# Finding Maxima and Minima for the Lorenz Attractor

Finding Maxima and Minima for the Lorenz Attractor

This Demonstration finds the maxima and minima of the Lorenz system:

dx

dt

dy

dt

dz

dt

For various selections of the model parameters , , and , you can observe periodic behavior, period doubling, or chaotic behavior. For example, , , and shows chaotic behavior, while , , and gives periodic behavior.

σ

r

b

σ=16

r=45.92

b=4

σ=19.8

r=56

b=1

The maxima and minima are easily determined using the built-in Mathematica 9 function WhenEvent. Finally, once the maxima or minima are found, a relatively straightforward extension of the present code allows the determination of all types of bifurcation diagrams.