Strange attractors in 3D

Thomas attractor

Parameter:

System:

$$\left\{ \begin{eqnarray*} \frac{dx}{dt}&=&\sin y -bx\\ \frac{dy}{dt}&=&\sin z -by\\ \frac{dz}{dt}&=&\sin x-bz \end{eqnarray*}\right. $$

Aizawa attractor

Parameters:

System:

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

Lorenz attractor

Parameters:

System:

$$\left\{ \begin{eqnarray*} \frac{dx}{dt}&=&p (-x + y)\\ \frac{dy}{dt}&=& -x z + r x - y \\ \frac{dz}{dt}&=& x y - b z \end{eqnarray*}\right. $$

Chen attractor

Parameters:

System:

$$\left\{ \begin{eqnarray*} \frac{dx}{dt}&=&\alpha x- y z\\ \frac{dy}{dt}&=&\beta y + x z \\ \frac{dz}{dt}&=&\delta z + x y/3 \end{eqnarray*}\right. $$

Lorenz84 attractor

Parameters:

System:

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

Rössler attractor

Parameters:

System:

$$\left\{ \begin{eqnarray*} \frac{dx}{dt}&=&-(y+z)\\ \frac{dy}{dt}&=&x+ay\\ \frac{dz}{dt}&=&b+z(x-c) \end{eqnarray*}\right. $$

Halvorsen attractor

Parameter:

System:

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

Rabinovich-Fabrikant attractor

Parameters:

System:

$$\left\{ \begin{eqnarray*} \frac{dx}{dt}&=&y ( z - 1 + x^2 ) + \gamma x\\ \frac{dy}{dt}&=&x ( 3 z + 1 - x^2 ) + \gamma y\\ \frac{dz}{dt}&=& - 2 z ( \alpha + x y ) \end{eqnarray*}\right. $$

Three-Scroll Unified Chaotic System attractor

Parameter:

System:

$$\left\{ \begin{eqnarray*} \frac{dx}{dt}&=&a(y-x)+d x y \\ \frac{dy}{dt}&=& bx-x z + f y \\ \frac{dz}{dt}&=& cz+xy-ex^2 \end{eqnarray*}\right. $$

Sprott attractor

Parameters:

System:

$$\left\{ \begin{eqnarray*} \frac{dx}{dt}&=& y + a x y +x z \\ \frac{dy}{dt}&=& 1 - b x^2 +yz \\ \frac{dz}{dt}&=& x-x^2-y^2 \end{eqnarray*}\right. $$

Wang-Su attractor

Parameter:

System:

$$\left\{ \begin{eqnarray*} \frac{dx}{dt}&=& ax+yz \\ \frac{dy}{dt}&=& b x + cy - xz \\ \frac{dz}{dt}&=& -z-xy \end{eqnarray*}\right. $$