在Python中:如何绘制变参数值下Lorenz系统的分叉图？

import numpy as np
import matplotlib.pyplot as plt

def lorenz(x, y, z, sigma, beta, rho):
    dx = sigma * (y - x)
    dy = x * (rho - z) - y
    dz = x * y - beta * z
    return dx, dy, dz

sigma_vals = np.linspace(0, 10, 100)   # sigma取值范围
rho = 28.0   # 常量rho
beta = 8.0 / 3.0   # 常量beta
x_vals = []   # 用于存储x坐标的列表
y_vals = []   # 用于存储y坐标的列表
z_vals = []   # 用于存储z坐标的列表

for sigma in sigma_vals:
    x = 1.0   # 初始x坐标
    y = 1.0   # 初始y坐标
    z = 1.0   # 初始z坐标
    
    # 进行Lorenz系统的数值积分
    dt = 0.01   # 时间步长
    num_steps = 10000   # 积分步数
    for _ in range(num_steps):
        dx, dy, dz = lorenz(x, y, z, sigma, beta, rho)
        x += dx * dt
        y += dy * dt
        z += dz * dt
    
    # 存储计算得到的坐标值
    x_vals.append(x)
    y_vals.append(y)
    z_vals.append(z)

plt.plot(sigma_vals, x_vals, 'b.')
plt.xlabel('sigma')
plt.ylabel('x')
plt.title('Bifurcation diagram of the Lorenz system')
plt.show()