# The Lorenz-63 system¶

The Lorenz-63 system is a system of ordinary differential equations that has chaotic solutions for some parameter values and initial states.

$\begin{split}\frac{dx}{dt} &= \sigma (y - x) \\ \frac{dy}{dt} &= x (\rho - z) - y \\ \frac{dz}{dt} &= xy - \beta z \\\end{split}$

In this guide, we will focus on the system dynamics obtained with the following parameter values:

$\begin{split}\sigma &= 10 \\ \rho &= 28 \\ \beta &= \frac{8}{3}\end{split}$