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