The Lorenz chaotic system



1 The Lorenz chaotic system

This example shows how to solve the chaotic Lorenz’ dynamical system—you know the one of the butterfly. The differential equations are

\begin{cases} \dot{x} &= \sigma \cdot (y - x)\\ \dot{y} &= x \cdot (r - z) - y\\ \dot{z} &= xy - bz\\ \end{cases}

where \sigma=10, b=8/3 and r=28 are the classical parameters that generate the butterfly as presented by Edward Lorenz back in his seminal 1963 paper Deterministic non-periodic flow.

1.1 lorenz.was

Please note the beauty of both the Lorenz system and the associated wasora input.

The ability to solve the Lorenz system—that has both intrigued and inspired me since I was old enough to understand differential equations—with such simple and concise instructions shows me that indeed wasora has something to provide to the scientific/engineering community.

Lorenz as a function of time
Lorenz as a function of time
The Lorenz attractor in phase space
The Lorenz attractor in phase space