I have been trying to execute this code but it won't produce any output no matter what I need to get the figures I am trying to show down here import numpy as np from scipy integrate import solve ivp import matplotlib pyplot as plt Parameters sigma 1 0 r 2 8 b 8 3 Lorenz system def lorenz ( t , state, reverse False ) x , y , z state dxdt sigma ( y x ) dydt x ( r z ) y dzdt x y b z return dxdt , dydt , dzdt if reverse else dxdt , dydt , dzdt Initial conditions for the unstable manifold of the origin initial conditions o 0 0 1 , 0 0 1 , 0 0 1 Small perturbation Initial conditions for the stable manifolds initial conditions c plus np sqrt ( b ( r 1 ) ) 0 0 1 , np sqrt ( b ( r 1 ) ) 0 0 1 , r 1 initial conditions c minus np sqrt ( b ( r 1 ) ) 0 0 1 , np sqrt ( b ( r 1 ) ) 0 0 1 , r 1 Time span for integration t span ( 0 , 5 0 ) t eval np linspace ( t span 0 , t span 1 , 1 0 0 0 0 ) Solve the system for the unstable manifold of the origin solution o solve ivp ( lorenz , t span, initial conditions o , t eval t eval, method ' RK 4 5 ' ) Solve the system for the stable manifold of C ( reverse time ) solution c plus solve ivp ( lorenz , t span, initial conditions c plus, t eval t eval, method ' RK 4 5 ' , args ( True , ) ) Solve the system for the stable manifold of C ( reverse time ) solution c minus solve ivp ( lorenz , t span, initial conditions c minus, t eval t eval, method ' RK 4 5 ' , args ( True , ) ) Plot the results fig plt figure ( ) ax fig add subplot ( 1 1 1 , projection ' 3 d ' ) ax plot ( solution o y 0 , solution o y 1 , solution o y 2 , label 'Unstable Manifold of O ' ) ax plot ( solution c plus y 0 , solution c plus y 1 , solution c plus y 2 , label 'Stable Manifold of C ' ) ax plot ( solution c minus y 0 , solution c minus y 1 , solution c minus y 2 , label 'Stable Manifold of C ' ) ax set xlabel ( ' X ' ) ax set ylabel ( ' Y ' ) ax set zlabel ( ' Z ' ) plt title ( ' Manifolds in the Lorenz System' ) plt legend ( ) plt show ( ) import numpy as np from scipy integrate import solve ivp import matplotlib pyplot as plt Parameters sigma 1 0 r 2 8 b 8 3 Lorenz system def lorenz ( t , state, reverse False ) x , y , z state dxdt sigma ( y x ) dydt x ( r z ) y dzdt x y b z return dxdt , dydt , dzdt if reverse else dxdt , dydt , dzdt Initial conditions for the unstable manifold of the origin initial conditions 0 0 0 1 , 0 0 1 , 0 0 1 Small perturbation Initial conditions for the stable manifolds initial conditions c plus np sqrt ( b ( r 1 ) ) 0 0 1 , np sqrt ( b ( r 1 ) ) 0 0 1 , r 1 initial conditions c minus np sqrt ( b ( r 1 ) ) 0 0 1 , np sqrt ( b ( r 1 ) ) 0 0 1 , r 1 Time span for integration t span ( 0 , 2 0 ) t eval np linspace ( t span 0 , t span 1 , 5 0 0 0 ) Solve the system for the unstable manifold of the origin solution 0 solve ivp ( lorenz , t span, initial conditions o , t eval t eval, method ' RK 4 5 ' ) Solve the system for the stable manifold of C ( reverse time ) solution c plus solve ivp ( lorenz , t span, initial conditions c plus, t eval t eval, method ' RK 4 5 ' , args ( True , ) ) Solve the system for the stable manifold of C ( reverse time ) solution c minus solve ivp ( lorenz , t span, initial conditions c minus, t eval t eval, method ' RK 4 5 ' , args ( True , ) ) Plot the results fig plt figure ( ) ax fig add subplot ( 1 1 1 , projection ' 3 d ' ) ax plot ( solution o y 0 , solution o y 1 , solution o y 2 , label 'Unstable Manifold of 0 ' ) ax plot ( solution c plus y 0 , solution c plus y 1 , solution c plus y 2 , label 'stable Manifold of C ' ) ax plot ( solution c minus y 0 , solution c minus y 1 , solution c minus y 2 , label 'stable Manifold of C ' ) ax set xlabel ( ' X ' ) ax set ylabel ( ' Y ' ) ax set zlabel ( ' Z ' ) plt title ( ' Manifolds in the Lorenz System' ) plt legend ( ) plt show ( )

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Question: I have been trying to execute this code but it won't produce any output no matter what. I need to get the figures I am

I have been trying to execute this code but it won't produce any output no matter what. I need to get the figures I am trying to show down here:

import numpy as np

from scipy.integrate import solve

_

ivp

import matplotlib.pyplot as plt

# Parameters

sigma

= 10

= 28

= 8 / 3

# Lorenz system

def lorenz

(

,

state, reverse

=

False

)

,

,

=

state

dxdt

=

sigma

* (

-

)

dydt

=

* (

-

) -

dzdt

=

*

-

*

return

[-

dxdt

, -

dydt

, -

dzdt

]

if reverse else

[

dxdt

,

dydt

,

dzdt

]

