def pr1c(file_prefix):
drive_freq = 7.4246
pfunc2 = pendulum.pendulum(0.1, 0.1, 0.25, ampl=1, freq=drive_freq)
ts2, xs2 = rungekutta.rk4(
pfunc2,
0.0,
numpy.array([3.0, 0.1], dtype=numpy.float64),
0.005,
1000000
)
xs2[0,:] = numpy.array(
[pendulum.mod2pi(x) for x in xs2[0,:]],
dtype=numpy.float64
)
points2 = xs2.transpose()
ps3 = poincare.section(ts2, points2, interval=2*numpy.pi/drive_freq)
plot.mod2pi(
ps3[:,0],
ps3[:,1],
'k.',
xlabel=r'$\theta$',
ylabel=r'$\omega$',
markersize=0.6,
title='Poincare Section (Chaotic Trajectory)',
file_prefix=_suffixed(file_prefix, '_1c')
)
def pr1d(file_prefix):
drive_freq = 7.4246
pfunc2 = pendulum.pendulum(0.1, 0.1, 0.25, ampl=1, freq=drive_freq)
ts3, xs3 = rungekutta.rk4(
pfunc2,
0.0,
numpy.array([3.0, 0.1], dtype=numpy.float64),
0.02,
250000
)
xs3[0,:] = numpy.array(
[pendulum.mod2pi(x) for x in xs3[0,:]],
dtype=numpy.float64
)
points3 = xs3.transpose()
ps4 = poincare.section(ts3, points3, interval=2*numpy.pi/drive_freq)
plot.mod2pi(
ps4[:,0],
ps4[:,1],
'k.',
xlabel=r'$\theta$',
ylabel=r'$\omega$',
markersize=0.6,
title='Poincare section, increased step size',
file_prefix=_suffixed(file_prefix, '_1d')
)
def pr1b(file_prefix, ts, points):
ps2 = poincare.section(ts, points, interval=0.51)
plot.render(ps2[:, 0],
ps2[:, 1],
'k.',
xbound=(-0.015, 0.015),
ybound=(-0.15, 0.15),
xlabel=r'$\theta$',
ylabel=r'$\omega$',
markersize=0.6,
title='Poincare Section (Irrational Frequency)',
file_prefix=_suffixed(file_prefix, '_1b'))
def pr1b(file_prefix, ts, points):
ps2 = poincare.section(ts, points, interval=0.51)
plot.render(
ps2[:,0],
ps2[:,1],
'k.',
xbound=(-0.015, 0.015),
ybound=(-0.15, 0.15),
xlabel=r'$\theta$',
ylabel=r'$\omega$',
markersize=0.6,
title='Poincare Section (Irrational Frequency)',
file_prefix=_suffixed(file_prefix, '_1b')
)
def pr1d(file_prefix):
drive_freq = 7.4246
pfunc2 = pendulum.pendulum(0.1, 0.1, 0.25, ampl=1, freq=drive_freq)
ts3, xs3 = rungekutta.rk4(pfunc2, 0.0,
numpy.array([3.0, 0.1], dtype=numpy.float64),
0.02, 250000)
xs3[0, :] = numpy.array([pendulum.mod2pi(x) for x in xs3[0, :]],
dtype=numpy.float64)
points3 = xs3.transpose()
ps4 = poincare.section(ts3, points3, interval=2 * numpy.pi / drive_freq)
plot.mod2pi(ps4[:, 0],
ps4[:, 1],
'k.',
xlabel=r'$\theta$',
ylabel=r'$\omega$',
markersize=0.6,
title='Poincare section, increased step size',
file_prefix=_suffixed(file_prefix, '_1d'))
def pr1c(file_prefix):
drive_freq = 7.4246
pfunc2 = pendulum.pendulum(0.1, 0.1, 0.25, ampl=1, freq=drive_freq)
ts2, xs2 = rungekutta.rk4(pfunc2, 0.0,
numpy.array([3.0, 0.1], dtype=numpy.float64),
0.005, 1000000)
xs2[0, :] = numpy.array([pendulum.mod2pi(x) for x in xs2[0, :]],
dtype=numpy.float64)
points2 = xs2.transpose()
ps3 = poincare.section(ts2, points2, interval=2 * numpy.pi / drive_freq)
plot.mod2pi(ps3[:, 0],
ps3[:, 1],
'k.',
xlabel=r'$\theta$',
ylabel=r'$\omega$',
markersize=0.6,
title='Poincare Section (Chaotic Trajectory)',
file_prefix=_suffixed(file_prefix, '_1c'))
def pr1a(file_prefix):
pfunc = pendulum.pendulum(0.1, 0.1, 0)
ts, xs = rungekutta.rk4(pfunc, 0.0,
numpy.array([0.01, 0.0], dtype=numpy.float64),
0.005, 80000)
points = xs.transpose()
ps = poincare.section(ts, points, interval=0.6346975625940523)
plot.render(ps[:, 0],
ps[:, 1],
'k.',
xbound=(-0.015, 0.015),
ybound=(-0.15, 0.15),
xlabel=r'$\theta$',
ylabel=r'$\omega$',
markersize=0.6,
title='Poincare Section (Natural Frequency)',
file_prefix=_suffixed(file_prefix, '_1a'))
return ts, points
def pr1a(file_prefix):
pfunc = pendulum.pendulum(0.1, 0.1, 0)
ts, xs = rungekutta.rk4(
pfunc,
0.0,
numpy.array([0.01, 0.0], dtype=numpy.float64),
0.005,
80000
)
points = xs.transpose()
ps = poincare.section(ts, points, interval=0.6346975625940523)
plot.render(
ps[:,0],
ps[:,1],
'k.',
xbound=(-0.015, 0.015),
ybound=(-0.15, 0.15),
xlabel=r'$\theta$',
ylabel=r'$\omega$',
markersize=0.6,
title='Poincare Section (Natural Frequency)',
file_prefix=_suffixed(file_prefix, '_1a')
)
return ts, points
def poincare_section(self, **kwargs):
t, theta, omega = self.__call__(**kwargs)
return poincare.section(t, theta, omega,
2 * np.pi / self.params["Omega_D"])
