import numpy as np import matplotlib.pyplot as plt  alpha = 1.1   # prey growth rate  beta = 0.4    # prey death rate  gamma = 0.4   # predator death rate  delta = 0.1   # predator growth rate  x0 = 10       # initial prey population y0s = [1, 2, 5, 7, 10, 12, 15] # initial predator population  fig, ax = plt.subplots(figsize=(6,6)) for y0 in y0s:      dt = 1e-3     T_MAX = 20     t = np.arange(0,T_MAX,dt)     x = np.zeros_like(t, dtype=np.float)     y = np.zeros_like(t, dtype=np.float)     x[0], y[0] = x0, y0      for i, tt in enumerate(t):         if i == 0:             continue         x[i] = x[i-1] + (alpha * x[i-1] - beta * x[i-1] * y[i-1]) * dt         y[i] = y[i-1] + (delta * x[i-1] * y[i-1] - gamma * y[i-1]) * dt              ax.plot(x, y, label='$y_0=%d$' % y0)  ax.grid(True) ax.legend() fig.savefig('predator_prey.svg',             bbox_inches='tight', transparent=True)