Main Concept

The Lorenz system is a system of ordinary differential equations that was originally derived by Edward Lorenz as a simplified model of atmospheric convection:

$$\begin{gathered} \frac{\partial x}{\partial t}\=\mathrm{\σ} \left(y-x\right)\, \\ \frac{\partial y}{\partial t}\=x \left(\mathrm{\rho }-z\right)-y\, \\ \frac{\partial z}{\partial t}\=-\mathrm{\β} z\+x y \end{gathered}$$

Interestingly, the evolution of the system for certain values of the parameters and initial conditions exhibits chaotic behavior. In particular the Lorenz attractor is the solution obtained for the Lorenz system with ρ = 28, σ = 10, and β = 8/3.

$\mathrm{\σ}$ =

$\mathrm{\ρ}$ =

$\mathrm{\β}$ =  

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