English: ```python

from matplotlib.widgets import AxesWidget import numpy as np import matplotlib.pyplot as plt from scipy.integrate import solve_ivp from scipy import optimize

for alpha in [0.09]:

 # Define the parameter values
 a = 0.7
 b = 2.0 # If b < 1.5, then there are stable loops. Else there are no loops.
 tau = 12.5
 R = 0.1
 I_ext_0 = (2/3 + (a-1)/b)/R
 I_ext_1 = (-2/3 + (a+1)/b)/R
 I_ext_min = min(I_ext_0, I_ext_1) - 2.0 / R
 I_ext_max = max(I_ext_0, I_ext_1) + 2.0 / R
 I_ext = I_ext_min * (alpha - 1.0)/(-2.0) + I_ext_max * (alpha + 1.0)/(+2.0)
 # If alpha < 1, then all trajectories fall to a stable equilibrium
 # If alpha > 1, and b < 1.5, then all trajectories fall to a stable loop.

 # Define the system of ODEs
 def system(t, y):
     v, w = y
     dv = v - (v ** 3) / 3 - w + R * I_ext
     dw = (1 / tau) * (v + a - b * w)
     return [dv, dw]
 def system_reversed(t, y):
     v, w = y
     dv = v - (v ** 3) / 3 - w + R * I_ext
     dw = (1 / tau) * (v + a - b * w)
     return [-dv, -dw]

 vmin, vmax, wmin, wmax = -2, 2, -2+R*I_ext, 2+R*I_ext

 t_span = [0, 100]
 trajectory_resolution = 10
 def fun(x):
   v = x[0]
   return v-v**3/3 + R * I_ext - (v+a)/b
 sol = optimize.root(fun, [0], method='hybr')
 x_root = sol.x[0]
 y_root = (x_root+a)/b

 # vmin, vmax, wmin, wmax = -1.5, -0.5, -1.1 +1/3 + R * I_ext, -0.8 +1/3 + R * I_ext
 # initial_conditions = [(-1.0, y) for y in np.linspace(-0.16, -0.03, 30)]
 initial_conditions = [(x, y) for x in np.linspace(vmin, vmax, trajectory_resolution) for y in np.linspace(wmin, wmax, trajectory_resolution)]
 epsilon = 0.005
 initial_conditions += [(x, y) for x in np.linspace(x_root - epsilon, x_root+epsilon, trajectory_resolution)  for y in np.linspace(y_root - epsilon, y_root+epsilon, trajectory_resolution)]
 sols = {}
 for ic in initial_conditions:
     sols[ic] = solve_ivp(system, t_span, ic, dense_output=True, max_step=0.1)
 sols_reversed = {}
 for ic in initial_conditions:
     sols_reversed[ic] = solve_ivp(system_reversed, t_span, ic, dense_output=True, max_step=0.1)

 vs = np.linspace(vmin, vmax, 200)
 v_axis = np.linspace(vmin, vmax, 20)
 w_axis = np.linspace(wmin, wmax, 20)

 v_values, w_values = np.meshgrid(v_axis, w_axis)

 dv = v_values - (v_values ** 3) / 3 - w_values + R * I_ext
 dw = (1 / tau) * (v_values + a - b * w_values)

 fig, ax = plt.subplots(figsize=(16,16))
 # integral curves
 for ic in initial_conditions:
   sol = sols[ic]
   ax.plot(sol.y[0], sol.y[1], color='k', alpha=0.4, linewidth=0.5)
   sol = sols_reversed[ic]
   ax.plot(sol.y[0], sol.y[1], color='k', alpha=0.4, linewidth=0.5)

 # vector fields
 arrow_lengths = np.sqrt(dv**2 + dw**2)
 alpha_values = 1 - (arrow_lengths / np.max(arrow_lengths))**0.4
 ax.quiver(v_values, w_values, dv, dw, color='blue', linewidth=0.5, scale=25, alpha=alpha_values)

 # nullclines
 ax.plot(vs, vs - vs**3/3 + R * I_ext,  color="green", alpha=0.4, label="v nullcline")
 ax.plot(vs, (vs + a) / b, color="red", alpha=0.4, label="w nullcline")

 # ax.set_xlabel('v')
 # ax.set_ylabel('w')

ax.set_title(f'FitzHugh-Nagumo Model\n$b={b:.2f}$\t\t$I_ = {I_ext:.2f

 # ax.legend()
 ax.set_xlim(vmin, vmax)
 ax.set_ylim(wmin, wmax)
 # ax.set_xticks([])
 # ax.set_yticks([])
 plt.show()