LORENZ83 ATTRACTOR

The Lorenz attractor is one of the most iconic strange attractors, resembling the shape of a butterfly or a mask. It was named after Edward Lorenz, an American meteorologist that discovered the attractor while developing a mathematical model to describe the Earth's atmosphere.

and a system of three ordinary differential equations describing the appropriate attractor are-

$\left\{ \begin{eqnarray*} \frac{dx}{dt}&=&-a x - y^2 - z^2 + a f\\ \frac{dy}{dt}&=& -y + x y - b x z + g\\ \frac{dz}{dt}&=& -z + b x y + x z \end{eqnarray*}\right. $

When a = 0.95, b = 7.91, f = 4.83, g = 4.66, a solution curve of this system has the shape of a complex wave and the position of particles will follow a similar path.

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