def iris_isochron_fig(a, border=1., phase_offset=0., l = default_lambda):
# set up the model parameters for this figure
l_cw = -l
l_ccw = 1
X = Y = 1.
# calculate the isochrons
mesh_points = 400
XX, YY = np.meshgrid(
np.linspace(-(2*X + a/2), (2*X + a/2), mesh_points),
np.linspace(-(2*Y + a/2), (2*Y + a/2), mesh_points),
)
isochrons = iris.iris_isochron(XX, YY, a=a, l_ccw=l_ccw,
l_cw=l_cw, X=X, Y=Y)
# create a new figure
fig = plt.figure(figsize=(6,6))
axes = fig.add_axes([0.1, 0.1, 0.8, 0.8])
indexes = np.array([[i, j] for i in range(-2,3) for j in range(-2,3)])
offsets = np.array([[i*2*X - a*j, j*2*Y + i*a] for i,j in indexes])
for i in range(len(offsets)):
if indexes[i].sum() % 2 == 0:
iris.draw_fancy_iris(axes, a, l_ccw, l_cw, X, Y, x0=np.nan,
offset = offsets[i,:2])
contours = phase_offset + np.linspace(
-3*math.pi, 14*math.pi, 128, endpoint=False)
cool_colors = [(0, 0.6 + 0.3*math.sin(c), 0.7 + 0.3*math.cos(c))
for c in contours]
hot_colors = [(0.6 + 0.3*math.cos(c), 0., 0.7 + 0.3*math.sin(c))
for c in contours]
# draw the other limit cycles
for i in range(len(offsets)):
if indexes[i].sum() % 2 == 0:
axes.contour(XX + offsets[i, 0], YY + offsets[i, 1], isochrons,
contours,
colors=(cool_colors, hot_colors)[indexes[i, 0] % 2])
# add lines at the edge of the squares to hide the contour discontinuity
# where the phase wraps from 2 \pi to zero
for i in range(len(offsets)):
axes.plot([ a/2, a/2] + offsets[i, 0],
[-a/2, -(2*Y+a/2)] + offsets[i, 1], 'k')
axes.plot([-a/2, -(2*X+a/2)] + offsets[i, 0],
[-a/2, -a/2] + offsets[i, 1], 'k')
# center the plot and clean up the scale bars
axes.set_xlim(-3*X-border, 3*X+border)
axes.set_ylim(-3*Y-border, 3*Y+border)
axes.set_xticks([])
axes.set_yticks([])
axes.set_frame_on(False)
return fig
def iris_timeplot_fig(a_vals = sample_a_vals, border = 0.3):
# set up the model parameters for this figure
l_cw = -default_lambda
l_ccw = 1
X = Y = 1.
n_phis = np.linspace(0, 2*math.pi, 20*4 + 1)
a_phis = np.linspace(0, 2*math.pi, 100*4 + 1)
dx = 1e-4
dy = 0.
mag = math.sqrt(dx**2 + dy**2)
phasescale = 4 / (2 * math.pi) # convert from (0,2 \pi) to (0,4)
# create a new figure
fig = plt.figure(figsize=(6,6))
width = 1./len(a_vals)
padding = 0.2*width
for i in range(len(a_vals)):
a = a_vals[i]
axes = plt.axes((2*padding, 1-(i+1) * width+padding,
1 - width - 2*padding, width - 1.5*padding))
# draw the trajectory components vs. time
r0 = iris.iris_fixedpoint(a, l_ccw, l_cw, X, Y, guess=1e-6*X)
T = 4 * iris.dwell_time(r0, l_ccw, l_cw, X, Y)
ts = np.linspace(0, 3*T, 1000);
vals = integrate.odeint(iris.iris,
[-a/2, -a/2 - Y + r0],
ts,
args=(a, l_ccw, l_cw, X, Y))
axes.plot(ts, vals[:,1], '-', color='0.8', lw=2)
axes.plot(ts, vals[:,0], 'k-', lw=2)
axes.set_xlim(0, 3*T)
# make the y-axis symmetric around zero
#ymaxabs = np.max(np.abs(axes.get_ylim()))
ymaxabs = 1.2
axes.set_ylim(-ymaxabs, ymaxabs)
# draw the phase plot for reference
axes = plt.axes((1-width, 1-(i+1) * width, width, width))
iris.draw_fancy_iris(axes, a, l_ccw, l_cw, X, Y,
scale=3.0, x0=np.nan)
# center the plot and clean up the scale bars
axes.set_xlim(-2*X-border, 2*X+border)
axes.set_ylim(-2*Y-border, 2*Y+border)
axes.set_xticks([])
axes.set_yticks([])
axes.set_frame_on(False)
return fig
def iris_fig(a, border=1., label_theta0=True):
# set up the model parameters for this figure
l_cw = -default_lambda
l_ccw = 1
X = Y = 1.
