Bifurcations
import numpy as np
import matplotlib.pyplot as plt
#params
r_min, r_max = 2.5, 4.0
n_r = 10000
n_transient = 1000
n_last = 100
r = np.linspace(r_min, r_max, n_r)
x = 0.5 * np.ones(n_r)
for i in range(n_transient):
x = r * x * (1-x)
r_list = []
x_list = []
for i in range(n_last):
x = r * x * (1-x)
r_list.append(r)
x_list.append(x)
r_plot = np.array(r_list).flatten()
x_plot = np.array(x_list).flatten()
plt.figure(figsize=(12,8))
plt.scatter(r_plot, x_plot, s=0.1, c='black', alpha=0.1)
plt.title('Bifurcation Diagram of the Logistic Map')
plt.xlabel('Growth Rate ($r$)')
plt.ylabel('Population ($x$)')
plt.xlim(r_min, r_max)
plt.ylim(0,1)
plt.grid(False)
plt.show()
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“We all die. The goal isn’t to live forever, the goal is to create something that will.” — Chuck Palahniuk
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Within this site you will find self-contained material in the form of project posts and blog posts, but also external links 1 to other work – my own as well as not.