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LogisticMap.py
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LogisticMap.py
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import os, shutil
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.animation import FuncAnimation
import theano
import theano.tensor as T
try:
os.mkdir(__file__.split('.')[0])
except OSError:
pass
r = T.fscalar()
N = T.iscalar()
x = T.fscalar()
def step(X):
X_ = r * X * (1.0 - X)
return X_
result, _ = theano.scan(fn=step,
outputs_info=x,
n_steps=N)
logistic_map = theano.function([x,r,N],
result,
allow_input_downcast=True)
def plot_bifurcation():
fig = plt.figure()
ax = fig.add_subplot(111)
fig.set_tight_layout(True)
for r in np.arange(2.0, 4.0, 0.001):
state_array = logistic_map(0.5, r, 1000)
ax.scatter(r*np.ones_like(state_array), state_array, c='C0', s=0.0005)
plt.savefig(os.path.join(__file__.split('.')[0], __file__.split('.')[0]+'.png'), dpi=400)
plt.show()
def main():
plot_bifurcation()
if __name__=='__main__':
main()