Hi all,
I was wondering if it is possible to produce animations
like
http://www.math.uh.edu/~josic/nonautonomous/
with pylab ?
Further information is available in a recent paper
by K. Josic and R. Rosenbaum published in SIAM Review.
See http://dx.doi.org/10.1137/060677057
Cheers,
Nils
from scipy.integrate import odeint
from scipy.linalg import eig
from pylab import plot, show, legend, xlabel, ylabel
from numpy import zeros, linspace, dot, sin, cos, exp
#
# K. Josic, R. Rosenbaum
# Unstable solutions of nonautonomous linear differential equations
# SIAM Review Vol. 50 No. 3 (2008) pp. 570--584
#
def A(t):
tmp = zeros((2,2),float)
tmp[0,0] = -1-9*(cos(6*t))**2+12*sin(6*t)*cos(6*t)
tmp[0,1] = 12*(cos(6*t))**2+9*sin(6*t)*cos(6*t)
tmp[1,0] = -12*(sin(6*t))**2+9*sin(6*t)*cos(6*t)
tmp[1,1] = -1-9*(sin(6*t))**2-12*sin(6*t)*cos(6*t)
return tmp
def func(x,t):
return dot(A(t),x)
x_0 = zeros(2,float) # Initial conditions
x_0[0] = -2.44
x_0[1] = 1.23
x_0[0] = 5.0
x_0[1] = 0.0
T = linspace(0,3,300)
x = odeint(func,x_0,T)
#
# Analytical solution of Vinograds example
#
y_1 = exp(2*T)*(cos(6*T)+2*sin(6*T))+2*exp(-13*T)*(2*cos(6*T)-sin(6*T))
y_2 = exp(2*T)*(2*cos(6*T)-sin(6*T))-2*exp(-13*T)*(cos(6*T)+2*sin(6*T))
plot(T,x[:,0])
plot(T,x[:,1])
plot(T,y_1,'r.')
plot(T,y_2,'g.')
xlabel(r'Time $t$[s]')
legend((r'$x_1$',r'$x_2$',r'$y_1$',r'$y_2$'))
for t in T:
w, vr = eig(A(t))
print vr[:,0], vr[:,1]
show()
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