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_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 nomenclature_fig():
# set up the model parameters for this figure
a = 0.1
l_cw = -default_lambda
l_ccw = 1
X = Y = 1.
def saddlefunc(y,t):
return [y[0]*l_cw, y[1]*l_ccw]
# create a new figure
fig = plt.figure(figsize=(6,6))
axes = fig.add_axes([0.1, 0.1, 0.8, 0.8])
# draw the axes
iris.draw_saddle_neighborhood(axes, -X, -Y, 2*X, 2*Y, True, False,
scale=0.7)
axes.text(-1.05, 0.5, '$Y$',
horizontalalignment = 'right', verticalalignment='center')
axes.text(0.5, -1.05, '$X$',
horizontalalignment = 'center', verticalalignment='top')
# draw the stable limit cycle
r0 = iris.iris_fixedpoint(a, l_ccw, l_cw, X, Y, guess=1e-6*X)
vals = integrate.odeint(saddlefunc, [X,r0],
np.linspace(0, iris.dwell_time(r0, l_ccw, l_cw, X, Y), 1000),
)#args=(a, l_ccw, l_cw, X, Y))
axes.plot(vals[:,0], vals[:,1], 'k', lw=2)
# draw a sample trajectory
x0 = [X, r0*2]
vals = integrate.odeint(saddlefunc, x0,
np.linspace(0, iris.dwell_time(x0[1], l_ccw, l_cw, X, Y), 1000),
)#args=(a, l_ccw, l_cw, X, Y))
axes.plot(vals[:,0], vals[:,1], 'b', lw=1)
# center the plot and clean up the scale bars
axes.set_xlim(-X, X)
axes.set_ylim(-Y, Y)
axes.set_xticks([])
axes.set_yticks([])
axes.set_frame_on(False)
return fig
