import numpy as np import matplotlib.pyplot as plt

1. Define the vector field

def f(x, y):

   return np.array([x + np.exp(-y), -y])

1. Define the domain

xmin, xmax, ymin, ymax = -1.7, -0.5, -1, 1

1. Define the grid

nx, ny = 80, 80 x = np.linspace(xmin, xmax, nx) y = np.linspace(ymin, ymax, ny) X, Y = np.meshgrid(x, y)

1. Evaluate the vector field on the grid

U, V = f(X, Y)

1. Plot the vector field

fig, ax = plt.subplots(figsize=(8, 8)) ax.set_xlim(xmin, xmax) ax.set_ylim(ymin, ymax)

1. Plot the integral curves

x0, y0 = np.meshgrid(np.linspace(-2, 0, 40), np.linspace(-1, 1, 40)) t = np.linspace(0, 5, 100) for i in range(x0.shape[0]):

   for j in range(x0.shape[1]):
       x, y = x0[i,j], y0[i,j]
       sol = np.zeros((2, t.size))
       sol[:,0] = [x, y]
       for k in range(1, t.size):
           sol[:,k] = sol[:,k-1] + f(sol[0,k-1], sol[1,k-1])*(t[k]-t[k-1])
       ax.plot(sol[0,:], sol[1,:], 'b-', linewidth=1, alpha=0.1)

plt.show()