"""
Exercise A.20 from a primer on. The same
model as ex. A.19, but we use a for-loop to perform
a parameter sweep and inspect the corresponding
solutions. The exercise asks us to create separate
plots and store them in file, but it is here modified
to plot all the curves in the same window. This is
usually more convenient, although the plot can get crowded. 
"""

import numpy as np
import matplotlib.pyplot as plt


def logistic(y0, q, N):
    y = np.zeros(N + 1)
    y[0] = y0
    for n in range(1, N + 1):
        y[n] = y[n-1] + q * y[n-1] * (1 - y[n-1])
    plt.plot(y, label=f'y0={y0},q={q}')
    

for y0 in 0.01, 0.3:
    for q in 0.1, 2, 3:
        logistic(y0, q, N=50)
     
#Display the labels defined for each curve:
plt.legend()
plt.show()