File:Intermittency in logistic map, cobweb diagram.png

import numpy as np import matplotlib.pyplot as plt

def logistic_map(x, r):

   return r * x * (1 - x)

def logistic_map_3(x, r):

   return logistic_map(logistic_map(logistic_map(x, r), r), r)

r = 3.8284 x_initial = 0.19 num_iterations = 75

1. Generate x values for the cobweb plot

x_values = np.linspace(0, 1, 1000) y_values = logistic_map_3(x_values, r)

1. Generate cobweb lines

x_cobweb = [x_initial] y_cobweb = [0]

for i in range(num_iterations):

   x_next = logistic_map_3(x_cobweb[-1], r)
   x_cobweb.append(x_cobweb[-1])
   y_cobweb.append(x_next)
   x_cobweb.append(x_next)
   y_cobweb.append(x_next)

1. Plot the logistic map

plt.plot(x_values, y_values, label='Logistic map', color='blue') plt.plot(x_values, x_values, label='y = x', color='green')

1. Plot the cobweb lines

plt.plot(x_cobweb, y_cobweb, color='red', alpha=0.5)

plt.xlabel('x') plt.ylabel('x_next') plt.legend() plt.title('Cobweb diagram for the logistic map with r = 3.8284')

plt.show()