# create a new figure
fig = plt.figure(figsize=(5,5))
axes = fig.add_axes([0., 0., 1., 1.])
iris.draw_fancy_iris(axes, a, l_ccw, l_cw, X, Y)
# add an arrow indicating theta = 0
if label_theta0:
r0s = iris.iris_fixedpoint(a, l_ccw, l_cw, X, Y, guess=1e-6*X)
if r0s != None:
axes.annotate(r'$\theta = 0$',
xy=(a/2, -X + r0s - a/2), xycoords='data',
xytext=(15,15), textcoords='offset points',
arrowprops=dict(arrowstyle='->',
connectionstyle='angle,angleA=180,angleB=240,rad=10')
)
r0u = iris.iris_fixedpoint(a, l_ccw, l_cw, X, Y, guess=1*X)
if a != 0 and r0u != None:
axes.annotate(r'',
xy=(-X + r0u - a/2, -a/2), xycoords='data',
xytext=(-15,15), textcoords='offset points',
arrowprops=dict(arrowstyle='->', color='r',
connectionstyle='angle,angleA=-180,angleB=-45,rad=0')
)
if a != 0 and r0u != None:
x0 = [-a/2, a/2 + Y - (0.9*r0u + 0.1*r0s)]
elif a == 0:
x0 = [-a/2, a/2 + Y - 0.9]
else:
x0 = [-a/2, 0.9*Y]
axes.annotate(r'',
xy=x0, xycoords='data',
xytext=x0 + np.r_[-1.0e-3, 0.5e-3], textcoords='data',
arrowprops=dict(arrowstyle='->', color='b',
connectionstyle='arc3,rad=0')
)
# center the plot and clean up the scale bars
axes.set_xlim(-2*X-border, 2*X+border)
axes.set_ylim(-2*Y-border, 2*Y+border)
axes.set_xticks([])
axes.set_yticks([])
axes.set_frame_on(False)
return fig
def iris_prc_fig(a_vals = sample_a_vals, border = 0.3):
# set up the model parameters for this figure
l_cw = -default_lambda
l_ccw = 1
X = Y = 1.
n_phis = np.linspace(0, 2*math.pi, 20*4 + 1)
a_phis = np.linspace(0, 2*math.pi, 100*4 + 1)
dx = 1e-4
dy = 0.
mag = math.sqrt(dx**2 + dy**2)
phasescale = 4 / (2 * math.pi) # convert from (0,2 \pi) to (0,4)
# create a new figure
fig = plt.figure(figsize=(6,6))
width = 1./len(a_vals)
padding = 0.2*width
for i in range(len(a_vals)):
a = a_vals[i]
axes = plt.axes((2*padding, 1-(i+1) * width+padding,
1 - width - 2*padding, width - 1.5*padding))
# draw the orthogonal prc found analytically
a_prc_o = np.array([
iris.analytic_phase_reset(phi, dx=-dy, dy=dx, a=a,
l_ccw=l_ccw, l_cw=l_cw)
for phi in a_phis
])
axes.plot(a_phis, a_prc_o/mag*phasescale, color='0.8')
# draw the orthogonal prc found numerically
n_prc_o = np.array([
iris.phase_reset(phi, dx=-dy, dy=dx, a=a, l_ccw=l_ccw, l_cw=l_cw,
steps_per_cycle=100000)
for phi in n_phis
])
axes.plot(n_phis, n_prc_o/mag*phasescale, 'o', markersize=3,
markeredgecolor='0.8', color='0.8')
# draw the prc found analytically
a_prc = np.array([
iris.analytic_phase_reset(phi, dx=dx, dy=dy, a=a,
l_ccw=l_ccw, l_cw=l_cw)
for phi in a_phis
])
axes.plot(a_phis, a_prc/mag*phasescale, 'k')
# draw the prc found numerically
n_prc = np.array([
iris.phase_reset(phi, dx=dx, dy=dy, a=a, l_ccw=l_ccw, l_cw=l_cw,
steps_per_cycle=100000)
for phi in n_phis
])
axes.plot(n_phis, n_prc/mag*phasescale, 'bo', markersize=3)
# clean up the axes
axes.set_xlim(0, 2*math.pi)
plt.xticks(np.arange(5.)*math.pi/2,
#['$0$', '$\\pi/2$', '$\\pi$',
# '$3\\pi/2$', '$2\\pi$'])
# phase rescaled from 0 to 4 to match analysis
['$0$', '$1$', '$2$', '$3$', '$4$'])
# make the y-axis symmetric around zero
ymaxabs = np.max(np.abs(axes.get_ylim()))
axes.set_ylim(-ymaxabs, ymaxabs)
# draw the phase plot for reference
axes = plt.axes((1-width, 1-(i+1) * width, width, width))
iris.draw_fancy_iris(axes, a, l_ccw, l_cw, X, Y,
scale=3.0, x0=np.nan)
# center the plot and clean up the scale bars
axes.set_xlim(-2*X-border, 2*X+border)
axes.set_ylim(-2*Y-border, 2*Y+border)
axes.set_xticks([])
axes.set_yticks([])
axes.set_frame_on(False)
return fig