绘制 Logistic 映射分叉图
逻辑斯蒂映射：
x
k
+
1
=
r
x
k
(
1
−
x
k
)
x_{k+1} = rx_k(1-x_k)
xk+1=rxk(1−xk)
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rcParams
from tqdm.notebook import tqdm
rcParams.update({'font.size': 18})
plt.rcParams['figure.figsize'] = [12, 12]
startval = 1
endval = 4
xvals = np.array([[],[]])
n_iter = 1000
n_plot = 100
def logistic(xk,r):
return r*xk*(1-xk)
for r in tqdm(np.arange(startval,endval,0.00025)):
x = 0.5
for i in range(n_iter):
x = logistic(x,r)
if i == n_iter-n_plot:
xss = x
if i > n_iter-n_plot:
xvals = np.append(xvals,np.array([[r],[x]]),axis=1)
if np.abs(x-xss) < 0.001:
break
plt.plot(xvals[0,:],xvals[1,:],'.',ms=0.1,color='k')
plt.ylim(0,1)
plt.xlim(1,endval)
局部放大
plt.plot(xvals[0,:],xvals[1,:],'.',ms=0.1,color='k')
plt.ylim(0,1)
plt.xlim(3.45,4)
plt.xlabel('r')
plt.ylabel(' fixed point')
