混沌的遍歷性圖(ergodicity)
阿新 • • 發佈:2018-12-17
以Logistic的Ergodicity為例
import matplotlib.pyplot as plt import numpy as np # Logistic的迭代方程 def logistic(x): x1=u*x*(1-x) return x1 #此函式用於畫Logistic的函式影象 def logistic_graph(): for i in np.arange(0,1.01,0.01): x=i x1=u*x*(1-x) listlogisticx.append(x) listlogisticy.append(x1) # 此函式用於畫y=x這條直線 def line_graph(): for i in np.arange(0, 1.01, 0.01): x = i x1 = x listlinex.append(x) listliney.append(x1) if __name__ == '__main__': listx = [] listy = [] listlogisticx=[] listlogisticy=[] listlinex=[] listliney=[] x0=0.9 # 迭代的初始值設定 u=4 # Logistic的控制引數 listx.append(x0) # 初始座標點為(x0,0) listy.append(0) for i in range(100): # 迭代次數 x1=logistic(x0) listx.append(x0) listy.append(x1) listx.append(x1) listy.append(x1) x0=x1 plt.title(r'$\mu$=4') plt.grid(linestyle='--') # 設定網格 plt.plot(listx,listy) # 畫遍歷圖 logistic_graph() plt.plot(listlogisticx,listlogisticy) # 畫Logistic的函式影象 line_graph() plt.plot(listlinex,listliney) # 畫y=x plt.show()
影象如下