Lorenz attractor

The Lorenz system is a system of ordinary differential equations (the Lorenz equations, note it is not Lorentz) first studied by Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, resemble a butterfly or figure eight.

In 1963, Edward Lorenz developed a simplified mathematical model for atmospheric convection. The model is a system of three ordinary differential equations now known as the Lorenz equations:

Here ${\displaystyle x}$, ${\displaystyle y}$, and ${\displaystyle z}$ make up the system state, ${\displaystyle t}$ is time, and ${\displaystyle \sigma }$, ${\displaystyle \rho }$, ${\displaystyle \beta }$ are the system parameters. The Lorenz equations also arise in simplified models for lasers,dynamos,thermosyphons, brushless DC motors,electric circuits,chemical reactions and forward osmosis.

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