title: Phase Portraits for systems of ODEs
body: <p>I want to produce a phase portrait of the system:</p>
  <p>x'=x(y-1) and y'=4-y^2-x^2</p>
  <p>My code below is what I have attempted so far. My issue is the ics and duration lines, Whenever I add more points I get red errors that will not show the output of the phase portrait.</p>
  <pre><code> import numpy as np
   from matplotlib import pyplot as plt
   from scipy.integrate import odeint
  
  
  # Define vector field
  def vField(x,t):
  u = x[0]*(x[1]-1)
  v = 4-(x[0])**2-(x[1])**2
  return [u,v]
  
  # Plot vector field
  
  X, Y = np.mgrid[-np.pi:np.pi:-30j,-6:6:30j]
  U, V = vField([X,Y],0)
  
  fig, ax = plt.subplots(figsize=(10, 10))
  ax.quiver(X, Y, U, V)
  
  ics  =      [[2,4],[2,0],[1,4], [2,4],[-2,4],[-2,0],[-1,4],[-2,4],   [-2,1],[2,-1]]
  durations = [[0,4],[0,8],[0,12],[0,4],[0,4],[0,8],[0,12],[0,4],   [0,12],[0,12]]
  vcolors = plt.cm.autumn_r(np.linspace(0.5, 1., len(ics)))  # colors      for each trajectory
  
  # plot trajectories
  for i, ic in enumerate(ics):
  t = np.linspace(durations[i][0], durations[i][1],100)
  x = odeint(vField, ic, t)
  ax.plot(x[:,0], x[:,1], color=vcolors[i], label='X0=(%.f, %.f)' %  (ic[0], ic[1]) )
  
  ic_x = [ic[0] for ic in ics]
  ic_y = [ic[1] for ic in ics]
  ax.scatter(ic_x, ic_y, color='blue', s=20)
  
  plt.xlabel('x')
  plt.ylabel('y')
  plt.xlim(-3.1,3.1)
  plt.ylim(-6,6)
  plt.legend()
  </code></pre>
  <p>This is what I obtain from the python code above. How do I go about completing this and finding what other points to use so that I get the final phase portrait? Thank you in advance</p>
  <p><a href="https://i.stack.imgur.com/8fopZ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/8fopZ.png" alt="enter image description here" /></a></p>