logistic用python画图

以下是使用Python画出逻辑斯蒂映射(logistic map)的分叉图的代码和步骤：

1.导入必要的库

import numpy as np
import matplotlib.pyplot as plt

2.定义逻辑斯蒂映射函数

def logistic_map(r, x):
    return r * x * (1 - x)

3.定义绘制分叉图的函数

def bifurcation_diagram(r_min, r_max, num_points, num_ignore):
    # 初始化参数
    r_values = np.linspace(r_min, r_max, num_points)
    last_x = 0.5

    # 忽略前num_ignore个点
    for i in range(num_ignore):
        last_x = logistic_map(r_values[0], last_x)

    # 绘制分叉图
    x_values = []
    r_values_to_plot = []
    for r in r_values:
        x = last_x
        for i in range(num_ignore):
            x = logistic_map(r, x)
        for i in range(num_points):
            x = logistic_map(r, x)
            x_values.append(x)
            r_values_to_plot.append(r)

    plt.scatter(r_values_to_plot, x_values, s=0.1, marker='.')
    plt.xlabel('r')
    plt.ylabel('x')
    plt.show()

4.调用函数绘制分叉图

bifurcation_diagram(2.5, 4.0, 10000, 1000)