lorenz_example.py

# coding=utf-8

import PyDSTool as dst
from PyDSTool import args
import numpy as np
from matplotlib import pyplot as plt

DSargs = args(name='Lorenz map')
DSargs.varspecs = {'z': 'a+b*(z-c)**2',  # note syntax for power
                   'zp': 'zp+log(abs(2*b*(z-c)))',
                   'L': 'zp/(t+1)'}  # L is an auxiliary variable
DSargs.tdomain = [0, 200]  # Default range of independent variable 't'
DSargs.pars = args(a=2.93,
                   b=-1.44,
                   c=1.85)  # Using args() class to specify parameters with less syntax than a dictionary

DSargs.vars = ['z', 'zp']  # Implicitly, then, L will be an auxiliary variable
DSargs.ics = {'z': 2, 'zp': 0}  # Initial conditions
DSargs.ttype = int  # force independent variable type to be integer (discrete time)

lmap = dst.Generator.MapSystem(DSargs)  # an instance of the 'Generator' class for maps.
traj = lmap.compute('test')  # compute a trajectory named 'test'
pts = traj.sample()  # sample the points from the trajectory

# PyPlot commands
plt.figure(1)
plt.plot(pts['t'], pts['z'], 'ko-')
plt.title(lmap.name)
plt.xlabel('t')
plt.ylabel('z')

plt.figure(2)
plt.plot(pts['t'], pts['L'], 'ro')
plt.title('Lyapunov exponent')
plt.ylabel('L')
plt.xlabel('t')
plt.show()