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import numpy as n p import matplotlib.pyplot as plt # Step 1 : Loop 1 - Varying mu _ values = np . linspace ,

import numpy as np
import matplotlib.pyplot as plt
# Step 1: Loop 1- Varying
mu_values = np.linspace , num=1000)
#Step 2: Loop 2- Transient Iteration
n_trans =100
x_transient =[]
for mu in mu_values:
x=0.5
for _ in range(n_trans):
x=**x**(1-x)
x_transient.append (x)
# Step 3: Loop 3- Data Iteration
n_data =500
x_data =[]
for mu, x_transient_last in zip(mu_values, x_transient):
x=x?transientlast
x_values =[]
for _ in range (n_data):
x=**x**(1-x)
x?values. append (x)
x_data.apped(x_values)
# Step 4: Plotting the Bifurcation Diagram
plt.figure(figsize=(10,6))
for i, mu in enumerate(mu_values):
plt.plot([mu]*n_data, x_data[i],', k', alpha=0.25)
plt.title("Bifurcation Diagram for Logistic Map")
plt.xlabel("(Parameter)")
plt.ylabel("x (Population)")
plt.xlim(2.4,4.0)
plt.ylim(,1
plt.show()
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