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Maps.py
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Maps.py
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import pylab
import math
import numpy as np
def Henon(a, b, x_initial, y_initial, iterations):
X=[x_initial]
Y=[y_initial]
## X=[1.]
## Y=[1.]
## a=1.4
## b=0.3
for n in range(1, iterations+1):
X+=[1-a*X[n-1]**2+Y[n-1], ]
Y+=[b*X[n-1], ]
pylab.plot(X, Y, 'ro', ms=1)
pylab.xlabel('X')
pylab.ylabel('Y')
pylab.show()
def Henon2(a, b, x_initial, y_initial, iterations):
X=[x_initial]
Y=[y_initial]
## X=[1.]
## Y=[1.]
## a=1.4
## b=0.3
for n in range(1, iterations+1):
X+=[1-a*X[n-1]**2+Y[n-1], ]
Y+=[b*X[n-1], ]
return X
##Henon(1.4, 0.3, 1., 1., 10001)
def bifurcation_henon(A, x_initial, y_initial, iterations):
for a in A:
X=Henon2(a, 0.3, x_initial, y_initial, iterations)[100:]
pylab.plot([a]*len(X), X, 'mo', ms=2)
pylab.xlabel('a')
pylab.ylabel('X')
pylab.xlim(1, 1.5)
pylab.ylim(-0.5, 0.5)
pylab.title('Bifurcation diagram fro Henon map')
## pylab.show()
A1=list(np.linspace(1., 1.5, 300))
##bifurcation_henon(A1, 1., 1., 1000)
def Lozi(a, b, x_initial, y_initial, iterations):
X=[x_initial]
Y=[y_initial]
## X=[1.]
## Y=[1.]
## a=1.4
## b=0.3
for n in range(1, iterations+1):
X+=[1-a*abs(X[n-1])+Y[n-1], ]
Y+=[b*X[n-1], ]
pylab.plot(X, Y, 'ro', ms=1)
pylab.xlabel('X')
pylab.ylabel('Y')
pylab.show()
##Lozi(1.4, 0.3, 1., 1., 10001)
def Lozi2(a, b, x_initial, y_initial, iterations):
X=[x_initial]
Y=[y_initial]
## X=[1.]
## Y=[1.]
## a=1.4
## b=0.3
for n in range(1, iterations+1):
X+=[1-a*abs(X[n-1])+Y[n-1], ]
Y+=[b*X[n-1], ]
return X
def bifurcation_Lozi(A, x_initial, y_initial, iterations):
for a in A:
X=Lozi2(a, 0.3, x_initial, y_initial, iterations)[100:]
pylab.plot([a]*len(X), X, 'yo', ms=2)
pylab.xlabel('a')
pylab.ylabel('X')
pylab.xlim(1, 1.5)
pylab.ylim(-0.5, 0.5)
pylab.title('Bifurcation diagram for Lozi map')
## pylab.show()
A2=list(np.linspace(1., 1.5, 300))
##bifurcation_Lozi(A2, 1., 1., 500)
def Mira(a, b, x_initial, y_initial, iterations):
def F(x): return a*x+2*(1-a)*x**2/(1+x**2)
X=[x_initial]
Y=[y_initial]
for n in range(1, iterations+1):
X+=[b*Y[n-1]+F(X[n-1]), ]
Y+=[-X[n-1]+F(X[n]), ]
pylab.plot(X, Y, 'ro', ms=1)
pylab.xlabel('X')
pylab.ylabel('Y')
pylab.show()
##Mira(0.2, 1.0, 12., 0., 50001)
##Mira(0.31, 1.0, 12., 0., 50001)
##Mira(0.4, 1.0, 12., 0., 50001)
##Mira(0.7, 0.9998, 9., 0., 100001)
##Mira(0.7, 0.9998, 12.1, 0., 50001)
##Mira(0.7, 0.9998, 15., 0., 200001)
def Mira2(a, b, x_initial, y_initial, iterations):
X=[x_initial]
Y=[y_initial]
for n in range(1, iterations+1):
X+=[Y[n-1]+a*(1-0.05*Y[n-1]**2)*Y[n-1]+b*X[n-1]+2*(1-b)*X[n-1]**2/(1+X[n-1]**2), ]
Y+=[-X[n-1]+b*X[n]+2*(1-b)*X[n]**2/(1+X[n]**2), ]
pylab.plot(X, Y, 'o', ms=1)
pylab.xlabel('X')
pylab.ylabel('Y')
pylab.show()
##Mira2(0.009, math.cos(4*math.pi/5)+0.008, 0.5, 0.5, 200000)
##Mira2(0.008, -0.496, 0.5, 0.5, 200000)
##Mira2(0.008, -0.486, 0.5, 0.5, 200000)
def tinkerbell(a, b, c, d, x_initial, y_initial, iterations):
X=[x_initial]
Y=[y_initial]
for n in range(1, iterations+1):
X+=[X[n-1]**2-Y[n-1]**2+a*X[n-1]+b*Y[n-1], ]
Y+=[2*X[n-1]*Y[n-1]+c*X[n-1]+d*Y[n-1], ]
pylab.plot(X, Y, 'yo', ms=1)
pylab.xlabel('X')
pylab.ylabel('Y')
pylab.show()
##tinkerbell(0.9, -0.6013, 2., 0.5, -0.72, -0.64, 200000)
##tinkerbell(0.3, 0.6, 2., 0.27, -0.5, -0.64, 200000)
def logistic(r, x_initial, iterations):
X=[x_initial]
for n in range(1, iterations+1):
X+=[r*X[n-1]*(1-X[n-1]), ]
pylab.plot(range(iterations+1), X)
pylab.xlabel('X')
pylab.ylabel('t')
pylab.show()
##logistic(3.78, 0.1, 63)
import numpy as np
def logistic2(r, x_initial, iterations):
X=[x_initial]
for n in range(1, iterations+1):
X+=[r*X[n-1]*(1-X[n-1]), ]
return X
def bifurcation_logistic(R, x_initial, iterations):
for r in R:
X=logistic2(r, x_initial, iterations)[100:]
pylab.plot([r]*len(X), X, 'ro', ms=2)
pylab.xlabel('r')
pylab.ylabel('X')
pylab.title('Bifurcation diagram for Logistic map')
## pylab.show()
R=np.linspace(0, 4, 300)
##bifurcation_logistic(R, 0.1, 1000)
pylab.subplot(3, 1, 1)
bifurcation_henon(A1, 1., 1., 1000)
pylab.subplot(3, 1, 2)
bifurcation_Lozi(A2, 1., 1., 500)
pylab.subplot(3, 1, 3)
bifurcation_logistic(R, 0.1, 1000)
pylab.show()