In [4]:

    

import numpy as np
from scipy import integrate

import matplotlib.pylab as plt
%config InlineBackend.figure_format = 'retina'
%matplotlib inline


    

In [5]:

    

# Parameters specified by Abbott 2009.
def lorentz((x, y, z), t0, **kwargs):
    if 'rho' in kwargs:
        rho = kwargs['rho']
    else:
        rho = 28
    if 'sigma' in kwargs:
        sigma = kwargs['sigma']
    else:
        sigma = 10.0
    if 'beta' in kwargs:
        beta = kwargs['beta']
    else:
        beta = 8./3.
    return [sigma * (y - x), x * (rho - z) - y, x * y - beta * z]


    

In [8]:

    

T = 5000 # period
x0 = [1, 1, 1]  # starting vector
t = np.linspace(0, 30, T)  # one thousand time steps
x_t = integrate.odeint(lorentz, x0, t)


    

In [9]:

    

plt.plot(t[:T/2], x_t[T/2:,1]);
plt.xlabel('t', fontsize=14)
plt.ylabel('x', fontsize=14)


    

    
Out[9]:





<matplotlib.text.Text at 0x1093015d0>






    

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