# Initial conditions for the unstable manifold of the origin

initial

_

conditions

_

= [0.01, 0.01, 0.01]

# Small perturbation

# Initial conditions for the stable manifolds

initial

_

conditions

_

_

plus

= [

.

sqrt

(

* (

- 1)) + 0.01,

.

sqrt

(

* (

- 1)) + 0.01,

- 1]

initial

_

conditions

_

_

minus

= [-

.

sqrt

(

* (

- 1)) + 0.01, -

.

sqrt

(

* (

- 1)) + 0.01,

- 1]

# Time span for integration t

_

span

= (0, 50)

_

eval

=

.

linspace

(

_

span

[0],

_

span

[1], 10000)

# Solve the system for the unstable manifold of the origin

solution

_

=

solve

_

ivp

(

lorenz

,

_

span, initial

_

conditions

_

,

_

eval

=

_

eval, method

='

45')

# Solve the system for the stable manifold of C

+ (

reverse time

)

solution

_

_

plus

=

solve

_

ivp

(

lorenz

,

_

span, initial

_

conditions

_

_

plus, t

_

eval

=

_

eval, method

='

45',

args

= (

True

,))

# Solve the system for the stable manifold of C

- (

reverse time

)

solution

_

_

minus

=

solve

_

ivp

(

lorenz

,

_

span, initial

_

conditions

_

_

minus, t

_

eval

=

_

eval, method

='

45',

args

= (

True

,))

# Plot the results fig

=

plt

.

figure

()

=

fig.add

_

subplot

(111,

projection

=' 3

')

.

plot

(

solution

_

.

[0],

solution

_

.

[1],

solution

_

.

[2],

label

=

'Unstable Manifold of O

')

.

plot

(

solution

_

_

plus.y

[0],

solution

_

_

plus.y

[1],

solution

_

_

plus.y

[2],

label

=

'Stable Manifold of C

+')

.

plot

(

solution

_

_

minus.y

[0],

solution

_

_

minus.y

[1],

solution

_

_

minus.y

[2],

label

=

'Stable Manifold of C

-')

.

set

_

xlabel

('

')

.

set

_

ylabel

('

')

.

set

_

zlabel

('

')

plt

.

title

('

Manifolds in the Lorenz System'

)

plt

.

legend

()

plt

.

show

() ` ` `

import numpy as np

from scipy.integrate import solve

_

ivp

import matplotlib.pyplot as plt

# Parameters

sigma

= 10

= 28

= 8 / 3

# Lorenz system

def lorenz

(

,

state, reverse

=

False

)

,

,

=

state

dxdt

=

sigma

* (

-

)

dydt

=

* (

-

) -

dzdt

=

*

-

*

return

[-

dxdt

, -

dydt

, -

dzdt

]

if reverse else

[

dxdt

,

dydt

,

dzdt

]

# Initial conditions for the unstable manifold of the origin

initial

_

conditions

_0 = [0.01, 0.01, 0.01]

# Small perturbation

# Initial conditions for the stable manifolds

initial

_

conditions

_

_

plus

= [

.

sqrt

(

* (

- 1)) + 0.01,

.

sqrt

(

* (

- 1)) + 0.01,

- 1]

initial

_

conditions

_

_

minus

= [-

.

sqrt

(

* (

- 1)) + 0.01, -

.

sqrt

(

* (

- 1)) + 0.01,

- 1]

# Time span for integration

_

span

= (0, 20)

_

eval

=

.

linspace

(

_

span

[0],

_

span

[1], 5000)

# Solve the system for the unstable manifold of the origin

solution

_0 =

solve

_

ivp

(

lorenz

,

_

span, initial

_

conditions

_

,

_

eval

=

_

eval, method

='

45')

# Solve the system for the stable manifold of C

+ (

reverse time

)

solution

_

_

plus

=

solve

_

ivp

(

lorenz

,

_

span, initial

_

conditions

_

_

plus, t

_

eval

=

_

eval, method

='

45',

args

= (

True

,))

# Solve the system for the stable manifold of C

- (

reverse time

)

solution

_

_

minus

=

solve

_

ivp

(

lorenz

,

_

span, initial

_

conditions

_

_

minus, t

_

eval

=

_

eval, method

='

45',

args

= (

True

,))

# Plot the results

fig

=

plt

.

figure

()

=

fig.add

_

subplot

(111,

projection

=' 3

')

.

plot

(

solution

_

.

[0],

solution

_

.

[1],

solution

_

.

[2],

label

=

'Unstable Manifold of

0')

.

plot

(

solution

_

_

plus.y

[0],

solution

_

_

plus.y

[1],

solution

_

_

plus.y

[2],

label

=

'stable Manifold of C

+')

.

plot

(

solution

_

_

minus.y

[0],

solution

_

_

minus.y

[1],

solution

_

_

minus.y

[2],

label

=

'stable Manifold of C

-')

.

set

_

xlabel

('

')

.

set

_

ylabel

('

')

.

set

_

zlabel

('

')

plt

.

title

('

Manifolds in the Lorenz System'

)

plt

.

legend

()

plt

.

show

()

` ` `

I have been trying to execute this code but it

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