HALVORSEN ATTRACTOR

System of three ordinary differential equations describing the structure as-

$\left\{ \begin{eqnarray*} \frac{dx}{dt}&=&-a x-4y-4z-y^2 \\ \frac{dy}{dt}&=& -a y-4z-4x-z^2 \\ \frac{dz}{dt}&=& -a z-4x-4y-x^2 \end{eqnarray*}\right. $

When a = 1.89 a solution curve of this system has the shape of wave like structure and the position of particles will follow a similar path.

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