Lorenz
First discovered by Konrad Lorenz, the solution to this set of equations forms a unique pattern.
\( \begin{align*} \frac{dx}{dt} &= \sigma (y-x) \\ \frac{dy}{dt} &= x (\rho - z) - y \\ \frac{dz}{dt} &= xy - \beta z \end{align*} \)
Rossler
\( \begin{align*} \frac{dx}{dt} &= -(y+z) \\ \frac{dy}{dt} &= x + ay \\ \frac{dz}{dt} &= b + z(x-c) \end{align*} \)
Thomas
\( \begin{align*} \frac{dx}{dt} &= \sin(y) - bx \\ \frac{dy}{dt} &= \sin(z) - by \\ \frac{dz}{dt} &= \sin(x) - bz \end{align*} \)
Aizawa
\( \begin{align*} \frac{dx}{dt} &= (z-b)x - dy \\ \frac{dy}{dt} &= dx + (z-b)y \\ \frac{dz}{dt} &= c + az - z^3/3 - (x^2+y^2)(1+ez)+fzx^3 \end{align*} \)
Dadras
\( \begin{align*} \frac{dx}{dt} &= y-ax+byz \\ \frac{dy}{dt} &= cy-xz+z \\ \frac{dz}{dt} &= dxy-ez \end{align*} \)
Halvorsen
\( \begin{align*} \frac{dx}{dt} &= -ax -4(y+z) -y^2 \\ \frac{dy}{dt} &= -ay -4(z+x) -z^2 \\ \frac{dz}{dt} &= -az -4(x+y) -x^2 \end{align*} \)
Rabinovich-Fabrikant
\( \begin{align*} \frac{dx}{dt} &= y(z-1+x^2)+\gamma x \\ \frac{dy}{dt} &= x(3z+1-x^2)+\gamma y \\ \frac{dz}{dt} &= -2z(\alpha+xy) \end{align*} \)
Sprott
\( \begin{align*} \frac{dx}{dt} &= y+axy+xz \\ \frac{dy}{dt} &= 1-bx^2+yz \\ \frac{dz}{dt} &= x - x^2 - y^2 \end{align*} \)
Four-wing
\( \begin{align*} \frac{dx}{dt} &= ax+yz \\ \frac{dy}{dt} &= bx+cy-xz \\ \frac{dz}{dt} &= -z-xy \end{align*} \)
