Meteorologist Ed Lorenz came up with the following system while attempting to model weather.
dx/dt = 10(y-x)
dy/dt = 28x-y-xz
dz/dt = -8/3z + xy
The parameter values are not set, I understand that these were the values Ed used. The system was one of the first studied exmaples of chaos in the mathematical sense and solutions tend to unpredictable orbits around two strange attractors.