AIZAWA ATTRACTOR

The Aizawa attractor is a system of equations that, when applied iteratively on three-dimensional coordinates, evolves in such a way as to have the resulting coordinates map out a three dimensional shape, in this case a sphere with a tube-like structure penetrating one of it's axis.

and a system of three ordinary differential equations describing the structure as-

$\left\{ \begin{eqnarray*} \frac{dx}{dt}&=&(z - b) x - d y\\ \frac{dy}{dt}&=& d x + (z - b) y\\ \frac{dz}{dt}&=&c + a z - \frac{z^3}{3} -\\& &\;(x^2+y^2)(1+e z)+f z x^3 \end{eqnarray*}\right. $

When a = 0.95, b = 0.7, c = 0.6, d = 3.5, e = 0.25 and f = 0.1, a solution curve of this system has the shape of sphere like structure and the position of particles will follow a similar path.

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