import numpy as np
import pylab as pl
import scipy.integrate as integrate

def derivs(state,t):
    x,y = state
    deltax = (y + x - (x**3 / 3)) * (1 / a)
    deltay = - (a * x)
    return deltax, deltay

a = 0.1
x0 = .5
y0 = .5
t = np.arange(0.0, 100, 0.1)                                 
z0 = [x0, y0]
z = integrate.odeint(derivs, z0, t)
x = z[:, 0]
y = z[:, 1]
w = np.arange(-3, 3, .01)
y1 = (-w + w**3 / 3)

pl.plot(x, y)
pl.plot(w, y1)
pl.text(1.0, 1.1, 'fast')
pl.text(1.6, -.5, 'slow', rotation = 35)
pl.show()