Завдання

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd

def f(x):
    return alpha * (1 - x) - x * np.exp(-2*epsilon*x)

def V(x):
    return -alpha*(x - (1/2)*x**2) + (1/4)*(-2 * x * epsilon * np.exp(-2*epsilon*x) - np.exp(-2*epsilon*x)) / (epsilon**2)

def alpha_st(x):
    return (x * np.exp(-2*epsilon*x)) / (1 - x)

def sts():
    x = dx
    while x <= (1 - dx):
        if ( (x - dx < 0) and (f(x) > 0) ) or ( (f(x - dx) > 0) and (f(x) < 0) ):
           y.append(x)
    x += dx

def grafik(x, y):

    plt.title(f"alpha(x)")
    plt.xlabel("alpha")
    plt.ylabel("x")
    plt.grid()
    for i in range(len(x)):
        plt.plot(x[i], y[i], 'o',  label=f'epsilon = {i+1}')
    plt.legend()
    plt.show()



X1 = []
Y1 = []
dx = 0.0001
alpha = 0
for i in range(1, 7):
    epsilon = i
    y = []
    dx = 0.0001
    alpha = 0
    X = []
    Y = []
    while alpha < 0.15:
        x = 0
        while x <= (1 - dx):
            if (((f(x - dx) < 0) and (f(x) > 0)) or ((f(x - dx) > 0) and (f(x) < 0))):
                    X.append(alpha)
                    Y.append(x)


            x += dx
        alpha += 0.001
    X1.append(X)
    Y1.append(Y)

grafik(X1, Y1)

x_max = []
y_max = []
x_min = []
y_min = []
eps = np.arange(1, 6, 0.1)
for epsilon in eps:
    x = 2 * dx
    while x < (1.0 - dx):

        a1 = alpha_st(x - dx)
        a2 = alpha_st(x)
        a3 = alpha_st(x + dx)

        if (a1 < a2) and (a3 < a2):
            x_max.append(a2)
            y_max.append(epsilon)

        if (a1 > a2) and (a3 > a2):
            x_min.append(a2)
            y_min.append(epsilon)

        x += dx

plt.title(f"Фазова діаграма")
plt.xlabel("alpha")
plt.ylabel("eps")
plt.grid()
plt.plot(x_max, y_max, label='maximum')
plt.plot(x_min, y_min, label='minimum')
plt.legend()
plt.show()