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