Matplotlib Animation of Streamplot of Bifurcation

Question

I am currently trying to animate the dynamics of a typical saddle node bifurcation ode: dx/dt = r + x^2. Snapshots at specific values of r are realised with the streamplot function from r = -1 to 1. Unfortunately the init function and the animate function are not working properly because .set_array does not work for streamplots. I am also not sure how to update the streams at each iteration in the animate function. My question is how I should modify the animate and init function so that the funcanimation function gives a proper animated plot of the flows.

import matplotlib.pyplot as plt
import numpy as np
import matplotlib.animation as animation


nx, ny = .02, .02
x = np.arange(-15, 15, nx)
y = np.arange(-10, 10, ny)
X, Y = np.meshgrid(x, y)
dy = -1 + Y**2
dx = np.ones(dy.shape)

dyu = dy / np.sqrt(dy**2 + dx**2)
dxu = dx / np.sqrt(dy**2 + dx**2)


color = dyu
fig, ax = plt.subplots()
stream = ax.streamplot(X,Y,dxu, dyu, color=color, density=2, cmap='jet',arrowsize=1)
ax.set_xlabel('t')
ax.set_ylabel('x')

def init():
stream.set_array([])
return stream

def animate(iter):
    dy = -1 + iter * 0.01 + Y**2
    dx = np.ones(dy.shape)
    dyu = dy / np.sqrt(dy**2 + dx**2)
    dxu = dx / np.sqrt(dy**2 + dx**2)
    stream.set_array(dyu.ravel())

    return stream

anim =   animation.FuncAnimation(fig, animate, frames=100, interval=50, blit=False, repeat=False)
plt.show()

Answer 1

I worked around this by clearing the lines and arrows in every iteration:

ax.collections = [] # clear lines streamplot
ax.patches = [] # clear arrowheads streamplot

So, I modified your code like this:

#!/usr/bin/env python3
import matplotlib.pyplot as plt
import numpy as np
import matplotlib.animation as animation


nx, ny = .02, .02
x = np.arange(-15, 15, nx)
y = np.arange(-10, 10, ny)
X, Y = np.meshgrid(x, y)
dy = -1 + Y**2
dx = np.ones(dy.shape)

dyu = dy / np.sqrt(dy**2 + dx**2)
dxu = dx / np.sqrt(dy**2 + dx**2)

color = dyu
fig, ax = plt.subplots()
stream = ax.streamplot(X,Y,dxu, dyu, color=color, density=2, cmap='jet',arrowsize=1)
ax.set_xlabel('t')
ax.set_ylabel('x')

def animate(iter):
    ax.collections = [] # clear lines streamplot
    ax.patches = [] # clear arrowheads streamplot
    dy = -1 + iter * 0.01 + Y**2
    dx = np.ones(dy.shape)
    dyu = dy / np.sqrt(dy**2 + dx**2)
    dxu = dx / np.sqrt(dy**2 + dx**2)
    stream = ax.streamplot(X,Y,dxu, dyu, color=color, density=2, cmap='jet',arrowsize=1)
    print(iter)
    return stream

anim =   animation.FuncAnimation(fig, animate, frames=100, interval=50, blit=False, repeat=False)
anim.save('./animation.gif', writer='imagemagick', fps=60)
# plt.show()

Answer 2

CAUTION: @SebastianBeyer's previously working answer no longer works in 2022. For unknown (and presumably indefensible) reasons, Matplotlib now prohibits attempts to manually replace the axes.patches list by raising a non-human-readable exception resembling:

AttributeError: can't set attribute 'patches'

Thankfully, yet another working workaround exists. Inspired by @Sheldore's working answer here, you must now iteratively search for and remove all matplotlib.patches.FancyArrowPatch child artists from the streamplot's axes: e.g.,

# Rather than this...
ax.patches = [] # clear arrowheads streamplot

# ...you must now do this.
from matplotlib.patches import FancyArrowPatch
for artist in ax.get_children():
    if isinstance(artist, FancyArrowPatch):
        artist.remove()

In full, the post-2020 working solution is now:

#!/usr/bin/env python3
import matplotlib.pyplot as plt
import numpy as np
import matplotlib.animation as animation
from matplotlib.patches import FancyArrowPatch


nx, ny = .02, .02
x = np.arange(-15, 15, nx)
y = np.arange(-10, 10, ny)
X, Y = np.meshgrid(x, y)
dy = -1 + Y**2
dx = np.ones(dy.shape)

dyu = dy / np.sqrt(dy**2 + dx**2)
dxu = dx / np.sqrt(dy**2 + dx**2)

color = dyu
fig, ax = plt.subplots()
stream = ax.streamplot(X,Y,dxu, dyu, color=color, density=2, cmap='jet',arrowsize=1)
ax.set_xlabel('t')
ax.set_ylabel('x')

def animate(iter):
    ax.collections = [] # clear lines streamplot

    # Clear arrowheads streamplot.
    for artist in ax.get_children():
        if isinstance(artist, FancyArrowPatch):
            artist.remove()

    dy = -1 + iter * 0.01 + Y**2
    dx = np.ones(dy.shape)
    dyu = dy / np.sqrt(dy**2 + dx**2)
    dxu = dx / np.sqrt(dy**2 + dx**2)
    stream = ax.streamplot(X,Y,dxu, dyu, color=color, density=2, cmap='jet',arrowsize=1)
    print(iter)
    return stream

anim =   animation.FuncAnimation(fig, animate, frames=100, interval=50, blit=False, repeat=False)
anim.save('./animation.gif', writer='imagemagick', fps=60)
# plt.show()

Thanks alot, post-2020 matplotlib. </facepalm>