$endgroup$
– BigbearZzz
Jan 15 at 14:50
$begingroup$
Do you mean draw with a computer program or do a sketch by hand if no computer is available?
$endgroup$
– LutzL
Jan 15 at 16:11
$begingroup$
Do you mean draw with a computer program or do a sketch by hand if no computer is available?
$endgroup$
– LutzL
Jan 15 at 16:11
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
This may help you
generated with python:
import numpy as np
import matplotlib.pyplot as plt
xmin, xmax = -2.0, 2.0
ymin, ymax = -1.0, 1.0
x, y = np.meshgrid(np.linspace(xmin, xmax, 30, endpoint = True), np.linspace(ymin, ymax, 30, endpoint = True))
a = 1
u = y
v = x - x**3 - a * y - x**2 * y
plt.streamplot(x, y, u, v)
plt.show()
answered Jan 15 at 15:11
caveraccaverac
14.8k31130
$endgroup$
$begingroup$
Thank you very much, your answer has been very helpful.
$endgroup$
– Casti
Jan 15 at 17:16
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
This may help you
generated with python:
import numpy as np
import matplotlib.pyplot as plt
xmin, xmax = -2.0, 2.0
ymin, ymax = -1.0, 1.0
x, y = np.meshgrid(np.linspace(xmin, xmax, 30, endpoint = True), np.linspace(ymin, ymax, 30, endpoint = True))
a = 1
u = y
v = x - x**3 - a * y - x**2 * y
plt.streamplot(x, y, u, v)
plt.show()
answered Jan 15 at 15:11
caveraccaverac
14.8k31130
$endgroup$
$begingroup$
Thank you very much, your answer has been very helpful.
$endgroup$
– Casti
Jan 15 at 17:16
add a comment |
$begingroup$
This may help you
generated with python:
import numpy as np
import matplotlib.pyplot as plt
xmin, xmax = -2.0, 2.0
ymin, ymax = -1.0, 1.0
x, y = np.meshgrid(np.linspace(xmin, xmax, 30, endpoint = True), np.linspace(ymin, ymax, 30, endpoint = True))
a = 1
u = y
v = x - x**3 - a * y - x**2 * y
plt.streamplot(x, y, u, v)
plt.show()
answered Jan 15 at 15:11
caveraccaverac
14.8k31130
$endgroup$
$begingroup$
Thank you very much, your answer has been very helpful.
$endgroup$
– Casti
Jan 15 at 17:16
add a comment |
$begingroup$
This may help you
generated with python:
import numpy as np
import matplotlib.pyplot as plt
xmin, xmax = -2.0, 2.0
ymin, ymax = -1.0, 1.0
x, y = np.meshgrid(np.linspace(xmin, xmax, 30, endpoint = True), np.linspace(ymin, ymax, 30, endpoint = True))
a = 1
u = y
v = x - x**3 - a * y - x**2 * y
plt.streamplot(x, y, u, v)
plt.show()
answered Jan 15 at 15:11
caveraccaverac
14.8k31130
$endgroup$
This may help you
generated with python:
import numpy as np
import matplotlib.pyplot as plt
xmin, xmax = -2.0, 2.0
ymin, ymax = -1.0, 1.0
x, y = np.meshgrid(np.linspace(xmin, xmax, 30, endpoint = True), np.linspace(ymin, ymax, 30, endpoint = True))
a = 1
u = y
v = x - x**3 - a * y - x**2 * y
plt.streamplot(x, y, u, v)
plt.show()
answered Jan 15 at 15:11
caveraccaverac
14.8k31130
answered Jan 15 at 15:11
caveraccaverac
14.8k31130
answered Jan 15 at 15:11
caveraccaverac
14.8k31130
answered Jan 15 at 15:11
caveraccaverac
14.8k31130
14.8k31130
$begingroup$
Thank you very much, your answer has been very helpful.
$endgroup$
– Casti
Jan 15 at 17:16
add a comment |
$begingroup$
Thank you very much, your answer has been very helpful.
$endgroup$
– Casti
Jan 15 at 17:16
$begingroup$
Thank you very much, your answer has been very helpful.
$endgroup$
– Casti
Jan 15 at 17:16
$begingroup$
Thank you very much, your answer has been very helpful.
$endgroup$
– Casti
Jan 15 at 17:16
add a comment |
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$begingroup$
Improve your question, pls.
$endgroup$
– Word Shallow
Jan 15 at 14:33
$begingroup$
Why did you revert back the edit made by Key Flex?
$endgroup$
– BigbearZzz
Jan 15 at 14:50
$begingroup$
Do you mean draw with a computer program or do a sketch by hand if no computer is available?
$endgroup$
– LutzL
Jan 15 at 16:11